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A simplified framework for first-order languages and its formalization in Mizar

By Marco B. Caminati

Abstract

A strictly formal, set-theoretical treatment of classical first-order logic is given. Since this is done with the goal of a concrete Mizar formalization of basic results (Lindenbaum lemma; Henkin, satisfiability, completeness and Lowenheim-Skolem theorems) in mind, it turns into a systematic pursue of simplification: we give up the notions of free occurrence, of derivation tree, and study what inference rules are strictly needed to prove the mentioned results. Afterwards, we discuss details of the actual Mizar implementation, and give general techniques developed therein.Comment: Ph.D. thesis, defended on January, 20th, 201

Topics: Mathematics - Logic, Computer Science - Logic in Computer Science, 03C07, 97N80, 03B70
Year: 2012
OAI identifier: oai:arXiv.org:1205.4316

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