A Hilbert Calculus for Logic of Truth-Functional Contingency
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Last updated：2022-10-23
Studies in Logic, Vol. 14, No. 3 (2021): 24–36 PII: 1674-3202(2021)-03-0024-13
Fei Liang Zhongxu Tian Xinyu Yang
Abstract.
A statement is truth-functionally contingent, if it is neither a tautology nor a contradiction in classical propositional logic. The logic of truth-functional contingency, is to capture all these contingent statements. In this paper, we introduce a sound and complete Hilbert calculus for the logic of truth-functional contingency, where every formula introduced in a deduction is a contingent formula, and it is introduced only if it is a contingent axiom, or it follows by one of the contingent rules of inference from contingent formulas introduced earlier in the deduction.