Arnon Avron, Furio Honsell, Marino Miculan and Cristian Paravano

Encoding Modal Logics in Logical Frameworks.


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 lambda-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.

Keywords: Hilbert and Natural-Deduction proof systems for Modal Logics, Logical Frameworks, Typed lambda-calculus, Proof Assistants.