English

A Kripke Semantics for Hajek's BL

Logic in Computer Science 2023-08-10 v1

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.

Keywords

Cite

@article{arxiv.2308.04518,
  title  = {A Kripke Semantics for Hajek's BL},
  author = {Andrew Lewis-Smith},
  journal= {arXiv preprint arXiv:2308.04518},
  year   = {2023}
}

Comments

In Proceedings AMSLO 2023, arXiv:2308.03679

R2 v1 2026-06-28T11:51:14.871Z