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part ii quantificational logic - New York University
contains a proof of PL's completeness, and chapter 6, an argument for its adequacy. ... Chapter 1. Syntax ... language of classical sentential logic and has an alphabet of sentence letters ... formula of m(π) is a degree-n predicate letter followed by n occurrences of ... The symbol } in clause vii is called the existential quantifier.
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1 Logic, language and meaning - University of Chicago
thereby learning about the properties of natural language meaning from the ... If γ is a two place predicate and α and β are names then γ(α, β) is a formula. ... complex expressions of Lx : the interpretation of a formula (sentence) of the language ...
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Dynamic Predicate Logic1 - University of Amsterdam
If we use standard first-order predicate logic (henceforth, PL) in translating a natural language sentence or discourse, anaphoric pronouns will turn up as bound variables. In many ..... meaning between the formula ∃xP x∧Qx and the formula ∃x[Px∧Qx]. From the latter fact it is ..... and ∀, and identity =. Definition 1 (Syntax).
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Per Lindström FIRST-ORDER LOGIC
May 15, 2006 ... Predicate logic was created by Gottlob Frege (Frege (1879)) and first- ... elementary, needed in these applications are stated without proof. P. L. ... §1 Syntax of L1. 5 .... definitions of “term” (noun phrase), “formula”, “sentence” ( formula without .... The primitive symbols of a first-order language are the logical.
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Dynamic Predicate Logic - Computer Science Department
If we use standard first-order predicate logic (henceforth, PL) in translating a natural language sentence or discourse, anaphoric pronouns will turn up as bound variables. In many ..... meaning between the formula ∃xP x∧Qx and the formula ∃x[Px∧Qx]. From the latter fact it is ..... and ∀, and identity =. Definition 1 (Syntax).
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Lecture Notes on Mathematical Logic - Department of Computer
Jan 16, 2009 ... In logic and in linguistics, we distinguish between two languages: the one that is the ... 1 Syntax and Semantics of Propositional Formulas ... 2-place, or binary connectives; ¬ (negation) is a 1-place, or unary connective; ...... Problem 3.8 Represent the following English sentences by first-order for- mulas:.
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0. Introduction
Logic based on a “propositional” version of the Leibniz rule (Propositional Strong. Leibniz, or ... Equational or Calculational Logic, introduced by Dijkstra and Scholten [2] ... der language, namely, an enumerable set of object variables x1,x2 , . ... for example, A = B where A and B are formulas, meaning that the strings A and B.
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Type-Driven Natural Language Analysis - ScholarlyCommons
widen logic programming, to account for the syntax of filler-gap ... 2.2.1 Syntax. 8 ..... formula: (whom A (NP > S)) > REL. Or consider the following assignment of a ... Logic programming and natural language processing have in the past been fruit- ..... mapping its non-terminals into two-place predicates taking as arguments  ...
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Exceptions for algebraic specifications: on the meaning of “but”
The language of SFOL is formed on basis of symbols declared in a signature _Y, which ... An algebra A satisfies a formula for a valuation V, denoted A ~= v if: A~= VP(tl e . . . , tn) lff .... Propositional logic equipped with this closeness will be called PL. ..... Definition 4.1.1. Syntax It is often useful to be able to order not only two ...
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Description Logic Rules – Markus Kroetzsch
Jun 7, 2010 ... This leads to expressive DL rule languages with high computational ... proposed as a logic in the “expressive intersection” of DLs and .... 3.1.1 Syntax . .... 6.3 Definition of pl+(D) and pl−(D) . ..... above statement as a predicate logic formula ( see Section 3.2 for ..... A sentence (or closed formula) is a formula.
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Automated Theorem Proving by Translation to Description Logic
Dec 10, 2015 ... expressivity: Propositional Logic, Description Logic, Effectively ... lated directly to Conjunctive Normal Form, or indirectly by translation via inter- ... 2.1.1 Syntax . ..... tive, in which the meaning of the sentences is considered. .... tional Logic (PL), Description Logic (DL), First Order Form (FOF), Conjunctive.
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The Logic of Choice - Microsoft Research
choice logic and the witness operator studied in Abiteboul-Vianu 1991]. 1.1 The " ... Notice that FO+" formulas are evaluated at structures equipped with a choice ..... Construct an FO+" sentence ' in the language of graphs that asserts that the ...... of ordinary propositional logic PL (that is if their nondeterministic variables are.
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Fixed-Choice and Independent-Choice Logics - CiteSeerX
One way to do that is to restrict attention to FO+" formulas whose meaning does ... expressible by a sentence which is "-invariant over nite structures Otto 1998]. ..... Construct an FO+" sentence ' in the language of graphs that asserts that the ..... ordinary propositional logic PL (that is if their nondeterministic variables are ...
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Copyright © Leo Obrst, MITRE, 2009 - C4I Center
9:00-10:20: Part 1: Syntax, Semantics, Ontology .... Express the meaning in a loose/strict, natural language definition or ... To form a sentence? ... Formulas ( Well-formed Formulas or WFFs) of PL (we will call these ... Order Predicate Logic: ∀x.
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Counterpart Semantics for Quantified Modal Logic - esslli 2012
Aug 13, 2012 ... 3.2.1 Syntax . .... In order to know the meaning of a sentence in turn it suffices to know the meaning .... The standard semantics of modal propositional logic, and the semantics in- .... For all n-place formulas ϕ, models M = (D, V ), ..... of natural language, possible-worlds-analyses of modality are an instance of.
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Development of Correct Real-Time Systems by Refinement - FB IKS
Apr 2, 1997 ... 2 Modal Logic and the Duration Calculus ... 2.5.1 Syntax of ITL . ... 3 Languages for Requirements and Program Specifications ... 5.1 The Syntax of PL . ..... in the following way: \Symbol" is any word of a formal language, be it a .... can be linked by a logical formula L(O1,O2) and implementation then means.
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Fastidious distributivity
Keywords: distributivity, nominal predicates, team logic .... more rich languages. ... listener-pl. 'Loads of boys were good listeners.' This is not what one would predict if there was agreement in number .... (24b) shows the meaning of the whole sentence. ... 4.1.1 Syntax and interpretation of atomic formulas in team logic.
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Computational Logic 320441 CompLog Lecture Notes - KWARC home
Nov 18, 2015 ... foundation of computational logic and logic engineering techniques. ... Here the game is to add new operators to the language and extend the reasoning ...... With formula schemata we mean representations of sets of formulae, we .... PL. 1 Syntax (Signature and Variables). Definition 7.1.1 First-order logic ...
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Temporal Meaning Representations in a Natural Language Front-End
related questions to suitable expressions of a temporal logic-like language, .... past tense, to ensure that a sentence like (3), where no adverbial is present, ... empty(tank5) is true, and et g It. (pl is a subperiod of pg, written p1 Q pg ifl' .... A special BOT predicate symbol port, similar to TOP's Part operator, allows variables.
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Logic for Philosophy - University of Idaho
Dec 4, 2007 ... I begin with a sketch of standard propositional and predicate logic (de- veloped more .... 2.6 Soundness and completeness of PL . ... 3.1.1 Symbolizing truth functions in propositional logic . . . 52 .... 8.3.1 Syntax of SC . ..... formal language (see below), one treats the sentences of the formal language as.
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