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Semantics for McCall's CC1
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DOI：10.1080/01445340.2026.2640808.png)
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Abstract
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McCall's 4-valued logic CC1 is one of the earliest and most influential systems of connexive logic. CC1 has been criticised because its truth values lack an intuitive interpretation. In this paper, we propose that the semantic value of a sentence in this logic is represented as an ordered pair consisting of a classical truth value (true or false) and a content polarity (positive or negative). In particular, the truth value of a connexive entailment is a function both of the truth values and of the content polarities of its antecedent and consequent. We develop this informal idea into a formal semantics and prove a completeness theorem for CC1 with respect to a class of algebraic models obtained via a certain construction on Boolean algebras.
Keywords:
Connexive logic
relevant logic
entailment
Storrs McCall
hyperintensional semantics
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19
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