From First-Order Logic to Assertional Logic
This work addresses foundational issues in knowledge representation for AI and logic, proposing a new paradigm rather than an incremental improvement.
The paper tackles the problem of knowledge representation by arguing that First-Order Logic (FOL) has critical issues and proposes assertional logic as an alternative, claiming it is simpler, more expressive, and extensible, with a case study showing its application to unify logic and probability in AI.
First-Order Logic (FOL) is widely regarded as one of the most important foundations for knowledge representation. Nevertheless, in this paper, we argue that FOL has several critical issues for this purpose. Instead, we propose an alternative called assertional logic, in which all syntactic objects are categorized as set theoretic constructs including individuals, concepts and operators, and all kinds of knowledge are formalized by equality assertions. We first present a primitive form of assertional logic that uses minimal assumed knowledge and constructs. Then, we show how to extend it by definitions, which are special kinds of knowledge, i.e., assertions. We argue that assertional logic, although simpler, is more expressive and extensible than FOL. As a case study, we show how assertional logic can be used to unify logic and probability, and more building blocks in AI.