APPLIED LOGIC

the study of the practical art of right reasoning. The formalism and theoretical results of pure logic can be clothed with meanings derived from a variety of sources within philosophy as well as from other sciences. This formal machinery also can be used to guide the design of computers and computer programs. The applications of logic cover a vast range, relating to reasoning in the sciences and in philosophy, as well as in everyday discourse. They include (1) the various sorts of reasoning affecting the conduct of ordinary discourse as well as the theory of the logical relations that exist within special realms of discoursebetween two commands, for example, or between one question and another, (2) special forms of logic designed for scientific applications, such as temporal logic (of what was or will be the case) or mereology (the logic of parts and wholes), and (3) special forms for concepts bearing upon philosophical issues, such as logics that deal with statements of the form I know that . . . , I believe that . . . , It is permitted to . . . , It is obligatory to . . . , or It is prohibited to . . . . Additional reading Applications of logic in unexpected areas of philosophy are studied in Evandro Agazzi (ed.), Modern LogicA Survey: Historical, Philosophical, and Mathematical Aspects of Modern Logic and Its Applications (1981). William L. Harper, Robert Stalnaker, and Glenn Pearce (eds.), IFs: Conditionals, Belief, Decision, Chance, and Time (1981), surveys hypothetical reasoning and inductive reasoning. On the applied logic in philosophy of language, see Edward L. Keenan (ed.), Formal Semantics of Natural Language (1975); Johan van Benthem, Language in Action: Categories, Lambdas, and Dynamic Logic (1991), also discussing the temporal stages in the working out of computer programs, and the same author's Essays in Logical Semantics (1986), emphasizing grammars of natural languages. David Harel, First-Order Dynamic Logic (1979); and J.W. Lloyd, Foundations of Logic Programming, 2nd extended ed. (1987), study the logic of computer programming. Important topics in artificial intelligence, or computer reasoning, are studied in Peter Grdenfors, Knowledge in Flux: Modeling the Dynamics of Epistemic States (1988), including the problem of changing one's premises during the course of an argument. For more on nonmonotonic logic, see John McCarthy, Circumscription: A Form of Non-Monotonic Reasoning, Artificial Intelligence 13(12):2739 (April 1980); Drew McDermott and Jon Doyle, Non-Monotonic Logic I, Artificial Intelligence 13(12):4172 (April 1980); Drew McDermott, Nonmonotonic Logic II: Nonmonotonic Modal Theories, Journal of the Association for Computing Machinery 29(1):3357 (January 1982); and Yoav Shoham, Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence (1988).