A Kripke Semantics for Hajek's BL
Year: 2023
Type: article
Abstract: We provide a generalisation of Kripke semantics for Petr Hajek's Basic Logic and prove soundness and completeness of the same with respect to our semantics. We find this semantics easily specialises to the linearly-ordered Kripke frames for Godel-Dummett logic, which BL properly contains. Our soundness, deduction theorem and completeness arguments further strengthen this analogy. This paper extends the insights of our previous paper, "A Kripke Semantics for Intuitionistic Lukasiewicz logic," to the case of Hajeks' BL.
DOI: 10.4204/eptcs.381.4
Author: Andrew Lewis-Smith
Institution: University of Sheffield
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4385448685