First-Order Logic: Deductive Systems

We extend the deductive systems$$ G $$and$$ H $$from propositional logic to first-order logic by adding axioms and rules of inference for the universal quantifier. (The existential quantifier is defined as the dual of the universal quantifier.) The construction of semantic tableaux for first-order l...

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Bibliographic Details
Published inMathematical Logic for Computer Science pp. 155 - 166
Main Author Ben-Ari, Mordechai
Format Book Chapter
LanguageEnglish
Published United Kingdom Springer London, Limited 2012
Springer London
Subjects
First-order Logic
Gentzen System
Gentzen's Proof
Mathematical foundations
Mathematical logic
Mathematical theory of computation
Semantic Tableaux
Universal Quantifier
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ISBN1447141288
9781447141280
DOI10.1007/978-1-4471-4129-7_8

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Summary:We extend the deductive systems$$ G $$and$$ H $$from propositional logic to first-order logic by adding axioms and rules of inference for the universal quantifier. (The existential quantifier is defined as the dual of the universal quantifier.) The construction of semantic tableaux for first-order logic included restrictions on the use of constants and similar restrictions will be needed here.
Bibliography:Original Abstract: We extend the deductive systems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ G $$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ H $$ \end{document} from propositional logic to first-order logic by adding axioms and rules of inference for the universal quantifier. (The existential quantifier is defined as the dual of the universal quantifier.) The construction of semantic tableaux for first-order logic included restrictions on the use of constants and similar restrictions will be needed here.
ISBN:1447141288
9781447141280
DOI:10.1007/978-1-4471-4129-7_8