Gradual Classical Logic for Attributed Objects
This work addresses foundational issues in logic for AI and knowledge representation, but it appears incremental as it builds on existing logical frameworks.
The paper tackles the problem of expressing tacit agreements about object-attribute relations by introducing a gradual logic that extends classical logic with a new connective, resulting in a formal semantics and proof of decidability.
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.