Cognitive Logic versus Mathematical Logic

First-order predicate logic meets many problems when used to explain or reproduce cognition and intelligence. These problems have a common nature, that is, they all exist outside mathematics, the domain for which mathematical logic was designed. Cognitive logic and mathematical logic are fundamentally different, and the former cannot be obtained by partially revising or extending the latter. A reasoning system using a cognitive logic is briefly introduced, which provides solutions to many problems in a unified manner. 1 Mathematical logic and cognition An automatic reasoning system usually consists of the following major components: 1. a formal language that represents knowledge, 2. a semantics that defines meaning and truth value in the language, 3. a set of inference rules that derives new knowledge, 4. a memory that stores knowledge, 5. a control mechanism that chooses premises and rules in each step. The first three components are usually referred to as a logic, or the logical part of the reasoning system, and the last two as an implementation of the logic, or the control part of the system. At the present time, the most influential theory for the logic part of reasoning systems is mathematical logic, especially, first-order predicate logic. For the control part, it is the theory of computability and computational complexity. Though these theories have been very successful in many domains, their application in cognitive science and artificial intelligence shows fundamental differences from human reasoning in similar situations.