Modal completeness of sublogics of the interpretability logic IL

2020/04/08 by Taishi Kurahashi, Kurahashi, Taishi, Yuya Okawa +1 · 1 citation
Computer Science · #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2004.03813

openalex publication_date 2020/04/08 · openalex created_date 2020/04/17 · openalex updated_date 2026/07/28

Abstract

We study modal completeness and incompleteness of several sublogics of the interpretability logic IL. We introduce the sublogic IL^-, and prove that IL^- is sound and complete with respect to Veltman prestructures which are introduced by Visser. Moreover, we prove the modal completeness of twelve logics between IL^- and IL with respect to Veltman prestructures. On the other hand, we prove that eight natural sublogics of IL are modally incomplete. Finally, we prove that these incomplete logics are complete with respect to generalized Veltman prestructures. As a consequence of these investigations, we obtain that the twenty logics studied in this paper are all decidable.

Citations

• Provability interpretations of modal logic

Cited by

• The fixed point and the Craig interpolation properties for sublogics of IL

Related

• Interpretability logics and generalized Veltman semantics
• Visser frames for sublogics of IL
• Completeness theorems for modal logic in second-order arithmetic
• Ł-Axiomatizability in intermediate and normal modal logics
• Assuring and critical labels for relations between maximal consistent sets for interpretability logics