Abstract

MIRANDA-PEREA, Favio E.; ESTRADA ZAVALETA, Ximena  and  GONZALEZ HUESCA, Lourdes del Carmen. Fitch-Style Modal Necessity as a Substructural Sequent-Style System. Comp. y Sist. [online]. 2023, vol.27, n.1, pp.315-326.  Epub June 16, 2023. ISSN 2007-9737.  https://doi.org/10.13053/cys-27-1-4542.

The question of defining a Jaśkowski-Fitch natural deduction system for modal logic has been settled since the very introduction of such formalisms in the middle of the last century. In contrast, a sequent-style formulation of this approach has only been discussed since the turn of this century but exclusively from the point of view of type theories. In this paper we propose a substructural sequent-style deductive system, based on previous ideas by Borghuis and Clouston, which captures Fitch-style for modal logic in a faithful way, meaning that the features of the original diagrammatic proofs are enforced by the sequent rules. This answers the question of what is a sequent-style version of Fitch-style natural deduction in the case of the necessity fragment of minimal modal logic $S4$.

Keywords : Natural deduction; fitch-style; modal necessity; substructural logics; sequents.

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