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 from existing knowledge, (4) a memory that stores knowledge, and (5) a control mechanism that chooses premises and rules in each inference 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, or the control part of the system. The most influential theory for the logic part of reasoning systems is the modern symbolic 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 to reasoning in practical situations shows fundamental differences from human reasoning in these situations. Traditional theories of reasoning are certain in several aspects, whereas actual human reasoning in practical situations is often uncertain in these aspects. The meaning of a term in traditional logic is determined according to an interpretation, therefore it does not change as the system runs. On the contrary, the meaning of a term in human mind often changes according to experience and context. Example: What is "game"? In traditional logic, the meaning of a compound term is completely determined by its "definition", which reduces its meaning into the meaning of its components and the operator (connector) that joins the components. On the contrary, the meaning of a term in human mind often cannot be fully reduced to that of its components, though is still related to them. Example: Is a "blackboard" exactly a black board? In traditional logic, a statement is either true or false, but people often take truth value of certain statements as between true and false. Example: Is "Tomorrow will be cloudy" true or false? In traditional logic, the truth value of a statement does not change over time. However, people often revise their beliefs after getting new information. Example: After learning that Tweety is a penguin, you may change some of your beliefs formed when you only know that it is a bird.
