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.

翻译：本文为彼得·哈耶克基本逻辑提供了一种克里普克语义的推广形式，并证明了该语义相对于该逻辑的可靠性与完全性。我们发现该语义可自然地特化为哥德尔-达梅特逻辑的线性序克里普克框架，而BL逻辑恰为哥德尔-达梅特逻辑的真扩展。本文的可靠性定理、演绎定理及完全性证明进一步强化了这一类比。本工作将前作《直觉主义卢卡西维茨逻辑的克里普克语义学》的洞见拓展至哈耶克BL逻辑的情形。