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1. Classical Logic (Stanford Encyclopedia Of Philosophy)
The following sections provide the basics of a typical logic, sometimes called Classical elementary logic or Classical firstorder logic .
http://plato.stanford.edu/entries/logic-classical/
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Classical Logic
First published Sat 16 Sep, 2000 Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language. The following sections provide the basics of a typical logic, sometimes called "classical elementary logic" or "classical first-order logic". Section 2 develops a formal language, with a rigorous syntax and grammar. The formal language is a recursively defined collection of strings on a fixed alphabet. As such, it has no meaning, or perhaps better, the meaning of the formulas is given by the deductive system and the semantics. Some of the symbols have counterparts in ordinary language. We define an argument to be a non-empty collection of formulas in the formal language, one of which is designated to be the conclusion. The other formulas (if any) in an argument are its premises. Section 3 sets up a deductive system for the language, in the spirit of natural deduction. An argument is

2. First-order Logic - Wikipedia, The Free Encyclopedia
Intuitionistic first order logic uses intuitionistic rather than Classical propositional calculus; for example, ¬¬ need not be equivalent to .
http://en.wikipedia.org/wiki/First-order_logic
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
First-order logic
From Wikipedia, the free encyclopedia
Jump to: navigation search First-order logic (FOL) is a formal deductive system used by mathematicians, philosophers, linguists, and computer scientists. It goes by many names, including: first-order predicate calculus FOPC the lower predicate calculus the language of first-order logic or predicate logic . Unlike natural languages such as English, FOL uses a wholly unambiguous formal language interpreted by mathematical structures. FOL is a system of deduction extending propositional logic by allowing quantification over individuals of a given domain (universe) of discourse. For example, it can be stated in FOL "Every individual has the property P". While propositional logic deals with simple declarative propositions, first-order logic additionally covers predicates and quantification. Take for example the following sentences: "Socrates is a man", "Plato is a man". In propositional logic these will be two unrelated propositions, denoted for example by

3. Classical First-Order Logic, Axiomatic Set Theory, And Undecidable Propositions
Archive Classical firstorder logic, Axiomatic Set Theory, and Undecidable Propositions Set Theory, logic, Probability, Statistics.
http://physicsforums.com/archive/index.php/t-152184.html
Physics Help and Math Help - Physics Forums Mathematics Set Theory, Logic, Probability, Statistics PDA View Full Version : Classical First-Order Logic, Axiomatic Set Theory, and Undecidable Propositions Gruppenpest It has been known for some time that the Axiom of Choice (if you treat it as a proposition to be proved rather than an axiom) and the Continuum Hypothesis are independent of Zermelo-Fraenkel set theory (ZF). These and other statements (Suslin's Problem, Whitehead's Problem, the existence of large cardinals...) can neither be proved true or false from the ZF axioms.
ZF itself is built over classical first-order logic which includes the law of the excluded middle, which requires a proposition to be either true or false.
Doesn't this result in an inconsistency? verty You first, does it? Gruppenpest Cagey, aren't you?
Alright. There is at first "glance" a loophole, which is a semantic one. If I recall correctly, the definition of truth and falsehood of mathematical propositions preferred by the mainstream comes down to us from Tarski which is "validity with respect to a structure". Truth as being able to prove truth and falsehood as being able to prove the negation is the intuitionistic/constructivist notion. The problem though is that undecidable/independent statements mean that models of the structure in question exist in which the statement is valid, as well as models where the statement is not valid.
So, as far as I see it at the moment, it does appear to result in an inconsistency.

4. First-Order Predicate Logic
The most well known, and probably the simplest of these logics is known as Classical or boolean, firstorder, predicate logic or, perhaps more appropriate
http://rbjones.com/rbjpub/logic/log019.htm
First-Order Predicate Logic
predicates in natural languages
quantifiers in natural languages

predicate logics
see also:
semi-formal
and formal descriptions of a first-order predicate logic.
informal
semi-formal and formal descriptions of propositional logic.
Predicates in Natural Languages
A predicate is a feature of language which you can use to make a statement about something, e.g. to attribute a property to that thing. If you say "Peter is tall", then you have applied to Peter the predicate "is tall". We also might say that you have predicated tallness of Peter or attributed tallness to Peter. A predicate may be thought of as a kind of function which applies to individuals (which would not usually themselves be propositions) and yields a proposition. They are therefore sometimes known as propositional function s Analysing the predicate structure of sentences permits us to make use of the internal structure of atomic sentences, and to understand the structure of arguments which cannot be accounted for by propositional logic alone.

5. Expressing Disjunctive And Negative Feature Constraints With Classical First-ord
Expressing disjunctive and negative feature constraints with Classical firstorder logic. Full text, Full text available on the Publisher site
http://portal.acm.org/citation.cfm?id=981823.981845&coll=GUIDE&dl=#url.dl

6. First-Order Logic With Quotation (FOLQ) On The Semantic Web
We suggest that RDF s limited expressive power can be extended safely to the level of Classical firstorder logic by using a combination of reification and
http://dev.w3.org/2000/10/swap/doc/paper200209.html
First-Order Logic with Quotation (FOLQ) on the Semantic Web
Status
EARLY NOTES (NOT EVEN A DRAFT) $Revision: 1.4 $ $Date: 2002/10/02 21:34:53 $ Text by Sandro Hawke. Ideas and work by W3C SWAD . Thanks to Bijan Parsia, Lynn Andrea Stein, Jim Hendler, and many others.
Outline
  • Introduction
      The Semantic Web (Documents expressing relations) Why Triples? (Simple model for humans, metadata) Why Logic? (Abstractions; Computers do it well; Documents=Programs) Why Quotation? (Reasoning about documents; Trust, Belief, Closing the World)
    Theory
      Extension By External Constraints (RDF Layering) the meaning depends on what the terms mean Reification Vocabularies strings, lists, sentences; dangers of RDF inference Truth Predicates how to avoid paradox Web Reference Predicates the simple and the complete First-Order Axioms map FOLQ to FOL; interative web-reference handling
    Practice
      Inference Tools Using Otter, XSB, cwm, CLIPS Applications Meeting Records
    Conclusions
or maybe just: intro serial syntaxes [ cover layering HERE ] graph syntax layering axioms inference tools application example
Introduction
To be part of the Semantic Web, a document must convey its content as machine-readable statements of relationships which exist between things. This is an abstract view of knowledge, rooted in formal logic, which is flexible, well-understood by experts, and suitable for processing by computers. Documents like this have an underlying similarity, despite possible differences in surface syntax, which allows software to reason about collections of the documents and their contents.

7. Classical First-order Predicate Logic
Classical firstorder predicate logic. Classical first-order predicate logic. Let $P$ be a predicate without free occurence of variable $x$ .
http://unit.aist.go.jp/cvs/Agda/tutorial/node158.html
Next: Exercises. Up: Examples Previous: Exercises. Contents Index
Classical first-order predicate logic
Let be a predicate without free occurence of variable . We shall prove a proposition
We need law of exclusive middle to prove it as we shall see later. Let us begin with a new package ClassicalPred The complete proof of the proposition in is in Figure Figure 10: Source code Let us work on the goal 0. Invoke Intro command at the goal 0, and we obtain the following: where the subgoal is of the following type. Let us give an informal proof of the proposition at first. We need to prove under the assumption of . We argue by cases whether proposition holds or not in the model with the universe . If holds in the model, then so does . If does not hold in the model, then must hold since holds. Thus we again obtain . Now we encode this proof in . We need the law of excluded middle for . Input em P in the goal 1 and invoke Case command C-c,C-c, and we obtain the following: where the subgoal is of the following type. The object em P represents a proof of . Instead of x and y , we shall use better names: Edit them to p and np , respectively. Then

8. Mason Archive Repository Service: MEBN: A Logic For Open-World Probabilistic Rea
However, such languages have lacked a logical foundation that fully integrates Classical firstorder logic with probability theory. This paper presents such
http://mars.gmu.edu/dspace/handle/1920/461
Mason Archival Repository Service
Mason Archive Repository Service Volgenau School of Information Technology and Engineering C4I Center ... C4I Papers
MEBN: A Logic for Open-World Probabilistic Reasoning
Permanent citation URL: http://hdl.handle.net/1920/461
Files in This Item:
Title: MEBN: A Logic for Open-World Probabilistic Reasoning Author(s): Laskey, Kathryn B. Keywords: multi-entity Bayesian networks Bayesian networks Bayesian learning graphical probability models ... probabilistic ontologies Issue Date: 3-Feb-2006 Series/Report no.: Abstract: URI: http://hdl.handle.net/1920/461 Appears in Collections: C4I Papers
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9. FTP'98 Extended Abstracts
An O((n.log n)^3)time transformation from Grz into decidable fragments of Classical first-order logic Stephane Demri and Rajeev Gore, pages 127-134
http://www.logic.at/ftp98/
Final Program List of Participants
FTP'98
International Workshop on
First order Theorem Proving
Schloss Wilhelminenberg, Vienna, Austria
November 23 - 25, 1998
Extended abstracts
This page gives access to the extended abstracts presented at FTP'98 ( BiBTeX entries ). Full versions of most papers were published in the volume Automated Deduction in Classical and Non-Classical Logics, LNCS 1761, Springer 2000
Front matter
The front matter consists of cover page, preface, list of persons involved (program committee, additional referees, steering committee), and table of contents.
Invited talks
  • Automated theorem proving in first-order logic modulo: on the difference between type theory and set theory
    Gilles Dowek , pages 1-21
    Abstract
    ; the full version will appear in spring 1999 in a volume on first-order theorem proving.) Higher-order modal logic - a sketch
    Melvin Fitting , pages 22-36
    Abstract
    ; the full version will appear in spring 1999 in a volume on first-order theorem proving.) Bertrand Russell, Herbrand's theorem, and the assignment statement
    Melvin Fitting , pages 37-49
    Published in J.Calmet and J.Plaza, editors

10. IngentaConnect First-Order Classical Modal Logic
firstorder Classical Modal logic. Authors Arló-Costa, Horacio1; Pacuit, Eric2. Source Studia logica, Volume 84, Number 2, November 2006 , pp. 171-210(40)
http://www.ingentaconnect.com/content/klu/stud/2006/00000084/00000002/00009010
var tcdacmd="dt";

11. Leeds Logic Seminar 2000 - Abstracts
The Classical decision problem to single out expressive and decidable fragments of first-order logic - has a long history and hardly needs any
http://www.maths.leeds.ac.uk/Pure/logic/Seminar/Logic.Seminar/AbstractsLogic/log
UNIVERSITY OF LEEDS
Department of Pure Mathematics
MATHEMATICAL LOGIC SEMINAR
ABSTRACTS
Peter Hancock (Edinburgh)
Hancock's proof
May 10th
I recently finished a proof of half of something once known as Hancock's Conjecture. It has been 30 years in gestation, and should surely be known as Hancock's Proof; with this productivity rate there is little danger of a name clash. There were already unsensational proofs of HC about 25 years ago, which are OK, but a little sleazy and ad hoc. Besides being more modern and therefore better, my proof has been machine checked by a very sacred Swedish type-checker ("Agda"); at last, the question can be left to fade peacefully into oblivion. The subject (well ordering proofs in type theory) is a little exotic, and to explain its interest adequately would take a long time. Instead I'll just state what the problem is, and describe the overall form of its solution. This centres around the notion of a certain magnificatory gadget which I call a "lens". The proof is in effect a program in dependent type theory (though it is a challenge to imagine circumstances in which anyone would want to run it). One novelty on which I shall focus is that it uses a cumulative sequence of (quite parsimonious) universe types (ie. types of types) besides conventional data structures.

12. Explanation Of The Distinction
The formula `Fx is well known from Classical firstorder logic; when we use Fx to represent such sentences as `John is happy , `Clinton is president ,
http://mally.stanford.edu/distinction.html
Home Page
Further Explanation of the Distinction Underlying the Theory
Exemplification and Classical First-Order Logic Mally's distinction between exemplifying and encoding a property is formally represented in the theory as the distinction between the atomic formulas ` Fx x exemplifies F ') and ` xF x encodes F '). The formula ` Fx ' is well known from classical first-order logic; when we use Fx to represent such sentences as `John is happy', `Clinton is president', and `Socks is a cat', we are assuming that in each case, the predicate ` F ' (`is happy', `is president', `is a cat') denotes a property, and that the object term ` x ' (`John', `Clinton', `Socks') denotes an object. The formal notation ` Fx ' expresses the fact that the property F is predicated of the object; the mode of predication is exemplification . Exemplification can be generalized. Objects x and y can exemplify the 2-place relation R, and when that happens, we write ` Rxy '. Examples are `John loves Mary' (` Ljm '), `Clinton met Yeltsin' (` Mcy '), and so on. Similarly, objects

13. ScienceDirect - Journal Of Symbolic Computation : Preface To First Order Theorem
Many modal logics can be translated to Classical firstorder logic and thus are amenable to first-order logic methods. A new decision procedure for a
http://linkinghub.elsevier.com/retrieve/pii/S0747717103000221
Athens/Institution Login Not Registered? User Name: Password: Remember me on this computer Forgotten password? Home Browse My Settings ... Help Quick Search Title, abstract, keywords Author e.g. j s smith Journal/book title Volume Issue Page Journal of Symbolic Computation
Volume 36, Issues 1-2
, July-August 2003, Pages 1-3
First Order Theorem Proving
Abstract
Full Text + Links PDF (23 K) Related Articles in ScienceDirect Preface: Volume 86, Issue 1
Electronic Notes in Theoretical Computer Science

Preface: Volume 86, Issue 1
Electronic Notes in Theoretical Computer Science Volume 86, Issue 1 May 2003 Pages 204-205
Ingo Dahn and Laurent Vigneron
Abstract
This volume contains the proceedings of FTP'2003, the fourth in a series of workshops intended to focus effort on First-Order Theorem Proving as a core theme of Automated Deduction, and to provide a forum for presentation of recent work and discussion of research in progress. The previous workshops of this series were held at Schloss Hagenberg, Austria (1997), Vienna, Austria (1998), St Andrews, Scotland (2000). In 2001, FTP was part of the IJCAR Conference, held in Siena, Italy. FTP'2003 is one of the three main events of the Federated Conference on Rewriting, Deduction and Programming (RDP'03), together with RTA (the 14th International Conference on Rewriting Techniques and Applications), and TLCA (the 6th International Conference on Typed Lambda Calculi and Applications). FTP'2003 was hold on June 12-14,2003, in Valencia, Spain.

14. Tuple Relational Calculus And The Domain Relational Calculus
Both the tuple relational calculus and the domain relational calculus are based on Classical firstorder logic. Queries have the form
http://cs.wwc.edu/~aabyan/415/TCaRC.html

15. LeanCoP: Lean Connection-Based Theorem Proving
leanCoP is a compact Prolog theorem prover for Classical firstorder logic which is based on the connection calculus. It is sound, complete,
http://www.leancop.de/
Lean Connection-Based Theorem Proving
What is leanCoP ? Documentation Related Links Contact Us ... Intellectics Group
What is leanCoP ?
leanCoP is a compact Prolog theorem prover for classical first-order logic which is based on the connection calculus. It is sound, complete, and demonstrates a comparatively strong performance. Due to the compact code the program can easily be modified for special purposes or applications. New: ileanCoP is an intuitionistic version of leanCoP. It is a theorem prover for intuitionistic first-order logic. Features of leanCoP
  • Theorem prover for classical first-order logic. Based on the connection method, i.e. connection-driven proof search technique. Source code size of the minimal version is only 333 bytes. Sound and complete. Decision procedure for propositional logic. Source code available for popular Prolog systems, including ECLiPSe Prolog, SWI-Prolog and SICStus Prolog. Comparatively strong performance.

16. MATHEMATICAL LOGIC FOR COMPUTER SCIENCE
including Classical logic, constructive logic, and modal logic. Classical firstorder logic Proposition Functions and Quantifiers; first-order
http://www.worldscibooks.com/compsci/3434.html
Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... World Scientific Series in Computer Science - Vol. 47
MATHEMATICAL LOGIC FOR COMPUTER SCIENCE
2nd Edition

by Lu Zhongwan (Chinese Academy of Science, Beijing)
Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science. In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.
Contents:
  • Prerequisites: Sets
  • Inductive Definitions and Proofs
  • Notations
  • Classical Propositional Logic: Propositions and Connectives
  • Propositional Language
  • Structure of Formulas
  • Semantics
  • Tautological Consequence
  • Formal Deduction
  • Disjunctive and Conjunctive Normal Forms
  • Adequate Sets of Connectives
  • Classical First-Order Logic: Proposition Functions and Quantifiers
  • First-Order Language
  • Semantics
  • Logical Consequence
  • Formal Deduction
  • Prenex Normal Form
  • Axiomatic Deduction System: Axiomatic Deduction System
  • Relation between the Two Deduction Systems
  • Soundness and Completeness: Satisfiability and Validity
  • Soundness
  • Completeness of Propositional Logic
  • Completeness of First-Order Logic
  • Completeness of First-Order Logic with Equality
  • Independence

17. FLoC 2006 - IJCAR
We present DFOL, an extension of Classical firstorder logic with dependent types, i.e., as in Martin-Lof type theory, signatures may contain type-valued
http://www.easychair.org/FLoC-06/IJCAR-day230.html
IJCAR 2006 3rd International Joint Conference on Automated Reasoning
Seattle, August 17 - 20, 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
IJCAR on Saturday, August 19th
Chair: Franz Baader
Location: Grand Ballroom B
Chair: Bernhard Beckert
Location: Grand Ballroom B
Juergen Giesl (RWTH Aachen)
Peter Schneider-Kamp
(RWTH Aachen)
Rene Thiemann
(RWTH Aachen)
AProVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework
AProVE 1.2 is one of the most powerful systems for automated termination proofs of term rewrite systems (TRSs). It is the first tool which automates the new dependency pair framework and therefore permits a completely flexible combination of different termination proof techniques. Due to this framework, AProVE 1.2 is also the first termination prover which can be fully configured by the user. Boontawee Suntisrivaraporn (Dresden University of Technology)
Franz Baader
(TU Dresden)
Carsten Lutz
(Institute for Theoretical Computer Science, TU Dresden)

18. The Dialectica Interpretation Of First-order Classical Affine Logic
We give a Dialecticastyle interpretation of first-order Classical affine logic. By moving to a contraction-free logic, the translation (a.k.a.
http://www.tac.mta.ca/tac/volumes/17/4/17-04abs.html
The Dialectica interpretation of first-order classical affine logic
Masaru Shirahata
Keywords: linear logic, dialectica interpretation, categorical logic 2000 MSC: 03B47 Theory and Applications of Categories, Vol. 17, 2006, No. 4, pp 49-79.
http://www.tac.mta.ca/tac/volumes/17/4/17-04.dvi

http://www.tac.mta.ca/tac/volumes/17/4/17-04.ps

http://www.tac.mta.ca/tac/volumes/17/4/17-04.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/17/4/17-04.dvi
...
TAC Home

19. Courses
The thrust of the course will be on natural language constructions that are difficult to describe using the formulation of Classical firstorder logic.
http://www.sfu.ca/~jeffpell/courses.html
Courses
Jeff Pelletier
Depts. of Philosophy Linguistics
Simon Fraser University
Research ... Research Links PHIL 210 : Natural Deductive Logic Fall Semester 2007 This course will study beginning symbolic logic. The thrust of the course is to develop techniques for translating natural language statements (and entire arguments) into a symbolic notation, and then to evaluate whether or not the arguments that are thus represented are valid. We will do this first for the sentence logic and then for predicate logic. This course will not contain any metatheory, but will provide the necessary background for Phil 214. PHIL 350: Ancient Greek Philosophy Spring Semester 2005 An introduction to Ancient Greek Philosophy, starting with the pre-Socratic (i.e., before Socrates) philosophers, discussing Socrates and Plato, and ending with Aristotle.. The thrust of the course will be on the methodology introduced into Western thought by these philosophers, particularly in their epistemology and metaphysics.. PHIL 467 and 812: Logic and Language Spring Semester 2004 An investigation into the relationship between natural language and formal logic.

20. Intuitionistic Logic -- From Wolfram MathWorld
Similarly, intuitionistic predicate logic is intuitionistic propositional logic combined with Classical firstorder predicate calculus.
http://mathworld.wolfram.com/IntuitionisticLogic.html
Search Site Algebra
Applied Mathematics

Calculus and Analysis
... Sakharov
Intuitionistic Logic The proof theories of propositional calculus and first-order logic are often referred to as classical logic Intuitionistic propositional logic can be described as classical propositional calculus in which the axiom schema is replaced by Similarly, intuitionistic predicate logic is intuitionistic propositional logic combined with classical first-order predicate calculus. Intuitionistic logic is a part of classical logic, that is, all formulas provable in intuitionistic logic are also provable in classical logic. Although, even some basic theorems of classical logic do not hold in intuitionistic logic. Of course, the law of the excluded middle does not hold in intuitionistic propositional logic. Here are some examples of propositional formulas that are not provable in intuitionistic propositional logic: Here are some examples of first-order formulas that are not provable in intuitionistic predicate logic: Truth tables for propositional connectives define the interpretation of classical propositional calculus over the domain of two elements: true and false . This interpretation is a model of classical propositional calculus, that is

21. Topics In Logic Syllabus (Spring 2002)
The course presupposes that you have taken a course which provides a good background in Classical firstorder logic, such as PHIL 2340, Symbolic logic;
http://www.trinity.edu/cbrown/topics_in_logic/syllabus.html
Philosophy 3349
Topics in Logic
Syllabus
Curtis Brown
Spring, 2002
This is an intermediate-level course in formal logic. The course presupposes that you have taken a course which provides a good background in classical first-order logic, such as PHIL 2340, Symbolic Logic; MATH 2326, Introduction to Abstract Mathematics; or CSCI 1323, Discrete Structures. The course will fall into two main parts. In the first part of the course, we will cover a number of metalogical results culminating in Gödel's incompleteness theorems. We will also consider relations between these metalogical results and results in computability theory, and will discuss arguments that these results have significant philosophical implications, notably Penrose's argument that the incompleteness theorems show that artificial intelligence is impossible and Hilary Putnam's argument that the Löwenheim-Skolem theorem shows that metaphysical realism is untenable. In the second part of the course, we will consider some proposed extensions and modifications of first-order logic. The principal extension we will consider is modal logic, which adds resources for dealing with the logic of possibility and necessity. Other possible extensions include deontic logic, doxastic logic, etc.

22. 2. FTP 1998, LNCS Volume
An O ((n·log n)3)Time Transformation from Grz into Decidable Fragments of Classical first-order logic. 152-166 Electronic Edition (Springer LINK) BibTeX
http://www.informatik.uni-trier.de/~ley/db/conf/ftp/ftp-lncs1998.html
FTP 1998: Schloss Wilhelminenberg, Vienna, Austria - LNCS Volume
Ricardo Caferra Gernot Salzer (Eds.): Automated Deduction in Classical and Non-Classical Logics, Selected Papers. Lecture Notes in Computer Science 1761 Springer 2000, ISBN 3-540-67190-0 BibTeX DBLP
Invited Papers
Contributed Papers

23. KWTR: First-order Logic - Ontoworld.org
firstorder logic is a well established formalism, and is the basis for many other and results of Classical logic in a rigorous mathematical style.
http://ontoworld.org/wiki/KWTR:_first-order_logic
KWTR: first-order logic
From Ontoworld.org
Jump to: navigation search
edit Contributors:
Jos de Bruijn, FUB Please add your CV in the list of contributors First-order logic is a well established formalism, and is the basis for many other subfields such as Description Logics and logic programming.
  • 1. CURRENT TRENDS IN SEMANTIC WEB (In the following part we intend to identify the state of the art of Semantic Web based theories, methods, applications and tools in your research field.)
    • 1.1. One or more examples (case studies) in which semantic web has been used.
    Name of the institutions: Industry / sector: Business activities improved by the SW solutions: Research Needs: Name of the project: Tools and applications implemented in the project:
    • 1.2. The first 4 Semantic Web based tools used in your research fields.
    Name: Website: Main characteristics: Open problems:
    • 1.3. A short summary of the first 3 best papers in the field.
    Reference: Melvin Fitting. First Order Logic and Automated Theorem Proving (second edition). Springer Verlag, 1996. Short abstract: This graduate-level text presents fundamental concepts and results of classical logic in a rigorous mathematical style. Applications to automated theorem proving are considered and usable Prolog programs provided. It will serve both as a first text in formal logic and an introduction to automation issues for students in computer science or mathematics. The book treats propositional logic, first-order logic, and first-order logic with equality. In each case the initial presentation is semantic, to define the intended subjects independently of the choice of proof mechanism. Then many kinds of proof procedure are introduced. Results such as completeness, compactness, and interpolation are established, and theorem provers are implemented in Prolog. This new edition includes material on AE calculus, Herbrand's Theorem, Gentzen's Theorem, and related topics.

24. FOL RuleML: The First-Order Logic Web Language
firstorder logic RuleML (FOL RuleML) is introduced here as a language for the first-order notably by Classical negation, for achieving FOL RuleML.
http://www.ruleml.org/fol/
R u l e M L
FOL RuleML: The First-Order Logic Web Language
Harold Boley Mike Dean Benjamin Grosof Michael Sintek ... Gerd Wagner
Version History, 2004-08-10: Version 0.7
Version History, 2004-11-02: Version 0.9
This paper describes First-Order Logic RuleML (FOL RuleML), which is planned to be the FOL sublanguage of RuleML 0.9, the rule component of SWRL FOL, and an FOL content language for SWSI. FOL RuleML is based on a modular combination of two syntactically characterized sublanguages: (1) Quantifier RuleML extends RuleML 0.87 by explicit quantifiers. (2) Disjunctive RuleML extends RuleML 0.87 by head disjunctions. Connectives for equivalence and negation are then modularly added for defining FOL RuleML. Its DTD is available for validation tests. Classical FOL model theory provides the semantics of FOL RuleML. FOL RuleML formulas can be used as the declarative content of KQML-like performatives 'Assert' and 'Query', which are augmented by a neutral 'Consider' performative.
Contents
Introduction
First-Order Logic RuleML (FOL RuleML) is introduced here as a language for the First-Order Logic Web on the basis of combining Quantifier RuleML and Disjunctive RuleML. This sublanguage combination is then enriched by further connectives, notably by classical negation, for achieving FOL RuleML. The markup language for first-order logic introduced here is itself proposed as a central RuleML sublanguage, extending the design of

25. AiML: Tools
SPASS A saturation-based resolution theorem prover for first-order logic with equality, sorted logic, and many non-Classical logics including traditional
http://www.cs.man.ac.uk/~schmidt/tools/
home news background conferences ... tools
In recent years the number of computational tools useful for modal logics, and related logics, has increased significantly, and is continuously increasing. The following is an incomplete list of
Your contribution
If you'd like something added or changed please let Renate Schmidt (schmidt@cs.man.ac.uk) know.
Accessible theorem provers
  • BLIKSEM - Hans de Nivelle's resolution based theorem prover for modal logic and first-order logic with equality. DLP - An experimental tableaux-based inference system by Peter Patel-Schneider for a range of description logics. FaCT++ - A tableaux-based description logic OWL reasoner by Ian Horrocks and Dmitry Tsarkov. Successor of FaCT Gost - A Lisp implementation of a tableau algorithm for GF1-, a sublogic of the "First Guarded Fragment". KtSeqC - A theorem prover for the minimal tense logic Kt. Logics Workbench (LWB) - A sequent based theorem prover for a range of propositional logics, including modal logics, temporal logics, intuitionistic logics and nonmonotonic logics. WWW interface ModLeanTAP - A lean implementation of a free variable tableau calculus for a range of propositional modal logics.

26. Categories: Re: Michael Healy's Question On Math And AI
One reason lies in the Classical firstorder logic itself. It works in a blandly uniform way on its formulae that ignores any difference in status as
http://north.ecc.edu/alsani/ct01(1-4)/msg00021.html
Date Prev Date Next Thread Prev Thread Next ... Thread Index
categories: Re: Michael Healy's question on math and AI

27. FOL RuleML: The First-Order Logic Web Language
Classical FOL model theory provides the semantics of FOL RuleML. firstorder logic RuleML (FOL RuleML) is introduced here as a language for the
http://www.w3.org/Submission/FOL-RuleML/
FOL RuleML: The First-Order Logic Web Language
W3C Member Submission 11 April 2005
This version:
http://www.w3.org/Submission/2005/SUBM-FOL-RuleML-20050411/
Latest version:
http://www.w3.org/Submission/FOL-RuleML/
Authors:
Harold Boley , National Research Council of Canada Mike Dean , BBN Technologies Benjamin Grosof , Sloan School of Management, MIT Michael Sintek , German Research Center for Artificial Intelligence (DFKI) GmbH Bruce Spencer , National Research Council of Canada Said Tabet , Macgregor, Inc. Gerd Wagner
This document is available under the W3C Document License . See the for additional information.
Abstract
This paper describes First-Order Logic RuleML (FOL RuleML), which is planned to be the FOL sublanguage of RuleML 0.9, the rule component of SWRL FOL, and an FOL content language for SWSI . FOL RuleML is based on a modular combination of two syntactically characterized sublanguages: (1) Quantifier RuleML extends RuleML 0.87 by explicit quantifiers. (2) Disjunctive RuleML extends RuleML 0.87 by head disjunctions. Connectives for equivalence and negation are then modularly added for defining FOL RuleML. Its DTD is available for validation tests. Classical FOL model theory provides the semantics of FOL RuleML. FOL RuleML formulas can be used as the declarative content of KQML-like performatives 'Assert' and 'Query', which are augmented by a neutral 'Consider' performative.
Status of this document
This is a member submission, offered by the National Research Council of Canada, Network Inference and Stanford University, on behalf of themselves and the authors, in association with the Joint US/EU ad hoc Agent Markup Language Committee (

28. Neil Tennant
We shall establish the decidability of Classical monadic firstorder logic. We shall isolate intuitionistic logic as a subsystem of Classical logic,
http://people.cohums.ohio-state.edu/tennant9/650.html
NEIL TENNANT
tennant.9@osu.edu
If you email me, please use the header PHIL 650: YOURNAME.
Professor
Department of Philosophy
Winter Term 2006
PHIL 650: Symbolic Logic
Lecture/seminar University Hall , Room 353
Times tba Aims of this course This course aims to provide a comprehensive coverage of the syntax and semantics of first-order languages, and the positive results concerning them. First-order languages contain the expressions "for some x ", "for every x " and " x is identical to y ", in addition to the connectives "not", "and", "or" and "if ... then ..." of propositional logic (which will have been studied in PHIL 250: Introduction to Symbolic Logic Topics We address various philosophical problems concerning reference, definite descriptions, predication, identity and existence; and cover the rudiments of informal set theory that are needed for a rigorous discussion of syntactic and semantic matters. We give a precise compositional grammar for the generation of well-formed expressions (both terms and formulae) of first-order languages. We give the famous Tarskian definition of

29. Book Many-dimensional Modal Logics : Theory Applications, (studies In Logic The
I Introduction 1 Modal logic basics 1.1 Modal axiomatic systems 1.2 Possible world semantics 1.3 Classical firstorder logic and the standard translation
http://www.lavoisier.fr/notice/gb402605.html
Search on All Book CD-Rom eBook Software The french leading professional bookseller Description
Author(s) : GABBAY D. M.
Publication date : 09-2003
Language : ENGLISH
766p. 22.9x15.9 Hardback
Status : In Print (Delivery time : 10 days)
Comment This book will be a valuable reference for the modal logic researcher. It can serve as a brief but useful introduction (....) for the suitably qualified newcomer. And it contributes a careful and rewarding comprehensive account of some of the latest foundational results in the area of combining modal logics. Mark Reynolds, The University of Western Australia. Studia Logica, 2004.
Description
Summary
Subject areas covered:
  • Mathematics and physics Applied maths and statistics Applied maths for it
New search Your basket Information New titles BiblioAlerts E-books Customer services Open an account Ordering non-listed items Order tracking Help Lavoisier.fr Back to the home page Company information Terms and conditions Partner's sites ... basket Special Offer www.Lavoisier.fr New Le capitalisme cognitif : apports et perspectives (European Journal of Economic and Social Systems Vol.20 n° 1/2007)

30. Ian Hodkinson: Monodic Fragments Of First-order Temporal Logic
In this paper, we introduce a new fragment of the firstorder temporal language, problem for a certain fragment of Classical first-order logic.
http://www.doc.ic.ac.uk/~imh/frames_website/monodic.html
Monodic fragments of predicate temporal logic
Go to home page Related Papers
Decidable fragments of first-order temporal logics
Ian Hodkinson, Frank Wolter, and Michael Zakharyaschev
Ann. Pure. Appl. Logic 106 (2000) 85-134.
Monodic packed fragment with equality is decidable
Ian Hodkinson
Studia Logica 72 (2002) 185-197. This paper proves decidability of satisfiability of sentences of the monodic packed fragment of first-order temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. It also proves decidability over models with finite domains, over flows of time including the real order.
Monodic fragments of first-order temporal logics: 20002001 A.D.
I Hodkinson, F Wolter, M Zakharyaschev
In R. Nieuwenhuis and A. Voronkov, editors, Logic for Programming, Artificial Intelligence and Reasoning, number 2250 of LNAI, Springer, 2001, pages 1-23. The aim of this paper is to summarize and analyze some results obtained in 20002001 about decidable and undecidable fragments of various first-order temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the `temporal community' to a number of interesting open problems.
Decidable and undecidable fragments of first-order branching temporal logics
I Hodkinson, F Wolter, M Zakharyaschev

31. Anna Mikhajlova And Joakim Von Wright, Proving Isomorphism Of First-Order Logic
We prove in HOL that three proof systems for Classical firstorder predicate logic, the Hilbertian axiomatization, the system of natural deduction,
http://historical.ncstrl.org/litesite-data/tucs_fi/TR169.html
Anna Mikhajlova and Joakim von Wright,
Proving Isomorphism of First-Order Logic Proof Systems in HOL
TUCS Technical Report No. 169, March 1998
ISBN 952-12-0183-5
ISSN 1239-1891
Abstract
Keywords : Formalised mathematics, theorem-proving in higher-order logic, first-order proof theories, meta-logical reasoning, Hilbertian axiomatization, natural deduction, sequent calculus. Full paper in PostScript format (742 Kb) and in compressed PostScript format (128 Kb). Last modified on March 24, 1998 by Nina Kivinen (nikivine@abo.fi)

32. Theorem Proving
Lecture 14 Theorem Proving in Classical Propositional and first-order logic. History; Syntax and semantics of propositional and first-order logic
http://www.ags.uni-sb.de/~chris/lectures/fol-hol-tp/index.html
Automated Theorem Proving in First-Order and Higher-Order Logic
Dates
Thursday, 16:15 -17:45, Room: HS 002, Bldg.: 45
Classification:
Special Course, Logic and Computation, 6 Credit Points
Background Needed:
Basic knowledge about first-order logic and resolution based theorem proving is useful.
For some introductory reading see below (e.g. Huth, Fitting).
Related Modules:
Automated Reasoning (Vorlesung)

Lecturer Christoph Benzmueller , Room 2.12, Tel. 4574, Email: chris@ags.uni-sb.de Preliminary Module Outline The following module outline is preliminary and may be changed: Due to the overlap with the two related modules mentioned above the idea is to concentrate more on semantics and mechanisation of higher-order logic. This means that we will probably skip Lectures 1-5 and instead more deeply concentrate on the topics of Lectures 6-12. Le cture 1-4 Theorem Proving in Classical Propositional and First-Order Logic
  • History Syntax and semantics of propositional and first-order logic Resolution for Propositional and first-order logic Completeness of first-order resolution via abstract consistency
Lecture 5: First-Order Theorem Provers in Practice
  • Playing with some first-order theorem provers The TPTP library and format The comfortable use of theorem provers via the MathWeb software bus
Lecture 6-8: Introduction to Classical Higher-Order Logic
  • Motivation and history Lambda calculus Syntax and semantics of higher-order logic Higher-order unification
Lecture 9+10: Theorem Proving in Higher-order Logic
  • Resolution

33. Mechanized Reasoning Systems
GETFOL a proof system for sorted first order logic based on R. . proofs in Classical firstorder logic using deductive tableaux graphical notation.
http://www.calculemus.org/MathUniversalis/3/listsoft.html
Database of Existing Mechanized Reasoning Systems
This page represents the current state of an ongoing effort to collect information about existing automated reasoning systems. One objective is to provide concise useful information for people who have need for such a system and don't want to `roll their own'. Another objective is to provide a single place where information about existing systems can be accessed, thus providing an overview of the state of the art. This page is split into two parts: available systems and others . Entries in the available systems part are restricted to reasoning systems and tools that are implemented and available to outside users. Systems falling outside that category are listed in the others part. Click here or here for a general mechanized reasoning page. We attempt to provide for each entry: a one sentence description; a link to a brief overview; contact information; a link to a home page for the entry; and possibly other relevant information or links. In addition to individual there is a list of automated reasoning related mailing lists, and a list of related pages. Please send email to Michael Kohlhase kohlhase@cs.uni-sb.de

34. PlanetMath: First Order Logic
first order logic is owned by Henry. Other names, Classical first order logic, FO This is version 4 of first order logic, born on 200208-28,
http://planetmath.org/encyclopedia/FirstOrderLogic.html
(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
Papers

Books

Expositions

meta Requests
Orphanage

Unclass'd

Unproven
...
Classification

talkback Polls
Forums
Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About first order logic (Definition) A logic is first order if it has exactly one type . Usually the term refers specifically to the logic with connectives , and and the quantifiers and , all given the usual semantics
  • is true iff is not true is true if either is true or is true is true iff is true for every object (where is the result of replacing every unbound occurrence of in with is the same as is the same as is the same as is the same as
However languages with slightly different quantifiers and connectives are sometimes still called first order as long as there is only one type. "first order logic" is owned by Henry view preamble View style: HTML with images page images TeX source Other names: classical first order logic, FO

35. JSTOR Denial In First Order Logic
By first order logic one means the logic of truthfunctions and quantification. . and ambiguities can be expressed in Classical first order logic.
http://links.jstor.org/sici?sici=0003-2638(196704)27:5<171:DIFOL>2.0.CO;2-R

36. DI & CoS - Classical And Intuitionistic Logic
We present an inference system for Classical first order logic in which each inference rule, including the cut, only has a finite set of premises to choose
http://alessio.guglielmi.name/res/cos/CL/index.html
This page is no longer updated, please refer to this page Alessio Guglielmi's Research Deep Inference and the Calculus of Structures / Classical and Intuitionistic Logic
Deep Inference and the Calculus of Structures
Classical and Intuitionistic Logic
So far, for classical logic in the calculus of structures we achieved:
  • the cut rule trivially reduces to atomic form; one can show cut elimination for the propositional fragment by the simplest argument to date; the propositional fragment is fully local, including contraction; first order classical logic can be entirely made finitary; cut elimination and decomposition theorems are proved.
We can present intuitionistic logics in the calculus of structures with a fully local, cut-free system. The logic of bunched implications BI can be presented in the calculus of structures. Japaridze's cirquent calculus benefits from a deep-inference presentation, in particular in the case of propositional logic. The basic proof complexity properties of propositional logic are known.
  • Atomic Cut Elimination for Classical Logic
System SKS is a set of rules for classical propositional logic presented in the calculus of structures. Like sequent systems and unlike natural deduction systems, it has an explicit cut rule, which is admissible. In contrast to sequent systems, the cut rule can easily be restricted to atoms. This allows for a very simple cut elimination procedure based on plugging in parts of a proof, like normalisation in natural deduction and unlike cut elimination in the sequent calculus. It should thus be a good common starting point for investigations into both proof search as computation and proof normalisation as computation.

37. Logic Jnl IGPL -- Sign In Page
Their recommendations never go beyond the realm of Classical first order logic. Is that enough? Some of the papers of this issue can be seen as an
http://jigpal.oxfordjournals.org/cgi/content/full/15/4/289
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van Ditmarsch and Manzano Logic Jnl IGPL.
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38. Interpretation And Satisfiability In The First Order Logic
Interpretation and Satisfiability in the First Order logic. Edmund Woronowicz Warsaw University 4 Czeslaw Bylinski. A Classical first order language.
http://mizar.org/JFM/Vol2/valuat_1.html
Journal of Formalized Mathematics
Volume 2, 1990

University of Bialystok

Association of Mizar Users
Interpretation and Satisfiability in the First Order Logic
Edmund Woronowicz
Warsaw University, Bialystok
Supported by RPBP.III-24.C1.
Summary.
The main notion discussed is satisfiability. Interpretation and some auxiliary concepts are also introduced.
MML Identifier:
The terminology and notation used in this paper have been introduced in the following articles [ Contents (PDF format)
Bibliography
1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences Journal of Formalized Mathematics
2] Czeslaw Bylinski. Functions and their basic properties Journal of Formalized Mathematics
3] Czeslaw Bylinski. Functions from a set to a set Journal of Formalized Mathematics
4] Czeslaw Bylinski. A classical first order language Journal of Formalized Mathematics
5] Piotr Rudnicki and Andrzej Trybulec. A first order language Journal of Formalized Mathematics
6] Andrzej Trybulec. Tarski Grothendieck set theory Journal of Formalized Mathematics Axiomatics
7] Andrzej Trybulec.

39. CS3411 Advanced Knowledge Based Systems
The first part of the course will review the basic concepts of Classical first order predicate logic, and will give the student the ability to model reality
http://www.inf.unibz.it/~franconi/teaching/1999/3411/
Advanced Knowledge Based Systems
1999-2000 session
Lecturer: Enrico Franconi
Assessment: 2 hours examination (75%) + an individual class exercise (25%)
Aims and objectives
By the end of this module students will have acquired a method for designing knowledge bases and knowledge based systems and agents. The emphasis will be on a rigorous approach to knowledge representation and building ontologies. It is assumed that students are already familiar with the elements of logics and artificial intelligence.
The course is divided in three major parts. The first part of the course will review the basic concepts of classical first order predicate logic, and will give the student the ability to model reality using classical logic. At the end of the first part there will be an assessed class exercise.
The second part briefly surveys the standard technologies for ontological engineering and knowledge representation, reviewed from a logical perspective.
The third part of the course will present the most popular logic-based knowledge representation formalism, namely Description Logics. The simplest Description Logic will be deeply analysed from the logical point of view. Several extensions and uses of Description Logics will be briefly introduced at the end.
Illustrations of practical examples will be given.

40. Book Review Of The Classical Decision Problem By
After that I will add some remarks concerning tiling problems, other fragments of first order logic, and end with some personal remarks. The Classical
http://research.microsoft.com/~gurevich/Books/book3-review.html
Book review of
The classical Decision Problem
by
Review by Maarten Marx October 23, 1998
This book is about as its title suggests the classical decision problem, also known as Hilbert's Entscheidungsproblem . The preface promises a comprehensive modern treatment of the subject; indeed it does, in a very thorough but still, I think, to most of the intended audience (logicians, computer scientists, mathematicians and philosophers of science) rather accessible manner. The book contains an enormous wealth of techniques, tricks and methods for showing decidability or undecidability of logics, and, in the decidable cases, also methods to establish the exact complexity of the decision algorithms. I guess that not a lot of people would want to read it in one go. Browsing through it might be a dangerous experience though: on several occasions I was, without realising it, drawn deeply into it and the hours had flown by.
For everyone with an interest in decidability or complexity questions related to logic this book is a valuable reference which you will always want to have within reach. As a guide to the literature in the field the book is highly useful. Each chapter ends with a pleasantly written section containing historical remarks (having the additional advantage of not cluttering up the places where real work is to be done). The bibliography is an outstanding achievement. In more than 50 pages, 549 annotated references are given. The annotations not only contain a short abstract of the work, they also often make connections with other works or with the text itself.

41. FOL/Intuitionistic Logic Versus NAFL. Part 1. Failure Of Non-contradiction - Sci
You say syntax is as Classical first order logic. So what nonlogical axioms are allowed or disallowed by NAFL? I will get to these.
http://groups.google.nu/group/sci.logic/msg/5c6214c5513e5ae7
Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion FOL/Intuitionistic logic versus NAFL. Part 1. Failure of non-contradiction
The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful MoeBlee View profile More options Nov 14, 8:43 am Newsgroups: sci.logic From: Date: Wed, 14 Nov 2007 11:43:14 -0800 Local: Wed, Nov 14 2007 8:43 am Subject: Re: FOL/Intuitionistic logic versus NAFL. Part 1. Failure of non-contradiction Reply Reply to author Forward Print ... Find messages by this author On Nov 14, 5:42 am, "R. Srinivasan" <sradh
@hotmail.com> wrote:> On Nov 12, 5:47 am, "R. Srinivasan" <sradh
> > > Define an "intepretation" T* of T as follows.
Okay, thanks.
You've said that the syntax of NAFL is just as in classical first
order logic. So, what is an NAFL theory as distinct from just a
classical first order theory (as 'T is a classical first theory' can
be defined as 'T is a set of first order sentences closed under
classical provability' (actually, the property is usually closure

42. [Ber99] Intuitionistic Completness For First Order Classical Logic
@article{Berardi2JSL, number = {1}, volume = {64}, title = {Intuitionistic Completness for First Order Classical logic}, author = {Stefano Berardi},
http://www.di.unito.it/~lambda/biblio/entry-Berardi2-JSL.html
Chronological Overview Type-Hierarchical Overview Semantics and Logics of Computation
(Most of the papers antecedent to 1995
are not included in the list) FRAMES NO FRAME Berardi2:JSL (Article)
Author(s) Stefano Berardi Title Journal Journal of Symbolic Logic Volume Number Page(s) Year BibTeX code
Chronological Overview
Type-Hierarchical Overview Semantics and Logics of Computation
(Most of the papers antecedent to 1995
are not included in the list) FRAMES NO FRAME
This document was generated by
(Modified by Luca Paolini, under the GNU General Public License

43. Mbox: Spelling Out The Manifesto
The claim is that each proof of a result A in a logic L can be converted into a proof of the reification of A in Classical first order logic.
http://www-unix.mcs.anl.gov/qed/mail-archive/volume-2/0150.html
spelling out the Manifesto
John Staples staples@cs.uq.oz.au
Wed, 25 May 1994 15:08:01 +1000 (EST)
This is a comment on Mike B's `spelling out the Manifesto'.
It is not an author response since I was not one of the
authors.
In particular I want to comment on Mike's notion of
reification, which interprets various logics (or, their
theories) as theories based on classical first order logic.
So far, so good, but note that Mike's introduction of reification
in 2. does not discuss translation of inference rules. Perhaps for this
reason, I was uneasy to read `This can be done for EVERY logic'.
However, provided the other logic has a model theory comprehensible in classical logic, I don't have a solid objection. At Mike's point 4 I start to have real concerns. The claim is that each proof of a result A in a logic L can be converted into a proof of the reification of A in classical first order logic.

44. Proof Terms For Classical Logic In Natural Deduction Formulation
PROOF TERM ASSIGNMENT for Classical logic in NATURAL DEDUCTION FORMULATION In this note we will define a proof term calculus for First Order Classical logic
http://www.seas.upenn.edu/~sweirich/types/archive/1993/msg00133.html
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proof terms for classical logic in natural deduction formulation

45. KRR Research: ID-Logic Introduction
However, it itegrates ideas from this domain into the Classical, monotone setting of first order logic. As such, this logic provides a bridge across the
http://www.cs.kuleuven.be/~dtai/krr/idlogic/intro.html
Home KRR Research KRR Software KRR Members ... KRR Internal Information KRR Research: ID-Logic introduction DTAI KRR Research ID-Logic ... Introduction
On this page, you can find a basic introduction to ID-logic. The tone here will be a bit informal and we will just try to get the basic ideas across. If you would be more interested in a proper scientific introduction to ID-logic (with all the appropriate references to relevant literature and so on) we suggest you take a look at our papers section. The contents of this section consists of answers to the following questions: These answers are supposed to form a more-or-less coherent whole when read subsequently, so feel free to just start reading right here:
What is ID-logic? (short answer)
ID-logic extends classical logic with inductive definitions . The result is an expressive knowledge representation language, which is easy to understand, suitable for

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