A simplified definition of logically distributive categories
Marco Benini
TL;DR
This paper simplifies the definition of logically distributive categories by removing two distributivity requirements, potentially broadening their applicability in semantics for first-order logic.
Contribution
It introduces a simplified version of logically distributive categories by dropping two specific distributivity conditions, streamlining their theoretical framework.
Findings
Simplified the definition of logically distributive categories
Maintains soundness and completeness for first-order logic semantics
Reduces complexity of the categorical framework
Abstract
In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the definition of logically distributive category can be simplified by dropping two requirements, the one saying that product must distribute over sum, and the one saying that product must distribute over existential quantification.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge