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1. Languages & Structures languages structures (a subtopic of Representation) . (truthfunctional propositional logic and First-order predicate logic) and their metatheory. http://www.aaai.org/AITopics/html/struc.html

a subtopic of Representation THE TOPICS AI in the news AI Overview Agents Applications Cognitive Science Education Ethical/Social Expert Systems FAQs History Interfaces Machine Learning Natural Language Philosophy Reasoning Reference Shelf Representation Resources Robots Science Fiction Speech Turing Test Vision What's Left? QUICK START tips AI Overview A - Z Index AAAI Video Archive AI in the news Doing a Report for School Site Map Reference Shelf How to use this site Search Engine DIRECTORY How to use this site A - Z Index Site Map Reference Shelf Search Engine Contact AI Topics Notices Disclosures AI Topics Home AAAI Home AAAI Video Archive XML/RSS news feed Good Places to Start Readings Online Related Web Sites Related Pages ... More Readings see FAQ Recent News about THE TOPICS (annotated) AI Topics home AAAI home ... engine "The use of a representation as a medium of expression and communication matters because we must be able to speak the language to use it. If we can't determine how to say what we're thinking, we can't use the representation to communicate with the reasoning system." -excerpt from What Is a Knowledge Representation?

2. 03Cxx 03C07 Basic properties of Firstorder languages and structures model completeness and related topics; 03C13 Finite structures See also 68Q15, http://www.ams.org/msc/03Cxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Model theory 03C05 Equational classes, universal algebra [See also 03C07 Basic properties of first-order languages and structures 03C10 Quantifier elimination, model completeness and related topics 03C13 Finite structures [See also 03C15 Denumerable structures 03C20 Ultraproducts and related constructions 03C25 Model-theoretic forcing 03C30 Other model constructions 03C35 Categoricity and completeness of theories 03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 03C55 Set-theoretic model theory 03C57 Effective and recursion-theoretic model theory [See also 03C60 Model-theoretic algebra [See also 03C62 Models of arithmetic and set theory [See also 03C64 Model theory of ordered structures; o-minimality 03C65 Models of other mathematical theories 03C68 Other classical first-order model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators [See also 03C85 Second- and higher-order model theory 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

3. Mhb03.htm 03C07, Basic properties of Firstorder languages and structures. 03C10, Quantifier elimination, model completeness and related topics http://www.mi.imati.cnr.it/~alberto/mhb03.htm

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.)

4. LBase: Semantics For Languages Of The Semantic Web The resulting language is Firstorder in all the usual senses it is compact and incorporate all truths of a full theory of such structures into Lbase; http://www.w3.org/TR/lbase/

LBase: Semantics for Languages of the Semantic Web W3C Working Group Note 10 October 2003 This version: http://www.w3.org/TR/2003/NOTE-lbase-20031010/ Latest version: http://www.w3.org/TR/lbase Previous version: http://www.w3.org/TR/2003/NOTE-lbase-20030905 Authors: rguha@us.ibm.com Patrick Hayes phayes@ihmc.us MIT ... document use and software licensing rules apply. Abstract This document presents a framework for specifying the semantics for the languages of the Semantic Web. Some of these languages (notably RDF [ RDF-PRIMER RDF-VOCABULARY RDF-SYNTAX RDF-CONCEPTS ... RDF-SEMANTICS ], and OWL [ OWL ]) are currently in various stages of development and we expect others to be developed in the future. This framework is intended to provide a framework for specifying the semantics of all of these languages in a uniform and coherent way. The strategy is to translate the various languages into a common 'base' language thereby providing them with a single coherent model theory. We describe a mechanism for providing a precise semantics for the Semantic Web Languages (referred to as SWELs from now on. The purpose of this is to define clearly the consequences and allowed inferences from constructs in these languages. Status of This Document This section describes the status of this document at the time of its publication. Other documents may supersede this document. A list of current W3C publications and the latest revision of this technical report can be found in the

5. MathSC2000 < Mizar < Mizar TWiki General logic Classical Firstorder logic Primary classification Article 08Bxx, 18C05 03C07 Basic properties of First-order languages and structures . http://wiki.mizar.org/cgi-bin/twiki/view/Mizar/MathSC2000

Skip to topic Skip to bottom Jump: Mizar Mizar Web Mizar Web Home Changes Index Search Webs Main Mizar Sandbox TWiki ... Test My links My home page edit Edit Attach ... Printable Mizar.MathSC2000 r1.1 - 23 Oct 2006 - 21:50 - JosefUrban topic end Skip to actions List of pages with Mathematics Subject Classification of Mizar articles NOTE: Start a new topic for each tool. New tool (use a WikiWord title): Results from Mizar web MarcoRiccardi 04 Jan 2007 - 09:11 03 Mathematical logic and foundations Section P S 03A05 Philosophical and critical For philosophy of mathematics, see also 00A30 03B General logic 9 03C Model theory ... MarcoRiccardi 02 Nov 2006 - 21:11 NEW 03B General logic Section P S 03B05 Classical propositional logic 03B10 Classical first-order logic 9 03B15 Higher-order logic and type theory 03B20 Subsystems of ... MarcoRiccardi 02 Nov 2006 - 21:14 NEW General logic Classical first-order logic Primary classification # Article 1 qc lang1 A First Order Language Piotr Rudnicki and Andrzej Trybulec 2 qc lang2 Connectives ... MarcoRiccardi 02 Nov 2006 - 20:44 NEW 03C Model theory Section P S 03C05 Equational classes, universal algebra See also 08Axx, 08Bxx, 18C05 03C07 Basic properties of first-order languages and structures ...

6. First-order Model Theory (Stanford Encyclopedia Of Philosophy) Since we can recover the signature K from the Firstorder language L that it generates, we can and will refer to structures of signature K as L-structures. http://plato.stanford.edu/entries/modeltheory-fo/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free First-order Model Theory First published Sat Nov 10, 2001; substantive revision Tue May 17, 2005 First-order model theory, also known as classical model theory, is a branch of mathematics that deals with the relationships between descriptions in first-order languages and the structures that satisfy these descriptions. From one point of view, this is a vibrant area of mathematical research that brings logical methods (in particular the theory of definition) to bear on deep problems of classical mathematics. From another point of view, first-order model theory is the paradigm for the rest of model theory ; it is the area in which many of the broader ideas of model theory were first worked out. 1. First-order languages and structures 2. Elementary maps 3. Five grand theorems 4. Three useful constructions ... Related Entries 1. First-order languages and structures A a ). Two exceptions are that variables are italic ( x y ) and that sequences of elements are written with lower case roman letters (a, b).

7. JSTOR Cylindric Algebras Of First-Order Languages CYLINDRIC ALGEBRAS OF Firstorder languages PROOF. The number of isomorphism types of one element structures of a language with m predicate symbols is 2m http://links.jstor.org/sici?sici=0002-9947(197602)216<189:CAOFL>2.0.CO;2-D

8. Springer Online Reference Works If a collection of propositions in a Firstorder language of signature . of a formalized language and the study of classes of structures defined by means http://eom.springer.de/m/m064390.htm

Encyclopaedia of Mathematics M Article referred from Article refers to Model theory The part of mathematical logic studying mathematical models (cf. Model (in logic) The origins of model theory go back to the 's and 's, when the following two fundamental theorems were proved. Theorem 1 of propositions in a first-order language is consistent, then the whole collection is consistent (see Theorem 2 ). If a collection of propositions in a first-order language of signature has an infinite model, then it has a model of any infinite cardinality not less than the cardinality of Theorem 1 has had extensive application in algebra. On the basis of this theorem, A.I. Mal'tsev created a method of proof of local theorems in algebra (see Mal'tsev local theorems Let be an algebraic system of signature , let be the underlying set of , let , let denote the signature obtained from by the addition of symbols for distinguished elements for all , and let denote the algebraic system of signature which is an enrichment of in which for each the symbol is interpreted by the element . The set of all closed formulas of the signature in a first-order language which are true in the system is called the elementary diagram of the algebraic system (or the description of the algebraic system ), and the set

9. LOFOL Table Of Contents The Language of Firstorder Logic Table of Contents. Preface 11.1 First-order structures; 11.2 Spurious structures; 11.3 Truth and satisfaction, http://www-csli.stanford.edu/hp/LOFOLTOC.html

Back Tarski "Lite" Contents The Language of First-order Logic: Table of Contents Preface 1 Introduction 1.1 The special role of logic in rational inquiry 1.2 Why learn an artificial language? 1.3 About this book Part I: Propositional Logic 2 Atomic Sentences 2.1 Individual constants 2.2 Predicate symbols 2.3 Atomic sentences 2.4 The first-order language of set theory 2.5 Function symbols 2.6 The first-order language of arithmetic 2.7 General first-order languages 2.8 Methods of proof 2.9 Formal proofs 2.10 Alternative notation 3 Conjunctions, Disjunctions, and Negations 3.1 Negation symbol 3.2 Conjunction symbol 3.3 Disjunction symbol 3.4 Ambiguity and parentheses 3.5 Logical equivalence 3.6 Translation 3.7 Satisfiability and logical truth 3.8 Methods of proof involving negation, conjunction and disjunction 3.9 Formal proofs 3.10 Conjunctive and disjunctive normal forms 3.11 Truth-functional completeness 3.12 Alternative notation 4 Conditionals and Biconditionals 4.1 Material conditional symbol 4.2 Biconditional symbol 4.3 Conversational implicature

10. Deciding First-order Properties Of Locally Tree-decomposable Structures Deciding Firstorder properties of locally tree-decomposable structures Ullman, Universality of data retrieval languages, Proceedings of the 6th ACM http://portal.acm.org/citation.cfm?id=504798&dl=GUIDE,

11. George Luger His AI book, Artificial Intelligence structures and Strategies for Complex G. F. Diagnosis Using a Firstorder Stochastic Language That Learns. http://www.cs.unm.edu/~luger/

Professor George F. Luger FEC 349E George Luger has been a Professor in the UNM Computer Science Department since 1979. His two master's degrees are in pure and applied mathematics. He received his PhD from the University of Pennsylvania in 1973, with a dissertation focusing on the computational modeling of human problem solving performance in the tradition of Allen Newell and Herbert Simon. George Luger had a five year postdoctoral research appointment at the Department of Artificial Intelligence of the University of Edinburgh in Scotland. In Edinburgh he worked on several early expert systems, participated in development and testing of the Prolog computer language, and continued his research in the computational modeling of human problem solving performance. At the University of New Mexico, George Luger has also been made a Professor in the Psychology and Linguistics Departments, reflecting his interdisciplinary research and teaching in these areas. His most recent National Science Foundation supported research is in diagnostic reasoning, where he has developed stochastic models, mostly in an extended form of Bayesian Belief Networks. His book Cognitive Science was published by Academic Press in 1994.

12. Physics Help And Math Help - Physics Forums - View Single Post - What Is A Numbe Did you see the earlier mentions of theories, structures, and models? where L is a Firstorder language with one nonlogical binary predicate symbol, http://www.physicsforums.com/showpost.php?p=1049063&postcount=64

13. First-Order Queries On Finite Structures Over The Reals - Paredaens, Van Den Bus 83 Relational expressive power of constraint query languages Benedikt, Dong et al. - 1996 44 First-order queries on finite structures over the reals http://citeseer.comp.nus.edu.sg/449339.html

First-Order Queries on Finite Structures Over the Reals (1995) (Make Corrections) (44 citations) Jan Paredaens, Jan Van den Bussche, Dirk Van Gucht @ NUS Home/Search Context Related View or download: luc.ac.be/~vdbuss/ ueries_reals.ps.gz Cached: PS.gz PS PDF Image ... Help From: luc.ac.be/~vdbuss/pubs (more) (Enter author homepages) Rate this article: (best) Comment on this article (Enter summary) Abstract: We investigate properties of finite relational structures over the reals expressed by first-order sentences whose predicates are the relations of the structure plus arbitrary polynomial inequalities, and whose quantifiers can range over the whole set of reals. In constraint programming terminology, this corresponds to Boolean real polynomial constraint queries on finite structures. The fact that quantifiers range over all reals seems crucial; however, we observe that each sentence in the ... (Update) Context of citations to this paper: More ...suggests sparseness conditions on definable sets. One known positive case was that of the additive arithmetic of the reals investigated in Several people, 8 including the present authors, have conjectured that among linearly ordered background structures o...

14. Method And Apparatus For The Generation And Manipulation Of Data Structures - US A system for manipulating data structures includes a memory circuit configured Boolean Prolog is an algebraic Firstorder language based on two constant http://www.patentstorm.us/patents/5758152-description.html

Home Browse by Inventor Browse by Date Links ... Contact Us United States Patent 5758152 Method and apparatus for the generation and manipulation of data structures US Patent Issued on May 26, 1998 Inventor(s) Jack J. LeTourneau Assignee Prime Arithmetics, Inc. Application No. 623628 filed on 1990-12-06 Current US Class Generating database or data structure (e.g., via user interface) Examiners Primary: Joseph H Feild Attorney, Agent or Firm US Patent References Method of translating data from knowledge base to data base Issued on: June 4, 1991 Inventor: Kondo Method of generating and accessing a database independent of its structure and syntax Issued on: August 10, 1993 Inventor: Ohler, et al. High concurrency in use manager Issued on: November 23, 1993 Inventor: Nordstrom, et al. Abstract Claims Description Full Text Description FIELD This invention is in the field of digital computers. More particularly, it relates to methods and apparatus for the creation, manipulation, and display of data structures for use in digital computers. BACKGROUND The origins of computers and computer science are rooted in the concepts of algorithms and data structures. To date, the theoretical emphasis has been on the generation and efficient implementation of algorithms. Data structures, which originally included only numbers, were theoretically less well understood although known to be critical to the automation of various mechanical processes. Only recently has a theory of data structures, both as a vehicle to store information and as a tool to solve problems, been recognized and a general methodology of data structures developed.

15. FSU Computer Science - Graduate FAQ COP Computer Programming (languages, data structures, software systems, .. and proof theory of propositional logic and first order languages; http://www.cs.fsu.edu/current/grad/courses.php

@import url(../../css/global.css); @import url(../../css/page.css); Help Login Contact Site Map ... Graduate Program Graduate Courses Definition of Prefixes CAP - Computer Applications CDA - Computer Design/Architecture CEN - Computer Engineering Software CGS - Computer General Studies CIS - Computer and Information Systems (special topics) COP - Computer Programming (languages, data structures, software systems, operating systems, compiling) COT - Computer Theory Special Course Offerings There are various special courses offered every term. Special topics courses may evolve into regularly offered courses if they are successful, but they may also be once-only offerings. The latter is especially true if the enrollment of the first offering is low. To take a look at the special course offerings click here. 5000 Level Courses CAP 5415 Priniciples and Algorithms of Computer Vision (3). Prerequisites: COP 4530 This course covers the basic computational prinicples and algorithms to extract information from images and image sequences. Topics include imaging models, linear and non-linear filtering, edge detection, stereopsis and motion estimation, texture modelling, segmentaion and grouping, and deformable matching for recognition. CAP 5605. Artificial Intelligence (3).

16. First-Order Logic: Languages The Language of Firstorder Logic And Tarski s World redress one of the main unification forms are appropriate for implementing various structures. http://lycos.com/info/first-order-logic--languages.html

var topic_urlstring = 'first-order-logic'; var topic = 'First-Order Logic'; var subtopic_urlstring= 'languages'; LYCOS RETRIEVER Retriever Home What is Lycos Retriever? First-Order Logic: Languages built 93 days ago Retriever Science Math Logic and Foundations "The Language of First-order Logic [A]nd Tarski's World redress one of the main shortcomings of traditional beginning-level logic texts which emphasize the formal aspects of logic and pay scant attention to semantics. Tarski's World sets a high standard for those who follow." Kevin Compton, Journal of Symbolic Logic. Source: www-csli.stanford.edu In the mid 1960s First Order Logic was the most widely used knowledge representation language. However, to be useful the knowledge had to be processed and it was felt that a general problem solver should be defined. Such a problem solver would tackle a wide range of problems described by representing the initial situation, the goal situation and allowable actions. Source: comp.rgu.ac.uk Since the very start of machine learning, logic has been very popular as a representation language for inductive concept- learning and the possibilities for learning in a first order representation have been investigated. This is due to the fact that first order logic extends propositional representations and therefore ... the scope of machine learning. In database terminology, propositional techniques learn from a single relation in a relational database, whereas first order approaches cope with multiple relations. Learning in first-order logic is therefore of special interest to researchers and practitioners in machine learning, data mining, knowledge discovery in databases, knowledge representation and logic programming.

17. Scientific Commons Approximate Inference For First-Order Approximate Inference for Firstorder Probabilistic languages (2001) about relations among objects, where MCMC samples over relational structures. http://en.scientificcommons.org/465899

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18. Hashcollision I didn t get this so strongly before, but there s a correspondence between the language and structures of Firstorder logic, and the signatures and units of http://hashcollision.blogspot.com/

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?targetBlogID=18302393"); hashcollision (modulo life human-brain) > (and confusion inquiry) Sunday, November 25, 2007 zelda I held my sword in front, and approached the village cautiously. I would have to slaughter the terrible Yook monster disguised in one of the hapless villagers's homes. I pushed the doors open, ready to hack and slash. To my shock, all of the villagers looked exactly the same! And each had something to say about the other Anouki: * FoFo said that Gumo was honest. * Kumu said Mazo or Aroo was lying. * Dobo said Mazo was honest. * Gumo said Fofo or Aroo was lying. * Aroo said Kumu was lying. * Mazo said that he and Dobo were honest. How dastardly! Only the Yook would lie to me. And I couldn't just kill them all and let God sort them out. I had to think about this. So I did what anyone in this circumstance would do: I pulled out Alloy truthful: Boolean Fofo.truthful = True implies Gumo.truthful=True

19. Johan Van Benthem : Current Teaching Activities Firstorder language over the reals and related linear orders. On Tuesday, we did some basic modal structures in games http://staff.science.uva.nl/~johan/169-2004.html

Modal Logic This course is an introduction emphasizing major techniques, and a small tour of modern application areas for modal logic. Schedule Week 1 Basic Language and Expressive Power This week introduces the basic modal language, and its evaluation in possible worlds models. This is a paradigm for studying the diverse modal languages used in practice. Expressive power is measured by the modern technique of bisimulation invariance, also found in computer science. We can think of bisimulation in terms of playing games, a topic that will return in this course. basic language and semantics bisimulation and expressive power Week 2 Axiomatization and Complexity Here we look at the Balance found in any logical system. Expressive power comes at a price in terms of complexity for the basic tasks a logical system is used for, These are semantical evaluation/model checking, valid reasoning/ SAT-testing, and model comparison for language equiva- lence/structural similarity. This involves a brief excursion into computational complexity, a whole topic by itself. valid reasoning and axiomatics complexity of logical tasks Week 3 Translations and Extensions We now turn our working analogy between modal operators

20. IHPST - Philosophy - Logic And Language logic and language. research programs. ONTOLOGICAL STRUCTURE and SEMANTIC It was quickly noticed that standard Firstorder languages are not up to the http://www-ihpst.univ-paris1.fr/rub.php?lng=en&cat=_philo&rub=r01&srub=02

21. Are First-order Languages Adequate For Mathematics? Are Firstorder languages adequate for mathematics? The compactness theorem, in turn, implies that no structure which is constructed by a simple http://osdir.com/ml/science.mathematics.fom/2006-10/msg00181.html

var addthis_pub = 'comforteagle'; science.mathematics.fom Top All Lists Date Thread Are first-order languages adequate for mathematics? Subject Are first-order languages adequate for mathematics? List-id We should be able to prove that PA is complete in various relevant senses. We rediscovered the simple semantic conditions on a "logic" that forces it to be semantically equivalent to first order logic - it is due to Per Lindstrom. We should be able to 1. Analyze with extreme care just what first order logic does for foundations of mathematics. It does things that are not done by the kind of alternate logics you are discussing. More with this subject... Current Thread Previous by Date: Re: First-order arithmetical truth V . Sazonov-5fL7ta8dD402EctHIo1CcQ Next by Date: Re: First-order arithmetical truth V . Sazonov-5fL7ta8dD402EctHIo1CcQ Previous by Thread: Re: First-order arithmetical truth Harvey Friedman Next by Thread: First Order Logic/status Harvey Friedman Indexes: Date Thread Top All Lists Recently Viewed: qnx.openqnx.dev...

22. 23 Suchergebnisse Für [clls] This paper presents the Constraint Language for Lambda structures (CLLS), a Firstorder language for semantic underspecification that conservatively extends http://scidok.sulb.uni-saarland.de/scidoksearch?query=clls

23. Semantic Structures And Natural Language Parsers: A Case Study The meaning of natural language must be converted to a formal structure in the include First Order Logic, Instant Tense Logic, Period structures, http://www.tcnj.edu/~cs/studentpapers/MichaelBloodgood/MikeBloodgood.htm

Semantic Structures and Natural Language Parsers: A Case Study Michael Bloodgood Dr. Miroslav Martinovic Department of Computer Science, The College of New Jersey Abstract —QASTIIR is a part of an NSF-funded, collaborative project between The College of New Jersey and Villanova University. The ultimate goal of this project is the design, development, experimentation, and evaluation of a hybrid Question Answering (QA) system. An important role within this project is the semantic analysis of both, queries and potential answers. It is within this context that we are conducting this case study. One goal of this study is the identification and evaluation of state-of-the-art semantic parsers that are candidates for being implemented as a component of QASTIIR. The meaning of natural language must be converted to a formal structure in the linguistic component of QASTIIR. A second goal of this research is to acquire an understanding of the mathematical and logical techniques and structures that are used to represent meaning. The theoretical basis for using formal structures to represent meaning is considered.

24. Hudak: Building Domain-Specific Embedded Languages The use of monads PJW93, Wad90 to structure the design was critical. a simple Firstorder language with variables, then a higher-order language with http://www.cs.yale.edu/homes/hudak-paul/hudak-dir/ACM-WS/position.html

ACM Computing Surveys permissions statement below. Building Domain-Specific Embedded Languages Paul Hudak Yale University Department of Computer Science Box 208285, New Haven, CT 06520, USA hudak@cs.yale.edu http://www.cs.yale.edu/users/hudak-paul.html General Terms: Programming Languages, Interpreters, Functional Programming, Domain Specific Languages, Software Architecture I have believed for a very long time that abstraction is the most important factor in writing good software. As programming language researchers we design, and as software engineers we are trained to use, a variety of abstraction mechanisms: abstract data types, higher-order functions, monads, continuations, modules, classes, objects, etc. Particular languages support some of these mechanisms well, others not so well. An important point about these mechanisms is that they are fairly general -for example, most algorithmic strategies and computational structures can be implemented using either functional or object-oriented abstraction techniques. Although generality is good, we might ask what the "ideal" abstraction for a particular application is. In my opinion, it is a

25. Formal Logic, Or Mathematical Logic, Or Symbolic Logic -- Britannica Online Enc A Firstorder language is given by a collection S of symbols for relations, functions, and constants, which, in combination with the symbols of elementary http://www.britannica.com/eb/topic-213716/formal-logic

Already a member? LOGIN Encyclopædia Britannica - the Online Encyclopedia Home Blog Advocacy Board ... Free Trial Britannica Online Content Related to this Topic Shopping Revised, updated, and still unrivaled. 2008 Britannica Ultimate DVD/CD-ROM The world's premier software reference source. Great Books of the Western World The greatest written works in one magnificent collection. Visit Britannica Store formal logic, or mathematical logic, or symbolic logic A selection of articles discussing this topic. Main article: formal logic the abstract study of propositions, statements, or assertively used sentences and of deductive arguments. The discipline abstracts from the content of these elements the structures or logical forms that they embody. The logician customarily uses a symbolic notation to express such structures clearly and unambiguously and to enable manipulations and tests of validity to be more easily applied.... major reference analytic philosophy analytic philosophy (in analytic philosophy: The role of symbolic logic) For philosophers oriented toward formalism, the advent of modern symbolic logic in the late 19th century was a watershed in the history of philosophy, because it added greatly to the class of statements and inferences that could be represented in formal (i.e., axiomatic) languages. The formal representation of these statements provided insight into their underlying logical structures; at the... analytic philosophy (in analytic philosophy: Logical atomism) applied logic the study of the practical art of right reasoning. The formalism and theoretical results of pure logic can be clothed with meanings derived from a variety of sources within philosophy as well as from other sciences. This formal machinery also can be used to guide the design of computers and computer programs.

26. Finite Model Theory - Wikibooks, Collection Of Open-content Textbooks FMT is a restriction of MT to finite structures, such as finite graphs or strings. for all areas are introduced on the level of first order languages. http://en.wikibooks.org/wiki/Finite_Model_Theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikibooks"; Finite Model Theory From Wikibooks, the open-content textbooks collection Jump to: navigation search Finite Model Theory (FMT) is a subarea of Model Theory (MT). MT is the branch of mathematical logic which deals with the relation between a formal language (syntax) and its interpretations (semantics). FMT is a restriction of MT to finite structures, such as finite graphs or strings. Since many central theorems of MT do not hold when restricted to finite structures, FMT is quite different from MT in methods and application areas. So FMT has become an "unusually effective" instrument in computer science, like in database theory, model checking or for gaining new perspectives on computational complexity. The three main areas of FMT are presented here: Expressive Power of Languages, Descriptive Complexity and Random Structures. But first the results fundamental for all areas are introduced on the level of first order languages. Wikipedia has related information at Finite model theory Contents Basics Ehrenfeucht-Fraisse-Games for FO Expressive Power of Languages Descriptive Complexity ... edit Basics Why?

27. CS Website Course Description Page Introduction to algebraic structures in computing. The Prolog language is Apply the properties of Firstorder predicate calculus to determine whether a http://www.cs.pdx.edu/user/coursedetails/15

Contact PSU PSU FAQs Search future students ... Alumni + Friends I want to... access my records apply to PSU buy books check e-mail find a class find a job find a person/office get maps/directions get transcripts give to PSU register for classes see the calendar use course tools visit PSU Computer Science Maseeh College of Engineering and Computer Science home contact us Home ... Capstone CS 251 Discrete Structures II Credit Hours: Course Coordinator: Lois Delcambre Course Description: Continuation of CS 250. Logic: propositional calculus, first-order predicate calculus. Formal reasoning: natural deduction, resolution. Applications to program correctness and automatic reasoning. Introduction to algebraic structures in computing. The Prolog language is introduced and used for programming experiments. Prerequisite: CS 250. Prerequisites: Discrete Structures I Goals: CS 251 is the second term of the two term sequence CS 250-251. The main goal of the sequence is that students obtain those skills in discrete mathematics and logic that are used in the study and practice of computer science. A second goal is that students become familiar with Maple and Prolog as tools for doing laboratory experiments in discrete mathematics and logic. Upon the successful completion of this course students will be able to: Apply the properties of propositional calculus to: determine whether a wff is a tautology, a contradiction, or a contingency by truth tables and by Quine's method; construct equivalence proofs; and transform truth functions and wffs into conjunctive or disjunctive normal form.

28. Tortorelli: A Characterization Of Internal Sets This is a Firstorder structure on the First-order language EA, having as its symbols for constants all the elements of ~., and as the only binary http://www.numdam.org/numdam-bin/fitem?id=RSMUP_1989__81__193_0

29. Abstracts Of Malika More Let L be the Firstorder language with identity whose set of specific symbols . we give a precise characterization of equivalence between two structures, http://laic.u-clermont1.fr/~more/recherche/abstract2.html

Abstracts of some papers Malika More, Investigation of binary spectra by explicit transformations of graphs Theoretical Computer Science , 124, pp. 221-272, 1994 (Fundamental Study) Abstract : Let L be the first-order language with identity whose set of specific symbols consists of the binary predicate symbols R_1, ..., R_q. Let A be an L-sentence and let us denote by Gen(A) (generalized spectrum of A) the set of all finite models of A. We say that A represents gen(A). The spectrum S(A) of sentence A is the set of cardinalities of domains of elements of Gen(A) and A is also called a representation of S(A). Let A be some L-sentence and P be a polynomial of degree k of Z[X] asymtotically greater than or equal to identity function on N. We produce a sentence P(A) representing P(S(A)), i.e. S(P(A))=P(S(A)). The algorithm producing P(A) depends only on P and L and effectively one-to-one maps elements of Gen(A) onto elements of Gen(P(A)). This sentence P(A) is formalized in a binary language L* of cardinality 2q+k if k Nadia Creignou, Malika More

30. Mathematical Structures In Computer Science In addition to the classical algebraic structures there will be discussed also Predicates, kvantifiers, terms, formulas, Firstorder language anf its http://www.fit.vutbr.cz/study/course-l.php?id=137

31. MATHEMATICAL LOGIC FOR COMPUTER SCIENCE Propositional Language; Structure of Formulas; Semantics Classical Firstorder Logic Proposition Functions and Quantifiers; First-order Language 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

32. METU MATHEMATICS DEPARTMENT MATH 406 Introduction to Mathematical Logic and Model Theory (30)3 First order language, structures and satisfaction. Completeness and compactness theorems http://www.math.metu.edu.tr/courses/undergrad.shtml

UNDERGRADUATE CURRICULUM FIRST YEAR First Semester MATH 111 Fundamentals of Math. (3-0)3 MATH 115 Analytic Geometry (3-0)3 MATH 153 Calculus for MATH. Students I (4-2)5 PHYS 111 Physics I (4-2)5 ENG 101 Development of Reading and Writing Skills I (4-0)4 Second Semester MATH 112 Introductory Discrete Math. (3-0)3 MATH 116 Basic Algebraic Structures (3-0)3 MATH 154 Calculus for MATH. Students II (4-2)5 PHYS 112 Physics II (Electricity and Magnetism) (4-2)5 ENG 102 Development of Reading and Writing Skills II (4-0)4 IS 100 Introduction to Information Systems and Applications NC SECOND YEAR Third Semester MATH 251 Advanced Calculus I (4-0)4 MATH 261 Linear Algebra I (4-0)4 CENG 230 Introduction to C Programming (2-2)3 ENG 211 Advanced Reading and Oral Communication (3-0)3 Fourth Semester MATH 252 Advanced Calculus II (3-2)4 MATH 254 Introduction to Differential Equations I (4-0)4 MATH 262 Linear Algebra II (4-0)4 HIST 2202 Principles of Kemal Atat?rk II NC A non-departmental elective (3-0)3 THIRD YEAR Fifth Semester MATH 349 Int. to Math. Analysis (4-0)4

33. First-order Logic - Wikipedia, The Free Encyclopedia A Firstorder language cannot, however, categorically express the notion of arguments that rely on the internal structure of the propositions involved. 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

34. IngentaConnect A Calculus For First Order Discourse Representation Structures Nevertheless, even within the general setting of first order logic the structure of the ``formulas of DRSlanguages, i.e. of the Discourse Representation http://www.ingentaconnect.com/content/klu/jlli/1996/00000005/F0020003/00109526

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); A Calculus for First Order Discourse Representation Structures Authors: Kamp H. ; Reyle U. Source: Journal of Logic, Language and Information , Volume 5, Numbers 3-4, October 1996 , pp. 297-348(52) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: This paper presents a sound and complete proof system for the first order fragment of Discourse Representation Theory. Since the inferences that human language users draw from the verbal input they receive for the most transcend the capacities of such a system, it can be no more than a basis on which more powerful systems, which are capable of producing those inferences, may then be built. Nevertheless, even within the general setting of first order logic the structure of the ``formulas'' of DRS-languages, i.e. of the Discourse Representation Structures suggest for the components of such a system inference rules that differ somewhat from those usually found in proof systems for the first order predicate calculus and which are, we believe, more in keeping with inference patterns that are actually employed in common sense reasoning.

35. Work In Progress The overall structure of truth and the lattice of theories can be of first order language, first order modeltheoretic structure,first order theory and http://suo.ieee.org/IFF/work-in-progress/

Work in Progress conceptual scaling algebraic semiotic systems , and the development of a module representing common logic (CL). The overall structure of truth and the lattice of theories can be partitioned into conceptual scales according to topic, where one topic could be the metadata about the theories in the lattice. The IFF takes the high road to implementation. There is work in progress on an IFF representation of the Meta Object Facility (MOF) and the Model Driven Architecture (MDA) of the Object Management Group (OMG). In the other direction, there are on-going explorations to demonstrate how the MOF can be used for a high level specification of the IFF. IFF-OO: The Ontology (meta) Ontology (new version) Currently, the first revision of the IFF Ontology (meta) Ontology is under construction. This is a reasonably major revision. The purpose of this revision is to formulate the notion of a first order language, such that the categories of models and logics are cocomplete. The problem with the first version is briefly explained here. The IFF Ontology (meta) Ontology (IFF-OO) in the lower metalevel contains axiomatizations for the notions of first order language first order model-theoretic structure first order theory and first order logic . Obviously, these notions and the IFF-OO itself are first order representations for the theory of Information Flow, a theory that is implicit in the book by Barwise and Seligman and explicit in the paper "The Information Flow Foundation for Conceptual Knowledge Organization" by Kent (see the

36. First-Order Predicate Logic Though predicates are one of the features which distinguish Firstorder logic from propositional logic, these are really just a bit of extra structure 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.

37. PlanetMath: First-order Theory Crossreferences algorithm, finite, finitely axiomatizable, subset, Zorn s lemma, complete, inconsistent, consistent, iff, structure, First-order language, http://planetmath.org/encyclopedia/FinitelyAxiomatizableTheory.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 theory (Definition) In what follows, references to sentences and sets of sentences are all relative to some fixed first-order language Definition. A theory is a deductively closed set of sentences in ; that is, a set such that for each sentence only if Remark . Some authors do not require that a theory be deductively closed. Therefore, a theory is simply a set of sentences. This is not a cause for alarm, since every theory . Furthermore, is unique (it is the smallest deductively closed theory including ), and any structure is a model of iff it is a model of Definition. A theory is consistent if and only if for some sentence . Otherwise, is inconsistent . A sentence is consistent with if and only if the theory is consistent.

38. The Structure Of Language The Structure of Language. Below is section 28, pp 33-40, generated the first approximation by using a First-order Markov source with the appropriate http://members.cox.net/srice1/random/abramson.html

Additive Congruential Random Number Generators Source code for programmers who wish to test the randomness of a random number generator index Back to Deley's Homepage The Structure of Language [Below is section 2-8, pp 33-40, from the book INFORMATION THEORY AND CODING by Norman Abramson, Associate Professor of Electrical Engineering, Stanford University. McGraw-Hill Book Company, Inc. 1963 McGraw-Hill electronic Sciences Series.] In the previous sections of this chapter, we have defined a model of an information source, and brought out some simple properties of our model. It is of some interest to investigate how closely such a model approximates the physical process of information generation. A particularly important case of information generation is the generation of a message composed of English words. In this section we show how the generation of such a message may be approximated by a sequence of successively more and more complicated information sources. H(S) log 27 4.75 bits/symbol A typical sequence of symbols emitted by such a source is shown in Figure 2-6. We refer to this sequence as the zeroth approximation to English. Figure 2-6. Zeroth approximation to English.

39. Mbox: Title Of Articles In The Journal Formalized Mathematics Semigroup Operations on Finite Sequences The Collinearity Structure The Sum and Product of Finite Sequences of Real Numbers A Classical First Order Language http://www-unix.mcs.anl.gov/qed/mail-archive/volume-2/0012.html

Title of Articles in the Journal Formalized Mathematics Robert S. Boyer boyer@CLI.COM Fri, 19 Nov 93 17:06:02 CST Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Daniel W. Connolly: "Naive Observations [Was: Why should a mathematician be interested in QED? ]" Previous message: GETFOL Manager: "Re: Intermediate Value Theorem" Below I list the titles of the more than 300 articles so far published in the journal Formalized Mathematics, which I mentioned in my previous message. This is through Volume 3, anyway. All of these articles have been proof-checked with Mizar, starting from set theory at the very bottom. The text of the journal is set (in TeX) directly from the proof-checked input. I was too lazy to type in the names of the authors of each article after each article, but I do list at the end the 67 authors who have contributed these articles. Formalized Mathematics Table of Contents Volume 1(1), 1990 Tarski Grothendieck Set Theory Built-in Concepts Boolean Properties of Sets Enumerated Sets Basic Properties of Real Numbers The Fundamental Properties of Natural Numbers Some Basic Properties of Sets Functions and Their Basic Properties Properties of Subsets Relations and Their Basic Properties Properties of Binary Relations The Ordinal Numbers Tuples, Projections and Cartesian Products

40. Logic : Thomas Alspaugh : UCI A variable represents an object in the domain of a predicate logic or Firstorder logic language. Such a variable can appear wherever an object can be named http://www.ics.uci.edu/~alspaugh/logic/index.html

Last modified Fri Sep 28 13:36 2007) Logic Glossary of logic terms and concepts Propositional logic (PL) syntax semantics ... Modal and temporal logic What is logic? That's a good question ... some possible answers follow: and Logic is the abstraction of thought to its simplest possible components: we consider whether something is true or false only, and we analyze it based on its structure and whether its components are true or false. Logic is the study of reasoning made recursively compositional. In logic, we study structures whose meaning is determined by the meaning of their substructures and the fashion in which those substructures are combined. Perhaps it is more effective, especially at first, to talk about what we can do with logic. Some of the things we can do are: construct a formula whose structure mirrors that of an assertion in English (or some other natural language). determine whether a formula is never true, sometimes true, or always true. calculate whether one formula implies another.

41. The Definition Of Truth One approach is to work with a larger Firstorder language with constant symbols naming all elements of our structure M . This is convenient as it will http://web.mat.bham.ac.uk/R.W.Kaye/logic/tarski

author contents glossary next ... previous The definition of truth Introduction This web page presents and discusses the precise notion of semantics for first-order logic, in particular the definition of what it means for a sentence to be true in a structure M The definition of what it means for M This web page should be read in conjunction with Section 9.1 of The Mathematics of Logic . In particular we aim here to give more detail and information on Definition 9.23 Tarski's Definition of Truth The formal definition of M is by induction on the complexity of the statement , and there are several sub-clauses corresponding to the different kinds of sub-formulas that may occur in . But before we give these we indicate the main complication, which is that sub-formulas of are not necessarily sentences but are formulas, and as such contain free-variables which must be given specific meanings too during the inductive definition. There are two possible approaches to this problem, each with advantages and disadvantages. One approach is to work with a larger first-order language with constant symbols naming all elements of our structure M . This is convenient as it will eventually allow us to discuss with ease a great number of properties of M and its elements. It does however rely on the idea of substitution of terms for variables, another tricky technical issue that is addressed in these web pages elsewhere. To make this web page more self-contained, we approach the definition of truth by starting with a different way of attaching meanings to free variables.

42. Language Structure Some subtleties of language structure were studied by Plato and Aristotle. . write in a reformed language more like a first order predicate calculus. http://www.cas.buffalo.edu/classes/psy/segal/2472000/LanguageStructure.htm

Psychology 247 Cognitive Psychology Language Structure Erwin Segal Return to syllabus Language and its structure has been a field of study for many centuries. Even the Bible noted that people who speak different languages cannot communicate with one another. Some subtleties of language structure were studied by Plato and Aristotle. The invention of the alphabet by Phoenician scholars over 2500 years ago showed detailed study of language. Language is the most important social product for preserving and passing on culture; and its study can be seen to be an important window on the mind. A natural language is very complicated, yet easy for children to learn. Almost all normal children know a great deal about their language by 3 years old, and most subtle nuances by the time they are 10. Interestingly, people who learn a language when they are very young know subtle properties better than those who learned the language when they were older, and this difference tends not to be overcome with years of speaking. Language manifests structure at many different levels. The sequences of sounds are limited. The sequences of words are limited, and the same words in different orders mean different things.

43. First-order Approximation To Language - Research The News About First-order Appr The Language of Firstorder Logic. 3d ed. Stanford . represented the First-order structure of the square error of approximation (RMSEA, http://www.highbeam.com/search.aspx?q=first-order approximation to language&ref_