Displaying similar documents to “Maximum Cuts in Extended Natural Deduction”

Strong normalization proofs for cut elimination in Gentzen's sequent calculi

Elias Bittar (1999)

Banach Center Publications

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We define an equivalent variant L K s p of the Gentzen sequent calculus L K . In L K s p weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules L K s p by a finite rewriting system; the termination of this rewriting system can be machine checked. We give also a self-contained strong normalization proof by structural induction. We give another strong normalization proof by a strictly monotone subrecursive interpretation;...

The Derivations of Temporal Logic Formulas

Mariusz Giero (2012)

Formalized Mathematics

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This is a preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [12]. We introduce n-ary connectives and prove their properties. We derive temporal logic formulas.

Weak Completeness Theorem for Propositional Linear Time Temporal Logic

Mariusz Giero (2012)

Formalized Mathematics

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We prove weak (finite set of premises) completeness theorem for extended propositional linear time temporal logic with irreflexive version of until-operator. We base it on the proof of completeness for basic propositional linear time temporal logic given in [20] which roughly follows the idea of the Henkin-Hasenjaeger method for classical logic. We show that a temporal model exists for every formula which negation is not derivable (Satisfiability Theorem). The contrapositive of that...

Sequent Calculus, Derivability, Provability. Gödel's Completeness Theorem

Marco Caminati (2011)

Formalized Mathematics

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Fifth of a series of articles laying down the bases for classical first order model theory. This paper presents multiple themes: first it introduces sequents, rules and sets of rules for a first order language L as L-dependent types. Then defines derivability and provability according to a set of rules, and gives several technical lemmas binding all those concepts. Following that, it introduces a fixed set D of derivation rules, and proceeds to convert them to Mizar functorial cluster...