Gradual Classical Logic for Attributed Objects

TL;DR

This paper introduces gradual logic, an extension of classical logic with a new connective for object-attribute relations, providing formal semantics and decidability proofs, to better model nuanced knowledge and belief structures.

Contribution

It proposes a novel logical framework called gradual logic that captures the nuanced relation between objects and attributes, extending classical logic with a new connective.

Findings

Formal semantics for gradual logic are established.

Decidability of the logic is proved.

Comparison with other non-classical logics is provided.

Abstract

There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on assumptions about the relation between objects and their attributes, and studies a way of expressing them, presenting as the result what we term gradual logic in which the sense of truth gradually shifts. It extends classical logic instances with a new logical connective capturing the object-attribute relation. A formal semantics is presented. Decidability is proved. Para- consistent/epistemic/conditional/intensional/description/combined logics are compared.