This article presents a new (multivalued) semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions.

中文翻译：

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经典逻辑的分数语义

本文介绍了经典命题逻辑的新（多值）语义。我们首先最大限度地扩展后续证明的空间，以便接受以下证明任何逻辑公式；然后，我们通过关注证明的公理结构来提取新的语义。特别是，公式的解释是由恒等公理的数量与在其任何证明中出现的公理总数之间的比率给出的。结果是对传统布尔语义的信息改进，通过打破重言式和矛盾之间的对称性获得。