Intuitionistic monotone modal logic via translation

TL;DR

This paper introduces a new intuitionistic monotone modal logic via translation into first-order logic, providing axiomatization and semantics with intuitionistic neighbourhood models, and compares it with existing logics.

Contribution

It presents a novel monotone modal analogue of intuitionistic logic IK, with axiomatization, semantics, and embedding into multimodal IK, expanding the understanding of intuitionistic monotone modal logics.

Findings

Axiomatization of the new logic.

Semantics using intuitionistic neighbourhood models.

Embedding into a multimodal version of IK.

Abstract

We introduce a monotone modal analogue of the intuitionistic (normal) modal logic IK using a translation into a suitable (intuitionistic) first-order logic. We axiomatise the logic and give a semantics by means of intuitionistic neighbourhood models, which contain neighbourhoods whose value can change when moving along the intuitionistic accessibility relation. We compare the resulting logic with other intuitionistic monotone modal logics and show how it can be embedded into a multimodal version of IK.