×

Encoding modal logics in logical frameworks. (English) Zbl 0954.03021

Summary: 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.

MSC:

03B45 Modal logic (including the logic of norms)
03B35 Mechanization of proofs and logical operations
03B40 Combinatory logic and lambda calculus
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)

Software:

leanTAP; Coq
PDFBibTeX XMLCite
Full Text: DOI