Encoding modal logics in logical frameworks

Arnon Avron*, Furio Honsell, Marino Miculan, Cristian Paravano

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present and discuss various formal]zations of Modal Logics in Logical Frameworks based on Type Theories. We consider both Hubert- and Natural Deductionstyle 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 A-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.

Original languageEnglish
Pages (from-to)161-208
Number of pages48
JournalStudia Logica
Issue number1
StatePublished - 1 Jul 1998


  • Hubert and Natural-Deduction proof systems for Modal Logics
  • Logical Frameworks
  • Proof Assistants
  • Typed a-calculus


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