[论文解读] First-Order Implication-Space Semantics

Ulf Hlobil|arXiv (Cornell University)|Feb 14, 2026

Logic, Reasoning, and Knowledge被引用 0

一句话总结

延展 implication-space 语义以包含一阶量化，旨在在推理主义框架内在保持非单调和超经典蕴涵关系的同时恢复经典的一阶逻辑。

ABSTRACT

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 and disjunction simplification, while 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 virtues for which inferentialists and inferential expressivists praise propositional implication-space semantics.

研究动机与目标

• Explain the aims and constraints guiding the extension of implication-space semantics to first-order logic.
• Formulate a first-order implication-space semantics that satisfies MOF, SCL, DDT, DS, and LC constraints without endorsing standard quantifier rules.
• Demonstrate how to map Tarskian model theory into implication-space semantics to achieve supraclassicality.
• Outline why extending to first-order logic is nontrivial and what future work is needed to fully recover classical first-order logic.

提出的方法

• Present seven guiding constraints (MOF, SCL, DDT, DS, LC, plus logical expressivism) for first-order implication-space semantics.
• Define first-order implication-space semantics and show it can validate MOF, DDT, DS, LC without committing to ∀R and ∀L rules.
• Argue why the framework must accommodate nonmonotonic and hyperintensional consequence relations.
• Use arguments to show why standard possible-world semantics and other logics fail to meet the constraints.
• Map Tarskian model theory into implication-space semantics to obtain supraclassical consequences.
• Discuss the challenges and potential adjustments needed to incorporate quantification while preserving the desired properties.

实验结果

研究问题

• RQ1 Can first-order implication-space semantics validate MOF, DDT, DS, and LC simultaneously without adopting the classical ∀R and ∀L rules?
• RQ2 How can Tarskian model theory be integrated into implication-space semantics to ensure supraclassicality in a first-order setting?
• RQ3 What are the obstacles to recovering classical first-order logic within this framework, and how might they be overcome?

主要发现

• A first-order extension of implication-space semantics can meet MOF, DDT, DS, and LC constraints while not underwriting the usual quantifier rules ∀R and ∀L.
• Classical first-order logic can be recovered in implication-space semantics by mapping Tarskian model theory into the framework.
• Hyperintensionality and nonmonotonicity emerge as natural consequences of the combined constraints (MOF, DS, LC) in the first-order setting.
• Extant propositional implication-space semantics achieve classical propositional logic; the first-order extension remains nontrivial and requires careful handling of quantification rules.
• The work argues that nonmonotonic, supraclassical consequence relations can be achieved in a first-order inferentialist semantics without traditional quantifier rules.