Two-dimensional Kripke Semantics II: Stability and Completeness

Autor:	Kavvos, G. A.
Rok vydání:	2024
Předmět:	Computer Science - Logic in Computer Science Mathematics - Category Theory Mathematics - Logic 03B45 (Primary) 03B20 03B70 68Q55 06D20 06D22 06D05 06D50 18A15 18A40 18F20 18D60 18C10 (Secondary) F.4.1 F.3.2
Zdroj:	Electronic Notes in Theoretical Informatics and Computer Science, Volume 4 - Proceedings of MFPS XL (December 11, 2024) entics:14767
Druh dokumentu:	Working Paper
DOI:	10.46298/entics.14767
Popis:	We revisit the duality between Kripke and algebraic semantics of intuitionistic and intuitionistic modal logic. We find that there is a certain mismatch between the two semantics, which means that not all algebraic models can be embedded into a Kripke model. This leads to an alternative proposal for a relational semantics, the stable semantics. Instead of an arbitrary partial order, the stable semantics requires a distributive lattice of worlds. We constructively show that the stable semantics is exactly as complete as the algebraic semantics. Categorifying these results leads to a 2-duality between two-dimensional stable semantics and categories of product-preserving presheaves, i.e. models of algebraic theories in the style of Lawvere. Comment: Accepted at MFPS 2024
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2406.03578 Zobrazit plný text záznamu View this record from Arxiv