Relational semantics for flat Heyting-Lewis Logic
This work addresses a theoretical gap in modal logic semantics for researchers in mathematical logic, but it is incremental as it builds on existing frameworks.
The paper tackles the problem of providing relational semantics for flat Heyting-Lewis logic, a variant of intuitionistic logic with a strict implication modality, and proves completeness and the finite model property for this logic and its extensions.
We introduce relational semantics for "flat Heyting-Lewis logic" $\mathsf{HLC}^{\flat}$. This logic arises as the extension of intuitionistic logic with a Lewis-style strict implication modality that, contrary to its "sharp" counterpart $\mathsf{HLC}^{\sharp}$, does not turn meets into joins in its first argument. We prove completeness and the finite model property for $\mathsf{HLC}^{\flat}$ and for several extensions with additional axioms.