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1. 03Bxx
03B05 Classical propositional logic; 03B10 Classical firstorder logic 03B35 Mechanization of proofs and logical operations See also 68T15
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General logic
  • 03B05 Classical propositional logic 03B10 Classical first-order logic 03B15 Higher-order logic and type theory 03B20 Subsystems of classical logic (including intuitionistic logic) 03B22 Abstract deductive systems 03B25 Decidability of theories and sets of sentences [See also 03B30 Foundations of classical theories (including reverse mathematics) [See also 03B35 Mechanization of proofs and logical operations [See also 03B40 Combinatory logic and lambda-calculus [See also 03B42 Logic of knowledge and belief 03B44 Temporal logic ; for temporal logic see ; for provability logic see also 03B48 Probability and inductive logic [See also 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness [See also 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) 03B55 Intermediate logics 03B60 Other nonclassical logic 03B65 Logic of natural languages [See also 03B70 Logic in computer science [See also 68-xx 03B80 Other applications of logic 03B99 None of the above, but in this section

2. Mhb03.htm
03B35, Mechanization of proofs and logical operations See also 68T15. 03B40, Combinatory logic and lambdacalculus See also 68N18
03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

3. 03Bxx
03B05 Classical propositional logic 03B10 Classical firstorder logic 03B15 See also 03F35 03B35 Mechanization of proofs and logical operations See
General logic 03B05 Classical propositional logic 03B10 Classical first-order logic 03B15 Higher-order logic and type theory 03B20 Subsystems of classical logic (including intuitionistic logic) 03B22 Abstract deductive systems 03B25 Decidability of theories and sets of sentences [See also ] 03B30 Foundations of classical theories (including reverse mathematics) [See also ] 03B35 Mechanization of proofs and logical operations [See also ] 03B40 Combinatory logic and lambda-calculus [See also ; for temporal logic see ; for provability logic see also ] 03B50 Many-valued logic 03B52 Fuzzy logic; logic of vagueness [See also ] 03B53 Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) 03B55 Intermediate logics 03B60 Other nonclassical logic 03B65 Logic of natural languages [See also ] 03B70 Logic in computer science [See also 68-XX ] 03B80 Other applications of logic 03B99 None of the above, but in this section
Version of December 15, 1998

4. MathNet-Mathematical Subject Classification
03B35, Mechanization of proofs and logical operations See also 68T15. 03B40, Combinatory logic and lambdacalculus. 03B45, Modal and tense logic For

5. In-cites - University Of Warsaw
The research also touches related areas, in particular 03B35 Mechanization of proofs and logical operations, 03B70 Logic in computer science, 03D05 Automata


in cites
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Methods for Essential Science Indicators Essential Science Indicators Latest Version Classification of Papers in Multidisciplinary Journals New Entrants to ... About in cites Browse Back Issues Send in cites to a Colleague Research Services Group Contact Us
cites is an editorial component of Essential Science Indicators from Thomson Scientific in-cites, June 2004
Citing URL:
University of Warsaw
ate in 2003, the University of Warsaw entered the top 1% of institutions in terms of total citations in the field of Computer Science. According to the ISI Essential Science Indicators Web product, the institution’s current citation record in this field includes 227 papers cited a total of 499 times to date. In the brief interview below, Damian Niwinski, Vice-Director of the Institute of Informatics at the University of Warsaw, talks about the history of Computer Science at the university.

6. Sachgebiete Der AMS-Klassifikation: 00-09
of classical theories 03B35 Mechanization of proofs and logical operations, Other infinitary logic 03C80 Logic with extra quantifiers and operators,
Sachgebiete der AMS-Klassifikation: 00-09
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen
01-XX 03-XX 04-XX 05-XX 06-XX 08-XX
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

7. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
logic; logic of vagueness fuzzy 03B52 logical foundations of quantum mechanics; quantum logic 81P10 logical operations Mechanization of proofs and 03B35
linear integral equations # systems of
linear integral equations # systems of nonsingular
linear integral equations # systems of singular
linear logic and other substructural logics
linear logic, Lambek calculus, BCK and BCI logics) # substructural logics (including relevance, entailment,
linear mappings, matrices, determinants, theory of equation) # linear algebra. multilinear algebra. (vector spaces,
linear models # generalized
linear operators
linear operators # equations and inequalities involving
linear operators # equations with
linear operators # general theory of linear operators # groups and semigroups of linear operators # special classes of linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) # functions whose values are linear operators as elements of algebraic systems # individual linear operators) # linear relations (multivalued linear operators, their generalizations and applications # groups and semigroups of linear operators, with operator unknowns # equations involving

8. HeiDOK
03B35 Mechanization of proofs and logical operations ( 0 Dok. ) 03B40 Combinatory logic and lambdacalculus ( 0 Dok. ) 03B42 Logic of knowledge and belief

9. MSC 2000 : CC = 03B35
Question CC = 03B35. 03XX Mathematical logic and foundations. 03B35 Mechanization of proofs and logical operations See also 68T15

10. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A
edit 03B35 Mechanization of proofs and logical operations . edit 03C80 Logic with extra quantifiers and operators. All articles processed.
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations
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03-XX Mathematical logic and foundations
This list will be periodically updated. Each entry in the list has three fields:
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    11. BIB-VERSION CS-TR-v2.1 ID Ercim.cwi.demo//SEN-R0124 ENTRY
    with which both coinductive proofs and definitions can be formulated. .. Operators MSC 03B35 Mechanization of proofs and logical operations,
    BIB-VERSION:: CS-TR-v2.1 ID:: ercim.cwi.demo//SEN-R0124 ENTRY:: September 25, 2001 TITLE:: Typed combinators for generic traversal AUTHOR:: Laemmel, R. AUTHOR:: Visser, Joost M.W. DATE:: August 31, 2001 ABSTRACT::
    ORGANIZATION:: Amsterdam (NL) : Centrum voor Wiskunde en Informatica (CWI) TYPE:: Technical Report PAGES:: 61 OTHER_ACCESS:: URL: OTHER_ACCESS:: ISSN:1386-369X KEYWORDS:: Term rewriting KEYWORDS:: Generic programming KEYWORDS:: Term rewriting strategies KEYWORDS:: Traversal schemes KEYWORDS:: Type systems KEYWORDS:: Program transformation ACM:: D.1.1 Applicative (Functional) Programming ACM:: D.1.2 Automatic Programming ACM:: D.3.1 Formal Definitions and Theory ACM:: D.3.3 Language Constructs and Features ACM:: F.4.2 Grammars and Other Rewriting Systems ACM:: I.1.3 Languages and Systems ACM:: I.2.2 Automatic Programming SERIES:: SEN (Software Engineering (SEN)) END:: ercim.cwi.demo//SEN-R0122 BIB-VERSION:: CS-TR-v2.1 ID:: ercim.cwi.demo//SEN-R0121 ENTRY:: August 21, 2001 TITLE:: Term rewriting with traversal functions AUTHOR:: Brand, Mark van den AUTHOR:: Klint, Paul AUTHOR:: Vinju, Jurgen J. DATE:: July 31, 2001 ABSTRACT::
    Term rewriting is an appealing technique for performing program analysis and program transformation. Tree (term) traversal is frequently used but is not supported by standard term rewriting.

    12. PlanetMath: Inference Rule
    In logic, an inference rule is a rule whereby one may correctly draw a conclusion from General logic Mechanization of proofs and logical operations)
    (more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia



    meta Requests



    talkback Polls
    Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About inference rule (Definition) In logic , an inference rule is a rule whereby one may correctly draw a conclusion from one or more premises. For example, the law of the contrapositive allows one to conclude a statement of the form from a premise of the form Here, ` ' and ` ' are propositional variables , which can stand for arbitrary propositions . A popular way to indicate applications of rules of inference is to list the premises above a line and write the conclusions below the line. For instance, we might indicate the law of the contrapositive thus: A typical application of the law of contrapositive would be to conclude "If my clothes are dry, then it is not raining", from "If it rains, then my clothes will be wet." which could be expressed as follows using the notation described above: (In this instance

    13. General General Mathematics Mathematics For Nonmathematicians
    also 03F35 Mechanization of proofs and logical operations See also 68T15 prooftheoretic aspects see 03F52} Probability and inductive logic See

    14. Preface
    The next logical step would be to formulate the underlying principle in . The ACL2 Mechanization of some of the proofs was done by Kaufmann and Eric
    Next: Preface to the Hypertext Up: Contents Previous: Contents Contents
    It is not the purpose of this book to expound the principles of computer arithmetic algorithms, nor does it presume to offer instruction in the art of arithmetic circuit design. A variety of publications spanning these subjects have become available in recent years, including general texts as well as more specialized treatments, covering all areas of functionality and aspects of implementation. There is one relevant issue, however, that remains to be adequately addressed, namely the problem of eliminating human error from arithmetic hardware designs and establishing their ultimate correctness. As in all areas of computer architecture, the designer of arithmetic circuitry is preoccupied with efficiency. His objective is the rapid development of logic that maximizes execution speed, guided by established practices and intuition. Subtle conceptual errors and miscalculations are accepted as inevitable, with the expectation that they will be eliminated through extensive testing. Naturally, as implementations grow in complexity through the use of increasingly sophisticated techniques, errors become more difficult to detect. Experience has shown that testing alone is insufficient to provide a satisfactory level of confidence in the functional correctness of a state-of-the-art floating-point unit. In order to ensure the correctness of complex implementations of arithmetic operations while reducing reliance on testing, a more scrupulous approach to the design and analysis of arithmetic circuits is imperative. Loose concepts, intuition, and arguments by example must be replaced by formal development, explicit theorems, and rigorous proofs.

    15. Curriculum Vitae
    encoding of mathematical proofs and formulae in machine understandable formats and the Mechanization of mathematics (proof assistants and logical
    Curriculum Vitae
    Stefano Zacchiroli

    September 19, 2007
    Personal Data
    Stefano Zacchiroli
    Department of Computer Science,
    University of Bolona, Italy
    Work Address
    Mura Anteo Zamboni 7, 40127 Bologna, Italy
    Work Phone Work Fax Birthday E-Mail
    Homepage zack
    Public Key Fingerprint(s):
    I have been a Ph.D. student at the Department of Computer Science, University of Bologna. My Ph.D. advisor has been Professor Andrea Asperti. I have been a visiting researcher at the Computer Science Department of the Brown University, Providence, RI. There, I have been working on (wiki-like) collaborative technologies for the authoring of constrained documents. My advisor there has been Professor David G. Durand. CDuce programming language.
    Mar 2003
    I have got a Master Degree in computer science with a rating of 110/110 cum laude at the Department of Computer Science, University of Bologna. I have been an undergraduate Students of Computer Science, with specialization in Distributed Systems, of the faculty of Mathematical, Physical and Natural Science of the University of Bologna.

    16. MathML Conference 2002: Presentations
    Indexing and Classification (Q ``I have structure with two operations that commute and the Mechanization of mathematics (proof assistants and logical

    Call for Papers
    General Information Registration Accommodations ... Schedule
    MathML in the MOWGLI Project
    Andrea Asperti and Michael Kohlhase
    Università degli Studi di Bologna and Carnegie Mellon University
    Abstract M O W GL ... I (Mathematics On the Web: Get it by Logic and Interfaces) is a European Project founded by the European Community in the ``Information Society Technologies'' (IST) Program. The project partners are the University of Bologna (coordinator), the German Research Center for Artificial Intelligence (DFKI Saarbrücken), Katholieke Universiteit Nijmegen, Max Planck Institute for Gravitational Physics (Albert Einstein Institute, TU Berlin), and Trusted Logic (France). The aim of the project is the study and the development of a technological infrastructure for the the creation and maintenance of a virtual, distributed, hypertextual library of mathematical knowledge based on a content description of the information. Currently, almost all mathematical documents available on the Web are marked up only for presentation, severely crippling the potential for added-value services like concept-oriented navigation and information retrieval, data mining or document personalization. The goal of M O W GL ... I is to overcome these limitations, passing from a machine-readable to a machine-understandable representation of the information and developing the technological infrastructure for its exploitation. Essentially

    17. CSCI 8980: Computation And Deduction
    Here we will study lambda calculi as logical systems. proofs that are logic or that realizes relatively sophisticated operations on proofs or formulas.
    CSCI 8980: Computation and Deduction, Fall 2004
    Online discussion using HyperNews New Information
    • I have posted comments on the grading of homework 3 to the homeworks page.
    • Class presentations start on November 30. Information about these is posted here
    Table of Contents
    Contact Information
    • Lecture Times and Place: TTh 12:45 - 2:00 p.m., Akerman Hall, Room 317.
    • Instructor: Gopalan Nadathur (, EE/CSci 6-215, 612-626-1354.
      Office Hours: TTh 2:30 - 3:30 p.m.
    Course Prerequisites
    The main requirement will be mathematical maturity at the level expected of a graduate student or a motivated undergraduate. In particular, our discussions will require a facility with aspects of discrete structures and formal arguments especially ones based on induction. An interest in symbolic issues is also essential if the course is to provide a fulfilling experience. No specific knowledge of logic will be assumed. We will develop such knowledge as we go along.
    Course Texts and References
    There is no official textbook for this course. Some part of the discussion will be based on research papers that will be distributed during the term. The lectures on basic material draw on a number of sources some of which are listed below:

    18. Warsaw Univ. PL -- MATHESIS UNIVERSALIS: No.1, Winter 1996 -- "Mechanization Of
    Mechanization as formalization and Mechanization in the strict sense operations of the algebra of logic and their fundamental properties

    To Table of Contents No.1
    Witold Marciszewski and Roman Murawski
    A Schematic Historical Survey This survey is identical with the table of contents of the book by the same authors entitled Mechanization of Reasoning in a Historical Perspective , published by Editions Rodopi, Amsterdam 1995. The table is so detailed that that it can function as a distinct text (linked with with other ones in this issue), provided that it is introduced by the following comment. The development of logic displays new and illuminating aspects when seen from the angle of mechanized reasoning. Even those who doubt in the use of logical theories as a guide for common sense or scientific research have to agree that they proved indispensable for producing reasoning machines. The story has three turning points which most concisely can be listed with the three following terms: formalization (started in the Middle Ages, appreciated and developed by Leibniz), algebraization (started by Leibniz and his contemporaries, accomplished by Boole at al), elimination of the quantifiers (Skolem, Hilbert, Gentzen et al) to reduce the whole of logic to its algebraized and finitistic part.

    19. Claudio Sacerdoti Coen's Home Page
    Abstract In this paper we analyse the modifications on logical operations as proof checking, type inference, reduction and convertibility - that are
    About myself Short curriculum vitae Research topics Current work ... Tutorials Last update: 28/05/2007
    Claudio Sacerdoti Coen (aka CSC)
    Name: Claudio Surname: Sacerdoti Coen Birth place and date: Bologna (IT), 12/07/1976 Qualification: Ph.D. Doctor in Computer Science Employment: Lecturer in Computer Science Affiliation: Department of Computer Science, University of Bologna Office: via Mura Anteo Zamboni n. 7, 40127, Bologna (IT) Telephone number: Fax number: Home: via Treviso n. 1, 40139, Bologna (IT) E-Mail: reveal('splash')
    Short curriculum vitae
    I got my diploma the 25 of July 1995 (rating 60/60), after attending a school where I was taught in particular mathematics, physics and chemistry. I attended the course in Computer Science, specialisation in Software Systems, of the faculty of Mathematical, Physical and Natural Science of the University of Bologna , that I finished the 12th of October 2000 with rating 110/110 cum laude. The title of my Master Thesis (that gave me a title equivalent to baccalaureate + 5) was "Progettazione e realizzazione con tecnologia XML di basi distribuite di conoscenza matematica formalizzata" ("Design and implementation using XML tecnology of distributed libraries of formalized mathematical knowledge"). During the last four years of university I was also a system administrator of a Linux host of my department, thanks to the

    20. TPHOLs 2007: Accepted Papers
    Proof Pearl The power of higherorder encodings in the logical framework LF . existing low-level tactics for logical operations and three new tactics
    home cfp submission registration ... organisation
    List of Accepted Papers
    A formally verified prover for the ALC description logic
    Mar­a-Jos© Hidalgo Jos©-Antonio Alonso Joaqu­n Borrego-D­az Francisco-Jesus Martin-Mateos and Jos©-Luis Ruiz-Reina
    The Ontology Web Language (OWL) is a language used for the Semantic Web. OWL is based on Description Logics (DLs), a family of logical formalisms for representing and reasoning about conceptual and terminological knowledge. Among these, the logic ALC is a ground DL used in many practical cases. Moreover, the Semantic Web apears as a new field for the application of formal methods, that could be used to increase it reliability. A starting point could be the formal verification of satisfiability provers for DLs. In this paper, we present the PVS specification of a prover for ALC, as well as the proofs of its termination, soundness and completeness. We also present the formalization of the well-foundedness of the multiset relation induced by a well-founded relation. This result has been used to prove the termination and the completeness of the ALC prover.
    Proof Pearl: Looping around the Orbit
    Steven Obua
    We reexamine the While combinator of higher-order logic (HOL) and introduce the For combinator. We argue that both combinators should be part of the toolbox of any HOL practitioner, not only because they make efficient computations within HOL possible, but also because they facilitate elegant inductive reasoning about loops. We present two examples that support this argument.

    21. PVS Introduction
    PVS expressions provide the usual arithmetic and logical operators, proofs yield scripts that can be edited, attached to additional formulas, and rerun.
    Home Intro Wiki Docs ... FM Tools
    PVS Introduction
    PVS is a mechanized environment for formal specification and verification. It builds on over 25 years experience at SRI in developing and using tools to support formal methods. PVS consists of a specification language, a number of predefined theories, a type checker, an interactive theorem prover that supports the use of several decision procedures and a symbolic model checker, various utilities including a code generator and a random tester, documentation, formalized libraries, and examples that illustrate different methods of using the system in several application areas. By exploiting the synergy between a highly expressive specification language and powerful automated deduction, PVS serves as a productive environment for constructing and maintaining large formalizations and proofs.
    PVS Language
    PVS Theorem Prover
    PVS includes a BDD-based decision procedure for the relational mu-calculus and thereby provides an experimental integration between theorem proving and CTL model checking. PVS has recently been extended to use the Yices SMT solver as an endgame prover and an infinite-state bounded model checker, the PVSio framework for evaluating ground PVS expressions, and a random testing capability that can be used during proofs.
    PVS User Interface
    PVS uses Gnu or X Emacs to provide an integrated interface to its specification language and prover. Commands can be selected either by pull-down menus or by extended Emacs commands. Extensive help, status-reporting and browsing tools are available, as well as the ability to generate typeset specifications (in user-defined notation) using LaTeX. Proof trees and theory hierarchies can be displayed graphically using Tcl/Tk.

    22. Lorentz Center - Mathematics Algorithms And Proofs From 8 Jan
    Abstract We present a complete mechanized proof of the result in cases through a novel application of logical metatheorems for functional analysis,

    23. Research Laboratory For Logic And Computation, GC CUNY
    Feasibility of operations on proofs. Srikanth Gottipati. . the art is almost at the point where mechanized metatheoretical tools can be used routinely,
    Research Laboratory for Logic and Computation

    SPRING 2006

    CSc 85200.
    Seminar in Computational Logic
    Code: 94282
    Tuesday, 2pm - 4pm, room 3306 (Graduate Center)
    May 16 meeting

    Speaker: HIDENORI KUROKAWA (Graduate Center)
    Topic: Combining Classical and Constructive Logic In this talk we first present some new results concerning intuitionistic logic with classical atoms (IPCca): Craig interpolation theorem, arithmetical completeness, modal counterparts of IPCca, etc. Then, we compare IPCca with other known approaches to combining classical and constructive logic. May 9 meeting Speaker: Yegor Bryukhov (CCNY) Topic: Matrix-based proof method, part 2. In this second part of the talk we will try to use an implementation of matrix-based prover in MetaPRL for S4nJ. We'll try to prove some facts, talk about its performance and the ways of controlling the search space manually. Time permitting, I'll mention the recent paper of Jens Otten "Clausal Connection-Based Theorem Proving in Intuitionisitc First-Order Logic", how he performs a dynamic increase of multiplicity and how it can be added to the existing prover in MetaPRL. May 2 meeting Speaker: Bryan Renne (Graduate Center) Topic: Propositional games and explicit strategies We present a game semantics for the Logic of Proofs, where terms are interpreted as specific strategies on the subformula-choosing evaluation games familiar from propositional (or first-order) logic. Under this interpretation of terms, the LP term operations act as specific operations on strategies. We will close with a discussion of potential interaction with other logic games.

    24. Michael Beeson
    The Mechanization of mathematics, in Teuscher, C. (ed. This paper addresses the relationship between proofs in a typed logic and proofs in lambda logic
    Michael Beeson
    Publications, Chronological Order
    1. Dissertation: The metamathematics of constructive theories of effective operations . Stanford, 1972. 2. The non-derivability in intuitionistic formal systems of theorems on the continuity of effective operations, Journal of Symbolic Logic 3. The unprovability in intuitionistic formal systems of the continuity of effective operations on the reals, Journal of Symbolic Logic 4. Derived rules of inference related to the continuity of effective operations, Journal of Symbolic Logic 5. Continuity and comprehension in intuitionistic formal systems, Pacific J. Math 6. Principles of continuous choice and continuity of functions in formal systems for constructive mathematics, Annals of Mathematical Logic 7. Non-continuous dependence of surfaces of least area on the boundary curve, Pacific J. Math 8. The behavior of a minimal surface in a corner, Arch. Rat. Mech. Anal 9. A type-free Gödel interpretation, Journal of Symbolic Logic 10. Some relations between classical and constructive mathematics, Journal of Symbolic Logic 11. Goodman's theorem and beyond

    25. Hidden Algebra
    Stretching First order Equational Logic proofs with Partiality, Subtypes and Extends hidden algebra formalism with behaviourally coherent operations.
    Hidden Algebra Homepage Contents A Brief Overview of Hidden Algebra Hidden algebra aims to give a semantics for software engineering, and in particular for concurrent distributed object systems, supporting correctness proofs that are as simple and mechanized as possible. This emphasis on effective proofs rather than semantic modelling is supported by taking a calculational approach based on equations , rather than one based on, for example, higher order logic, type theory, denotational semantics, or any particular kind of model or set theory, because equational proofs achieve maximal simplicity and mechanization, while still allowing adequate expressiveness. It is also convenient that the models of a hidden algebraic specification are precisely its possible implementations. Hidden algebra effectively handles the most troubling features of large systems, including concurrency, distribution, nondeterminism, and local states, as well as the usual features of the object paradigm, including classes, subclasses (inheritance), attributes and methods, in addition to supporting logical variables (as in logic programming), abstract data types, generic modules and more generally, the very powerful module system of prameterized programming. Hidden algebra generalizes the process algebra and transition system approaches to include non-monadic operations, so that it can take advantage of equations involving methods and attributes parameterized by data; this extra power can also dramatically simplify proofs. Coinduction methods appear to be more effective for behavioral properties (including behavioral refinement) than any alternative of which we are aware, and moreover, they can be automated to a very significant degree.

    26. ACL2 Annotated Bibliography
    Structured Theory Development for a Mechanized Logic, M. Kaufmann and J . set operations and rewrite rules are provided, and pick a point proofs can be
    Books and Papers about ACL2 and Its Applications
    NOTE. See also the ACL2 workshops page for proceedings of ACL2 workshops, which contain numerous papers, many of them recent, that are not found below. This document is divided into the following sections.
    About ACL2: Quick Summary of What Can Be Done and How to Learn ACL2
    This link will take you to a page on which you can find:
    • a brief paper about ACL2 and applications;
    • exercises, which provide the best way to learn ACL2; and
    • a paper with lots of tips on how to program and prove theorems with ACL2.
    Books about ACL2 and Its Applications

    27. WoLLIC'2000
    (2) Replace some key logical operators by adequate classical equivalents (GödelGentzen We also discuss the extension of semantical proofs of st rong
    th Workshop on Logic, Language, Information and Computation

    August 15-18, 2000
    Hotel Barreira Roxa
    Natal Brazil Scientific Sponsorship

    Interest Group in Pure and Applied Logics ( IGPL
    European Association for Logic, Language and Information ( FoLLI
    Association for Symbolic Logic ( ASL

    Organisation CIn-UFPE DIMAP-UFRN
    Title and Abstract of Invited Talks
    XML and the hypertextual electronic library of mathematics by Andrea Asperti (Department of Computer Science, University of Bologna, Italy) There is a compelling need of integration between the current tools for automation of formal reasoning and mechanization of mathematics (proof assistants and logical frameworks) and the most recent technologies for the development of web applications and electronic publishing. We explain the pivotal role that should be played by the Extensible Markup Language in this integration process, and how the many different pieces of technology under development at World Wide Web Consortium (W3C) should naturally fit together for the creation and maintenance of a virtual, distributed, hypertextual library of formal mathematical knowledge. Definability, Measure and Randomized Algorithm

    28. Deduction In Classical And Multiple-Valued Logic
    Since the symbols (other than the logical operators) of a valid formula may be In a similar manner, dissolution can simulate another proof method,
    Neil V. Murray Research Synopsis: Automated Deduction concerns the automation of "theorem proving" and similar (sometimes more general) processes like "inference" or "deduction". As J. A. Robinson has elegantly stated: ``. . . a theorem-proving problem can be solved automatically if it can be solved at all. That is to say, if [a conclusion] B does follow from the given [hypotheses] A1, A2, ...,An then this fact can be detected, automatically, by executing a certain purely clerical algorithm on A1, ...,An and B as input.'' Most research efforts in (and the above remarks about) automatic theorem proving are based on Herbrand's theorem. This theorem helped lay the foundation for mechanizing the discovery of proofs in mathematical logic. Put in lay terms, Herbrand's theorem says that valid logical formulas can be proven to be so by analyzing only the structure and symbols of those formulas. Since the symbols (other than the logical operators) of a valid formula may be interpreted in arbitrary ways over arbitrary domains of discourse without affecting the truth of the formula, this is a remarkable theorem. Initially, Robinson's resolution rule dominated research into automated deduction; even now, it is the most widely employed technique, and it is the basis of OTTER, arguably the most successful theorem proving program ever developed. Robinson's rule, and many of its variants that have been subsequently introduced, require formulas to be normalized in special ways typically conjunctive or disjunctive normal form (CNF or DNF). Although such normalization simplifies analysis and implementation, it can be computationally expensive: Normalizing a formula may cause a great increase in size.

    29. Formal Verification Of Concurrent Programs Using The Larch Prover
    Next, we describe the Mechanization of the UNITY logic and we give the specifications of the temporal operators in the framework of LP.
    var sc_project=2763585; var sc_invisible=0; var sc_partition=28; var sc_security="3c678009"; var addtoLayout=0; var addtoMethod=0; var AddURL = escape(document.location.href); // this is the page's URL var AddTitle = escape(document.title); // this is the page title Advanced Search CS Search Google Search
    • Home Digital Library Podcasts Site Map ... Table of Contents Abstract
      January 1998 (Vol. 24, No. 1)
      pp. 46-62
      Formal Verification of Concurrent Programs Using the Larch Prover
      Boutheina Chetali

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      Abstract This paper describes the use of the Larch prover to verify concurrent programs. The chosen specification environment is UNITY, whose proposed model can be fruitfully applied to a wide variety of problems and modified or extended for special purposes. Moreover, UNITY provides a high level of abstraction to express solutions to parallel programming problems. We investigate how the UNITY methodology can be mechanized within a general-purpose first-order logic theorem prover like LP, and how we can use the theorem proving methodology to prove safety and liveness properties. Then we describe the formalization and the verification of a communication protocol over faulty channels, using the Larch prover LP. We present the full computer-checked proof, and we show that a theorem prover can be used to detect flaws in a system specification.

    30. Math Forum - Math Library - Software & Logic/Foundations & College
    Database of Existing Mechanized Reasoning Systems Kohlhase, Talcott. . A site for proofs and logic. Includes Metamath Solitairea Java applet that

    31. Credits
    A complete Mechanization (in the sense of a semidecision procedure) of classical It allows the extraction of a LISP program from a proof in a logical
    Coq is a proof assistant for higher-order logic, allowing the development of computer programs consistent with their formal specification. It is the result of about ten years of research of the Coq project. We shall briefly survey here three main aspects: the logical language in which we write our axiomatizations and specifications, the proof assistant which allows the development of verified mathematical proofs, and the program extractor which synthesizes computer programs obeying their formal specifications, written as logical assertions in the language.
    The logical language used by Coq is a variety of type theory, called the Calculus of Inductive Constructions . Without going back to Leibniz and Boole, we can date the creation of what is now called mathematical logic to the work of Frege and Peano at the turn of the century. The discovery of antinomies in the free use of predicates or comprehension principles prompted Russell to restrict predicate calculus with a stratification of types . This effort culminated with Principia Mathematica , the first systematic attempt at a formal foundation of mathematics. A simplification of this system along the lines of simply typed

    32. Verification Of Infinite State Systems
    This allows us to derive mechanized proofs of properties for . Focus Points and Convergent Process Operators. Logic Group Preprint Series 142.
    university search sitemap contact ... Links Institute of Formal Methods in Computer Science
    Software Reliability and Security Group
    Verification of Infinite State Systems

    Research on the verification of infinite-state systems was started in 1994. We follow essentially two lines of research: On the one hand, we study the decidability and complexity of verification problems for different classes of infinite automata that can be organized in a Chomsky-like hierarchy. On the other hand, we are interested in the machine-assisted verification of infinite-state and parameterized systems within process classes for which the verification is potentially undecidable. The results find application in the area of program optimization (in particular in the interprocedural dataflow analysis), and in the verification of parameterized systems.
    Decidability and Complexity of Verification Problems
    We have established several results about the decidability and computational complexity of the model checking problem for a hierarchy of Process Rewrite Systems (PRS) including context-free processes, Basic Parallel Processes, and Petri nets. The PRS hierarchy presents a unified view of all these models. It is strict with respect to bisimulation equivalence. I.e., in every class there exists a process that is not bisimilar to any process from the lower classes. Similar hierarchies have been defined by Stirling, Caucal, and Moller [
    The model checking problem is as follows:

    33. Why My Favourite Language Is .NET « Disshackled Transsanity
    Nonetheless such arguments for and against the human brain as a machine assume the consistency of the humans brain logical operation (note the use of
    Disshackled Transsanity
    Philosophy, mathematics, physics
    Why my favourite Language is .NET
    languages available for the platform which can be made to operate with each other with little to no effort. Why there can be no One Perfect Language All programming language, all computers, computers running programs by a certain language are all essentially formal systems. This feature allows us to discuss things and apply things and proofs from logic on the capabilities of languages. Formal System In the most basic sense, a formal system is a system of logic that allows us to "reason" mechanically. A formal system is composed of:
    • a syntax which describes how to form a proper expression in the system. Formally called well formed formulae A formal language, valid strings formed with our alphabet and some starting wffs or Axioms.
    A theorem in our system is a list of sentences with the first being an axiom or a proven wff (theorem) and every sentence within being a result of transformations which follow our rules - the last sentence in our string is a theorem. Formal Language A formal language is in the most basic sense a set of strings over some alphabet or rather, a proper subset of the set of all possible strings that may be composed with some alphabet, with an alphabet being no more than a set of symbols. Formal languages are devoid of ambiguities common to natural languages as English or Chinese (in fact there is no inherent meaning to the set of string or sentences formed in them), they are mechanically manipulable. That is, a computer can follow instructions formed in them. They were originally developed with formal logics and the wish to make math completely mechanized and in essence, air tight. All programming languages contain formal languages. In fact the term programming language is a misnomer since most programming languages are more than just languages. They are entire systems, indeed the term computer programming system would be more appropriate than computer programming language. This argument for this will be given informally later.

    34. JSTOR 2OBJ A Metalogical Framework Theorem Prover Based On
    Object logic structure is externalized, in that the inference rules of the object logic are encoded as primitive operations on an ADT of object logic proofs<69:2AMFTP>2.0.CO;2-

    35. 6th Panhellenic Logic Symposium :: Programme
    Lecture 1 will be devoted to the Logic of proofs LP which gives a Prodromos E. Gerakios and Nikolaos S. Papaspyrou A Mechanized Proof of Type Safety
    6th Panhellenic Logic Symposium
    Volos, Greece, 5-8 July 2007
    Thursday 5.7.07
    Registration - Opening
    Constantine Tsinakis (Vanderbilt University):
    Algebraic Methods in Logic Algebraic logic studies classes of algebras that are related to logical systems, as well as the process by which a class of algebras becomes the algebraic counterpart (semantics)" of a logical system. A field practitioner usually approaches the solution of a problem in logic by first reformulating it in the language of algebra; then by using algebra to solve the reformulated problem; and lastly by expressing the result into the language of logic. A representative association of the preceding kind is the one between the class of Boolean algebras and classical propositional calculus.
    The focus of this talk is substructural logics and their algebraic counterparts. Substructural logics are non-classical logics that are weaker than classical logic, in the sense that they lack one or more of the structural rules of contraction, weakening and exchange in their Genzen-style axiomatization. (It is, however, convenient to think of the classical logic and intuitionistic logic as substructural logics.) These logics encompass a large number of non-classical logics related to computer science (linear logic), linguistics (Lambek Calculus), philosophy (relevant logics), and multi-valued reasoning.
    The following are among the objectives of the talk:
    Propose a uniform framework for the study of the algebraic counter-parts of substructural propositional logics. These algebras, referred to as residuated lattices, have a recently discovered rich structure theory. (Note: The term "residuated lattice" has been used in the literature to refer to algebras that are integral, commutative and bounded. This class and its subclasses are not sufficiently general to provide semantics for all substructural logics.)

    36. Blake-d Digest Volume 1996 Issue 82 Today S Topics WILLIAM
    In Blake s terminology, intellect stands at a higher level of thought than reason , which means the mechanical or most superficial logical operations of
    To: Enjoyed the review mucho. And I am a looooong time resident of DC. And rehearsals are grueling now because we open in 4 daze. Hugh Walthall Date: Mon, 8 Jul 1996 10:01:41 -0400 (EDT) From: Nelson Hilton To: Subject: sweet Science Message-Id: To: Subject: Christianity/Experiment stew Message-Id: To: Cc:, Subject: BLKAKE CONTRA EMPIRICISM, OR 'THER IS NO NATURAL RELIGION' Message-Id: To: Subject: Re: Roob's new book with Blake's pics Message-Id: To: Subject: Re: sweet science Message-Id:

    37. PhD Programme Logic In Computer Science
    The mechanized theory supports the creation of an automatic proof tool which takes as For example, logical operations are to be categorized as being
    Your browser does not support frames. Continue.

    38. AARNEWS - October 2001
    Prove T in twovalued logic (TV). Finding a proof in TV often is .. aspects of the Mechanization of reasoning with analytic tableaux and related methods.
    Contents From the AAR Presidnet
    Results of the CADE Trustee Elections 2001

    A Strategy for Proving Theorems in Many-Valued Logic
    Abstract of Ph.D. Thesis CADE-18 Call for Papers
  • Call for Workshops and Tutorials Call for Papers
  • LICS 2002
  • CAV'02
  • RTA 2002
  • TABLEAUX 2002
    From the AAR President, Larry Wos...
    Developing methods and software to help mathematicians, scientists, and engineers with the deductive aspects of their work this has long been and remains one of the goals of automated reasoning. I am pleased, therefore, to note that in this issue of the AAR Newsletter, we have two contributions that accomplish that goal. One contribution, by Robert Veroff, focuses on proving theorems in many-valued logic; the second contribution, by Armando Tacchella, focuses on the design and implementation of procedures for automated deduction in propositional and other logics. Both contributions report real success: in proving challenging theorems and in verifying real hardware designs.
    Results of the CADE Trustee Elections 2001
    Maria Paola Bonacina
    (Secretary of AAR and CADE)
  • 39. JANCL: Volumes
    Realization of Intuitionistic Logic by Proof Polynomials S. N. Artemov . Review of Witold Marciszewski and Roman Murawski Mechanization of Reasoning
    Journal of Applied Non-Classical Logics
    Home Editorial board Submission Subscribe ... Restricted access
    List of Published Volumes
    Vol. 10-No
    Temporal logics with reference pointers and computation tree logics -Valentin Goranko
    A temporal negative normal form which preserves implicants and implicates - Inma P. de Guzman, Manuel Encisco, Pablo Cordero
    A multimodal logic for reasoning about complementarity -Ivo Düntsch, Beata Konikowska
    On representability of neatly embeddable cylindric algebras -Miklos Ferenczi
    HL2, an Inconsistency-adaptive and Inconsistency-resolving Logic for General Statements that might have Exceptions -Guido Vanackere
    A framework for iterated revision -Konieczny, R. Pino Perez
    A complete system of four-valued logic -P.H. Rodenburg
    Unification and passive inference rules for modal logics -V.V. Rybakov, M. Terziler and C. Gencer
    Vol. 10-No
    Abstracts On theorem proving in annotated logics - Mi Lu, Jinzhao Wu SAT vs. translation based decision procedures for modal logics: a comparative evaluation - Enrico Giunchiglia, Fausto Giunchiglia, Roberto Sebastiani, Armando Tacchella

    40. Formal Executable Models
    The work of Borger and Schulte 2 on Java exceptions is quite formal and accurate, but not supported by mechanized proofs. Mechanically checked proofs
    Next: Specification of the JVM Up: An Executable Formal Java Previous: Abstract
    Formal Executable Models
    ``Formal Methods'' is the name given to the computer science research area devoted to the use of formal mathematical logic to model and analyze the properties of computing systems. One advantage of modeling a system formally is that proofs about it can be checked by mechanical proof checkers. This increases the odds that the proofs are flawless. Automated mechanical theorem provers can be used to help discover proofs, which can significantly reduce the tedium of constructing formal proofs. This is not pie-in-the-sky formal methods proposal boilerplate. It is happening. At Advanced Micro Devices, Inc., formal models of the hardware designs for the floating-point FDIV instruction on the AMD Athlon have been mechanically proved to be compliant with the IEEE-754 standard. Indeed, all of the elementary floating-point operations on the Athlon (including addition, subtraction, multiplication, division, and square root) have been so proved. Important security properties of the IBM 4758 secure co-processor were mechanically verified at IBM Yorktown. The correctness of an auditor that checks the output of a compiler for safety-critical trainborn real-time control software for Union Switch and Signal was mechanically proved. A bit- and cycle-accurate model of a Motorola digital signal processor was mechanically proved to conform to a higher-level sequential view in which the pipeline was abstracted away - provided the microcode being executed was free of a well-defined set of hazards. Several microcoded DSP algorithms extracted from the ROM of that microprocessor were mechanically proved correct. These applications, and others, are described in [

    41. CLI Technical Reports September 6, 1994
    A premise of the ACL2 Project is that the Nqthm proof heuristics allow the Mechanization of the discovery of proofs in the ACL2 logic with the same degree
    CLI Technical Reports
    September 6, 1994
    Note that this list of abstracts is quite out of date. As of July, 1997 there were an additional 13 reports available. See the reports list Design Goals of ACL2 , by Matt Kaufmann and J Strother Moore. August, 1994, 41 pages. Interaction with the Boyer-Moore and Theorem Prover: A Tutorial Study Using the Arithmetic-Geometric Mean Theorem , by Matt Kaufmann (CLI) and Paolo Pecchiari (IRST, DIST). August, 1994, 115 pages. Specification and Verification of Gate-Level VHDL Models of Synchronous and Asynchronous Circuits by David Russinoff. May 10, 1994, 54 pages. We present a mathematical definition of a hardware description language (HDL) that admits a semantics-preserving translation to a subset of VHDL. Our HDL includes the basic VHDL propagation delay mechanisms and gate-level circuit descriptions. We also develop formal procedures for deriving and verifying concise behavioral specifications of combinational and sequential devices. The HDL and the specification procedures have been formally encoded in the computational logic of Boyer and Moore, which provides a LISP implementation as well as a facility for mechanical proof-checking. As an application, we design, specify, and verify a circuit that achieves asynchronous communication by means of the biphase mark protocol. A Formalized of a Subset of VHDL , by David M. Russinoff. April 28, 1994. 22 pages.

    42. Logic And Artificial Intelligence (Stanford Encyclopedia Of Philosophy)
    These include graphbased and proof-theoretic approaches to nonmonotonic the logical phenomena, an expectation that the important temporal operators
    Cite this entry Search the SEP Advanced Search Tools ...
    Please Read How You Can Help Keep the Encyclopedia Free
    Logic and Artificial Intelligence
    First published Wed 27 Aug, 2003 Artificial Intelligence (which I'll refer to hereafter by its nickname, "AI") is the subfield of Computer Science devoted to developing programs that enable computers to display behavior that can (broadly) be characterized as intelligent. Most research in AI is devoted to fairly narrow applications, such as planning or speech-to-speech translation in limited, well defined task domains. But substantial interest remains in the long-range goal of building generally intelligent, autonomous agents. Throughout its relatively short history, AI has been heavily influenced by logical ideas. AI has drawn on many research methodologies; the value and relative importance of logical formalisms is questioned by some leading practitioners, and has been debated in the literature from time to time. But most members of the AI community would agree that logic has an important role to play in at least some central areas of AI research, and an influential minority considers logic to be the most important factor in developing strategic, fundamental advances. The relations between AI and philosophical logic are part of a larger story. It is hard to find a major philosophical theme that doesn't become entangled with issues having to do with reasoning. Implicatures, for instance, have to correspond to inferences that can be carried out by a rational interpreter of discourse. Whatever causality is, causal relations should be inferrable in everyday common sense settings. Whatever belief is, it should be possible for rational agents to make plausible inferences about the beliefs of other agents. The goals and standing constraints that inform a rational agent's behavior must permit the formation of reasonable plans.

    43. ITPAR Workshop - Main.TalkAbstracts
    We have considered belief and goal as modal logic operators satisfying the KD45? and KD We also have proofs of soundness and completeness of the logic.
    @import url(; @import url(;
    ITPAR Workshop '05
    The first CS ITPAR Workshop on Knowledge Oriented Software Engineering
    view edit ... TalkAbstracts Keynote Addresses: Fausto Giunchiglia (University of Trento): Semantic Matching
    Abstract : This talk is in two parts. In the first part I'll describe my view of how meta-data (mainly ontologies) should be organized in the semantic Web. The idea is that we should allow the use of multiple ontologies and link concepts which are semantically related. The talk will briefly describe the language that we have defined, called C-OWL, and that allows this kind of representations.
    In the second part I'll describe an approach, called Semantic Matching, an algorithm and a system, called S-Match, which allows for the automatic computation of mappings/links between concepts of two ontologies/classifications. John Mylopoulos (University of Trento, Italy and Univeristy of Toronto, Canada): Software Engineering and Agent-Oriented Modelling

    44. Theory | Lambda The Ultimate
    This leads, in a very natural way, to the construction of a state diagram from a regular expression containing any number of logical operators.
    @import "misc/drupal.css"; @import "themes/chameleon/ltu/style.css";
    Lambda the Ultimate
    Home Feedback FAQ ... Archives
    User login
    A Dialogue on Infinity
    A Dialogue on Infinity, between a mathematician and a philosopher . Alexandre Borovik and David Corfield. A new blog... From the first post: The project concentrates on one of the principal purposes of the Exploring the Infinite Program: To understand the nature of and the role played by conceptualizations of infinity in mathematics. It will be shaped as a dialogue between a mathematician (AB) and a philosopher (DC) and will address one of the central paradoxes of mathematics: why are most uses of infinity in mathematics restricted to the recycling of a small number of “canonical” and ubiquitous structures? ...To put the study of infinity on a firm basis, we first have to discuss the issue of the identity and “sameness” of mathematical objects: infinity of what? This is pretty far out for LtU, but I suspect it will interest some more philosophically inclined readers. They will look at a number of disciplines

    45. CIAO-Talks
    Furthermore, we present our approach to the Mechanization of judgments about the grain size of mathematical proof steps. The data from the empirical study
    Dieter Hutter
    Wednesday, April 5, 2006
    Arrival in Braunshausen and informal gathering in the evening.
    Thursday, April 6, 2006
    Session 1: Welcome Note , Dieter Hutter (DFKI) Deductive Synthesis of Plans using Linear Logic in Isabelle , Lucas Dixon (University of Edinburgh) Reasoning about Incompletely Defined Programs , Christoph Walther (TU Darmstadt) Proof Critics in IsaPlanner , Moa Johansson (University of Edinburgh) Coffee Break Session 2: Inference Rules and their Application in the New Prover , Dominik Dietrich (Saarland University) Discovering Inductive Theorems in MATHsAiD , Roy McCasland (University of Edinburgh) Future Work in Edinburgh , Serge Autexier (Saarland University) Lunch Session 3: Adding Higher-Order Functions to VeriFun , Markus Aderhold (TU Darmstadt) Ordinals , Chad Brown (Saarland University) Polymorphic Specifications in VeriFun , Andreas Schlosser (TU Darmstadt) Coffee Break Session 4: A Hiproof-Based User Interface , Alan Bundy (University of Edinburgh) Mediating between Scientific Text Editors and Proof Assistance Systems , Marc Wagner (Saarland University) Towards the Mechanization of Granularity Judgments for Mathematics , Marvin Schiller (Saarland University) Business Meeting
    Friday, April 7, 2006

    46. @string{brics = {BRICS} } @string{daimi = Department Of Computer
    Order Logic (HOL) theorem proving system along with a Mechanization of proof .. restrictions on the topology of the graph or on the delete operation.

    47. Caml Weekly News
    The following openings might interest members of this list, as it is strongly concerned with (mechanized proofs of) pure functional programs.
    Previous week Up Next week Hello Here is the latest Caml Weekly News, for the week of October 24 to November 07, 2006.
  • dypgen : bug fixed and new manual macosx, ocaml, findlib and extlib Binary RPMs of OCaml 3.09.3 for Fedora 2-6 and Red Hat Enterprise Linux 4 are available. Olmar - almost a C++ parser for Ocaml ... Oracle OCCI C++ interface
  • dypgen : bug fixed and new manual
    Archive: Emmanuel Onzon announced:
    A new version of dypgen is available at It fixes bugs with merge functions and with the files testdyn1.tiny and testdyn2.tiny. The manual has been completed with examples and more details.
    macosx, ocaml, findlib and extlib
    Archive: Later in this thread, Pietro Abate announced:
    I've created two Mac packages for extlib and findlib and I've submitted patches respectively against extlib-1.5 and findlib-1.1.2pl1.  As far as 
I can see, these packages play well with the mac package of the ocaml 
toolchain from inria. For those who are interested, you can get patches and packages here.

    48. FLoC 2006 - LFMTP
    We propose specific criteria for evaluating the utility of mechanized We formalize in the logical framework ATS/LF a proof based on Tait s method that
    LFMTP'06 International Workshop on Logical Frameworks and Meta-Languages:Theory and Practice
    Seattle, August 16, 2006 FLoC Home About FLoC MEETINGS CAV ICLP IJCAR LICS ... Workshops (by conf.) PROGRAM Room Assignments FLoC at a glance Social Events Invited Talks ... Workshop Proceedings FACILITIES Conference Hotel Event Space Internet Access SEATTLE Travel to/in Seattle Dining Guide Sightseeing in Seattle ORGANIZATION Steering Committee Program Committee Organizing Committee Sponsors MISCELLANEOUS Related Events Site Design OUT-OF-DATE Registration Visa Information Student Travel Support
    LFMTP on Wednesday, August 16th
    Alwen Tiu (Australian National University)
    A Logic for Reasoning about Generic Judgments
    This paper presents an extension of a proof system for encoding generic judgments, the logic FOLD-nabla of Miller and Tiu, with an induction principle. The logic FOLD-nabla is itself an extension of intuitionistic logic with fixed points and a ``generic quantifier'', nabla, which is used to reason about the dynamics of bindings in object systems encoded in the logic. A previous attempt to extend FOLD-nabla with an induction principle has been unsuccessful in modeling some behaviours of bindings in inductive specifications. It turns out that this problem can be solved by relaxing some restrictions on nabla, in particular by adding the axiom B nabla x. B, where x is not free in B. We show that by adopting the equivariance principle, the presentation of the extended logic can be much simplified. Cut-elimination for the extended logic is stated, and some applications in reasoning about an object logic and a simply typed lambda-calculus are illustrated.

    49. Understanding Ontologies In Scholarly Disciplines
    logic technology, with visual language interfaces and control of proof techniques, provides very valuable tools for understanding the knowledge......
    Understanding Ontologies in Scholarly Disciplines
    Brian R Gaines
    Knowledge Science Institute
    University of Calgary, Alberta, Canada Description logics are valuable for modeling the conceptual structures of scientific and engineering research because the underlying ontologies generally have a taxonomic core. Such structures have natural representations through semantic networks that mirror the underlying description logic graph-theoretic structures and are more comprehensible than logical notations to those developing and studying the models. This article reports experience in the development of visual language tools for description logics with the objective of making research issues, past and present, more understandable.
    1 Introduction
    Scholarship may be conceptualized as the rational reconstruction of intuitive notions within the conventions of a discipline. When scholarly disciplines examine their foundations the outcome is generally a taxonomy based on logical definitions intended to capture the concepts of the primary researchers and to clarify the differences underlying disagreements. The development and analysis of such taxonomies can be helpful to active research communities attempting to clarify their activities, and it is also significant in retrospect to historians reconstructing the conceptual structures of those recognized as major contributors to the growth of human knowledge. Description logics managed through visual languages isomorphic to the underlying graph-theoretic structures, and visually transformable through well-defined deductive processes, offer an attractive technology to support both historic studies and active research communities.

    50. Projects
    Larry Paulson has mechanized the UNITY language using Isabelle/HOL. . This includes a Hoare Logic proof on the C/assembler implementation of seL4.
    • Home Overview Download Installation ... Community
      Site Mirrors:
      Researchers are applying Isabelle to a broad range of problems. Further work has been presented at the 2007 Isabelle Workshop and at many conferences, such as FME, CADE and TPHOLs. « means the material is included in the Isabelle distribution This page is based upon information supplied by the researchers themselves. Comments and corrections are welcome at
      Formalized Mathematics
      Simon Ambler and Roy Crole have used a deep encoding of syntax based on de Bruijn indices to formalize the operational semantics of a small functional programming language. This has enabled standard concepts of program equivalence to be presented uniformly through inductive and coinductive definitions. It is proved formally that applicative bisimulation is a congruence, and that it coincides with Morris-style contextual equivalence. A preliminary report is available as compressed postscript.

    51. DBLP: Stéphane Demri
    25, Stéphane Demri A Logic with Relative Knowledge Operators. 15, Stéphane Demri A Completeness Proof for a Logic with an Alternative Necessity
    List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... EE : Reasoning About Sequences of Memory States. LFCS 2007 EE Deepak D'Souza : A Decidable Temporal Logic of Repeating Values. LFCS 2007 EE Alexander Rabinovich : The Complexity of Temporal Logic with Until and Since over Ordinals. LPAR 2007 EE : The Effects of Bounding Syntactic Resources on Presburger LTL. TIME 2007 EE Ewa Orlowska : Relative Nondeterministic Information Logic is EXPTIME-complete. Fundam. Inform. 75 EE Ranko Lazic David Nowak : On the freeze quantifier in Constraint LTL: Decidability and complexity. Inf. Comput. 205 EE Deepak D'Souza : An automata-theoretic approach to constraint LTL. Inf. Comput. 205 EE David Nowak : Reasoning about Transfinite Sequences. Int. J. Found. Comput. Sci. 18 EE Alain Finkel Valentin Goranko ... Govert van Drimmelen : Towards a Model-Checker for Counter Systems. ATVA 2006 EE Denis Lugiez : Presburger Modal Logic Is PSPACE-Complete. IJCAR 2006 EE Ranko Lazic : LTL with the Freeze Quantifier and Register Automata. LICS 2006 EE Ranko Lazic David Nowak : On the freeze quantifier in Constraint LTL: decidability and complexity CoRR abs/cs/0609008 EE Ranko Lazic : LTL with the Freeze Quantifier and Register Automata CoRR abs/cs/0610027 EE Ph. Schnoebelen

    52. Teaching Freshman Logic With MIZAR-MSE
    The logic must be so automatic that you can focus on the problem at hand. The use of a mechanized proof checker is crucial in achieving this goal.
    Teaching freshman logic with MIZAR-MSE
    H. James Hoover and Piotr Rudnicki
    Department of Computing Science
    University of Alberta
    Edmonton, Alberta, Canada T6J 2H1
    [hoover,piotr][,] June 25, 1996
    We would like to share our experience of using a proof-checker in teaching introductory logic to first year science students who plan to enroll into computing science. For several years, we have been teaching an introduction to predicate logic as a part of a course which also covers: (a) elementary material of discrete mathematics (sets, relations, functions, and induction), and (b) reasoning about iterative programming constructs using variants and invariants. The presentation of the material from these three areas is spread over the thirteen week course. The logic component of the course stresses the practical skills of deductive reasoning in predicate calculus. We use the MIZAR-MSE proof-checker to check students' assignments-typically about 50 small proofs for the course. The syntax of the MIZAR-MSE input language is a notation of natural deduction derived from the style of Gentzen, Jaskowski and Fitch. We have chosen a logical system which is an extension of a natural deduction system for the following two reasons:
    • Jaskowski's goal (see [ ] reprinted in [ ]) was to identify the methods used by mathematicians in their proofs, ``to put those methods under the form of structural rules and to analyze their relation to the theory of deduction.'' Inspection shows that he has achieved his goal: indeed the proof structures of his logical system are frequently used by proof authors. It is worthwhile noting here that Jaskowski did not use the term

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