# From First-Order Logic to Assertional Logic

## TL;DR

This paper introduces assertional logic as a simpler, more expressive alternative to First-Order Logic for knowledge representation, capable of unifying logic and probability in AI.

## Contribution

The paper proposes assertional logic, a novel framework formalizing knowledge with set-theoretic assertions, extending it with definitions, and demonstrating its advantages over FOL.

## Key findings

- Assertional logic is more expressive than FOL.
- It can unify logic and probability in AI.
- It offers a simpler, extensible formalism for knowledge representation.

## Abstract

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.