Logic and Knowledge Bases

IntroductIon Knowledge bases (KBs) must be able to capture a wide range of situations. One must be able to represent and answer questions regarding indefinite information where it is not clear that there is a unique answer to a question. One must also represent and answer questions about negative information. We discuss a powerful way to represent such information, namely through reasoning about knowledge bases using logic. In the real world, information known at one time may change. However, in first-order logic, information once known cannot change. This phenomenon is known as monotonicity. Since KBs deal with incomplete information, they are not monotonic. We shall discuss a form of logic programming, below, which is able to handle nonmonotonic information and situations required by KBs such as definite and indefinite data, and logical and default negation. The question of how to adapt first-order logic to handle complex situations started in the 1950s. Early systems handled problems in an ad hoc way. Several primitive deductive databases (DDBs), function-free logic programs, were developed in the 1960s. Robinson (1965) developed a general method for automated theorem proving to perform deduction. This method is known as the Robinson Resolution Principle; it is a generalization of mo-dus ponens to first-order predicate logic. Green and Raphael (1968) were the first to recognize the importance and applicability of the work performed by Robinson and developed a system using this principle. November 1977 is generally considered to be the start of the modern era of DDBs. A workshop , " Logic and Data Bases, " was organized in Toulouse, France, by Gallaire and Nicolas in collaboration with Minker. The workshop included researchers who had performed work in deduction from 1969 to 1977 using the Robinson Resolution Principle. The book Logic and Data Bases, edited by Gallaire and Minker (1978), contained these papers. Many significant contributions were described in the book. Nicolas and 682 Logic and Knowledge Bases Gallaire discussed the difference between model theory and proof theory. They demonstrated that the approach taken by the database community was model theoretic—that is, the database represents the truths of the theory, and queries are answered by a bottom-up search. However, in logic programming, answers to a query use a proof theoretic approach, starting from the query, in a top-down search. Reiter discussed the closed world assumption (CWA), whereby in a theory, if one cannot prove that an atomic formula is true, …