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FORMALIZING THE META -THEORY OF FIRST-ORDER PREDICATE LOGIC

Title
FORMALIZING THE META -THEORY OF FIRST-ORDER PREDICATE LOGIC
Authors
Herberlin, HugoKim, SunYoungLee, Gyesik
Ewha Authors
김선영
SCOPUS Author ID
김선영scopus
Issue Date
2017
Journal Title
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
ISSN
0304-9914JCR Link2234-3008JCR Link
Citation
vol. 54, no. 5, pp. 1521 - 1536
Keywords
formal proofsfirst-order predicate logicKripke semanticssoundnesscompleteness
Publisher
KOREAN MATHEMATICAL SOC
Indexed
SCIE; SCOPUS; KCI WOS
Abstract
This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LIT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.
DOI
10.4134/JKMS.j160546
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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