Mathematical logic in artificial intelligence

This article concerns computer programs that represent information about their problem domains in mathematical logical languages and use logical inference to decide what actions are appropriate to achieve their goals. Mathematical logic is not a single language. There are many kinds of mathematical logic, and even choosing a kind does not specify the language. The language is determined by declaring what nonlogical symbols will be used and what sentences will be taken as axioms. The nonlogical symbols are those that concern the concrete subject matter to be stored in a computer's data base?for example, information about objects and their locations and motions. Whatever the choice of symbols, all kinds of mathematical logic share two ideas. First, it must be mathematically definite what strings of symbols are considered formulas of the logic. Second, it must be mathematically definite what inferences of new formulas from old ones are allowed. These ideas permit the writing of computer programs that decide what combinations of symbols are sentences and what inferences are allowed in a particular logical language. Mathematical logic has become an important branch of mathe matics, and most logicians work on problems arising from the internal development of the subject. Mathematical logic has also been applied to studying the foundations of mathematics, and there it has had its greatest success. Its founders, Aristotle, Leibniz, Boole, and