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First-Order Implication-Space Semantics
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AI
DOI：10.1007/s10992-026-09841-x.png)
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Abstract
En 中文
This paper extends implication-space semantics to include first-order quantification. Implication-space semantics has recently been introduced as an inferentialist formal semantics that can capture nonmonotonic and nontransitive material inferences. Extant versions, however, include only propositional logic. This paper extends the framework so as to recover classical first-order logic. The goal is to formulate a theory in which consequence relations can be nonmonotonic and supraclassical, while obeying the deduction-detachment theorem as well as disjunction simplification and also including conjunctions that behave multiplicatively as premises and counterexamples to the usual quantifier rules. The paper explains these constraints and shows how they can be met jointly. The result is a first-order version of implication-space semantics that has all the (logical) virtues for which inferentialists and logical expressivists praise propositional implication-space semantics.
Keywords:
Implication-space semantics
Inferentialism
Substructural logic
Defeasible reasoning
Material inferences
Logical expressivism
Journal
J
IF:
1
Papers:
38
Citations:
1.4K