# Interpretability logics and generalized Veltman semantics

## TL;DR

This paper establishes modal completeness, decidability, and finite model properties for interpretability logics using generalized Veltman semantics, introducing new proof techniques and constructions.

## Contribution

It provides new completeness proofs, shorter proofs for classical interpretability logics, and develops a construction potentially useful for future completeness results.

## Key findings

- Modal completeness of ILP_0 and ILR w.r.t. generalized Veltman semantics
- Decidability and finite model property for ILP_0 and ILR
- Development of a construction for future completeness proofs

## Abstract

We obtain modal completeness of the interpretability logics ILP_0 and ILR w.r.t. generalized Veltman semantics. Our proofs are based on the notion of smart (full) labels. We also give shorter proofs of completeness w.r.t. generalized semantics for many classical interpretability logics. We obtain decidability and finite model property w.r.t. generalized semantics for ILP_0 and ILR. Finally, we develop a construction that might be useful for proofs of completeness of extensions of ILW w.r.t. generalized semantics in the future, and demonstrate its usage with ILW* = ILM_0W.