Modal Linear Logic in Higher Order Logic, an experiment in Coq

Abstract

The sequent calculus of classical modal linear logic KDT 4lin is coded in the higher order logic using the proof assistant COQ. The encoding has been done using two-level meta reasoning in Coq. KDT 4lin has been encoded as an object logic by inductively defining the set of modal linear logic formulas, the sequent relation on lists of these formulas, and some lemmas to work with lists.This modal linear logic has been argued to be a good candidate for epistemic applications. As examples some epistemic problems have been coded and proven in our encoding in Coq::the problem of logical omniscience and an epistemic puzzle: ’King, three wise men and five hats’