We argue that extensibility is a key challenge for knowledge representation. For this purpose, we propose assertional logic - a knowledge model for easier extension with new AI building blocks. In assertional logic, all syntactic objects are categorized as set theoretic constructs including individuals, concepts and operators, and all kinds of knowledge are formalized by equality assertions. When extending with a new building block, one only needs to consider its interactions with the basic form of knowledge (i.e., equality assertions) without going deeper into its interactions with other existing ones. 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. As a case study, we show how assertional logic can be used to unify logic and probability, and more important AI building blocks including time.
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