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 LEGO | |||||||||
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Luca Viganò (2000). Labelled Non-Classical Logics. Kluwer Academic Publishers.
Roy A. Benton (2002). A Simple Incomplete Extension of T Which is the Union of Two Complete Modal Logics with F.M.P. Journal of Philosophical Logic 31 (6):527-541.
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
Marcus Kracht & Frank Wolter (1997). Simulation and Transfer Results in Modal Logic – a Survey. Studia Logica 59 (2):149-177.
Jc Beall, Ross Brady, Michael Dunn, Allen Hazen, Edwin Mares, John Slaney, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley & Richard Sylvan (2012). On the Ternary Relation and Conditionality. Journal of Philosophical Logic 41 (3):595-612.
David Basin, Seán Matthews & Luca Viganò (1998). Labelled Modal Logics: Quantifiers. Journal of Logic, Language and Information 7 (3):237-263.
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