Fitch-Style Modal Lambda Calculi
Abstract
Fitch-style modal deduction, in which modalities are eliminated by opening a subordinate proof, and introduced by shutting one, were investigated in the 1990s as a basis for lambda calculi. We show that such calculi have good computational properties for a variety of intuitionistic modal logics. Semantics are given in cartesian closed categories equipped with an adjunction of endofunctors, with the necessity modality interpreted by the right adjoint. Where this functor is an idempotent comonad, a coherence result on the semantics allows us to present a calculus for intuitionistic S4 that is simpler than others in the literature. We show the calculi can be extended \`{a} la tense logic with the left adjoint of necessity, and are then complete for the categorical semantics.
Keywords
Cite
@article{arxiv.1710.08326,
title = {Fitch-Style Modal Lambda Calculi},
author = {Ranald Clouston},
journal= {arXiv preprint arXiv:1710.08326},
year = {2018}
}
Comments
Accepted paper at the 21st International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2018). This version includes appendices containing many proof details