تقرير
Two-dimensional Kripke Semantics II: Stability and Completeness
| العنوان: | Two-dimensional Kripke Semantics II: Stability and Completeness |
|---|---|
| المؤلفون: | Kavvos, G. A. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | 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 |
| الوصف: | 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 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.03578 |
| رقم الأكسشن: | edsarx.2406.03578 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |