From First-Order Logic to Assertional Logic
  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.
