Interpretation of Hybrid Counterfactual Logic into Hybrid Tense Logic: and Comparison of Their Expressive Power on Temporal Sphere Models: Interpretation of Hybrid

• Published in: Journal of logic, language, and information language, and information, 2024, Vol.33 (4), p.391-418
• Main Author: Hosokawa, Yuichiro
• Format: Article
• Language: English
• Subjects: Education; Information Systems Applications (incl.Internet); Logic; Philosophy; Semantics
• ISSN: 0925-8531; 1572-9583
• DOI: 10.1007/s10849-024-09424-6

Lewis (Noûs 13:455–476, 1979) claimed that branching-time(-like) models can be derived from his sphere models. However, he did not present any specific construction of branching-time(-like) models from his sphere models formally. Meanwhile, Hosokawa (in: Modern logic of modality and its philosophical range: counterfactuals, Gettier problem, and information flow, Tokyo Metropolitan University, 2018) presented a logico-mathematically strict manner in which sphere models can be reconstructed from branching-time models. Subsequently, Hosokawa (J Logic Lang Inf 32:677–706, 2023) presented a proof-theoretically refined version of hybrid tense logic for a certain type of conditionals, which is referred to as hybrid tense logic for temporal conditionals ( HTL TC ). In this paper, we interpret a hybrid version V HC ( @ , ↓ ) of Lewis’s counterfactual logic V into HTL TC , and then prove that HTL TC is more expressive than V HC ( @ , ↓ ) on the class of temporal sphere models, i.e., sphere models derived from a type of branching-time models.