Dual and Axiomatic Systems for Constructive S4, a Formally Verified Equivalence | Zendy

Lourdes del Carmen González Huesca | Zendy; Favio E. Miranda-Perea | Zendy; P. Selene Linares-Arévalo | Zendy

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Dual and Axiomatic Systems for Constructive S4, a Formally Verified Equivalence

Author(s) -

Lourdes del Carmen González Huesca,

Favio E. Miranda-Perea,

P. Selene Linares-Arévalo

Publication year - 2020

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2020.02.005

Subject(s) - constructive , equivalence (formal languages) , axiom , dual (grammatical number) , axiomatic system , algebra over a field , mathematics , calculus (dental) , computer science , mathematical economics , pure mathematics , theoretical computer science , discrete mathematics , programming language , philosophy , geometry , medicine , linguistics , dentistry , process (computing)

We present a proof of the equivalence between two deductive systems for the constructive modal logic S4. On one side, an axiomatic characterization inspired by Hakli and Negriu0027s Hilbert-style system of derivations from assumptions for modal logic K. On the other side, the judgmental reconstruction given by Pfenning and Davies by means of a so-called dual natural deduction approach that makes a distinction between valid, true and possible formulas. Both systems and the proof of their equivalence are formally verified using the Coq proof assistant.

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