Tags:Completeness, Formal methods, Lean and Modal Logic

Abstract:

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell [10], except that it is given for a system based on a different choice of axioms. Here the proof is based on a Hilbert-style presentation better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2.

A Henkin-Style Completeness Proof for the Modal Logic S5