Premium
A Family of Kripke Contingency Logics
Author(s) -
Fan Jie
Publication year - 2020
Publication title -
theoria
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.34
H-Index - 16
eISSN - 1755-2567
pISSN - 0040-5825
DOI - 10.1111/theo.12260
Subject(s) - contingency , transitive relation , mathematics , modal logic , conjecture , kripke semantics , class (philosophy) , discrete mathematics , kripke structure , normal modal logic , epistemology , mathematical economics , calculus (dental) , algebra over a field , combinatorics , computer science , multimodal logic , pure mathematics , philosophy , modal , theoretical computer science , algorithm , description logic , polymer chemistry , medicine , chemistry , dentistry , model checking
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 iΔ i φ ∨ ψis 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.