A Family of Kripke Contingency Logics. Issue 4 (28th August 2020) - Fan, Jie
Abstract: In Fan's 2019 article, "Symmetric Contingency Logic with Unlimitedly Many Modalities", it is left as an open question in Fan (2019b) how to (completely) axiomatize contingency logic over the class of symmetric and transitive frames, and conjectured that ℂ LB 4 = ℂ LB + Δ i φ → Δ i Δ i φ ∨ ψ is the desired axiomatization. In the current article, we show that the conjecture is false, and then propose a desired axiomatization, thereby answering the open question. Beyond these results, we also present a family of axiomatizations of contingency logic over Kripke frames.