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Encoding modal logics in logical frameworks
Studia Logica 60 (1):161-208 (1998)
Abstract
We present and discuss various formalizations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hilbert- and Natural Deduction-style proof systems for representing both truth (local) and validity (global) consequence relations for various Modal Logics. We introduce several techniques for encoding the structural peculiarities of necessitation rules, in the typed -calculus metalanguage of the Logical Frameworks. These formalizations yield readily proof-editors for Modal Logics when implemented in Proof Development Environments, such as Coq or LEGOAuthor's Profile
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Citations of this work
Natural Deduction, Hybrid Systems and Modal Logics.Andrzej Indrzejczak - 2010 - Dordrecht, Netherland: Springer.
Axiomatic and dual systems for constructive necessity, a formally verified equivalence.Lourdes del Carmen González-Huesca, Favio E. Miranda-Perea & P. Selene Linares-Arévalo - 2019 - Journal of Applied Non-Classical Logics 29 (3):255-287.
References found in this work
Modal logic and classical logic.Johan van Benthem - 1983 - Atlantic Highlands, N.J.: Distributed in the U.S.A. by Humanities Press.
A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
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