deep structure See GRAMMAR, PHILOSOPHY OF LAN-. GUAGE , TRANSFORMATION RUL. default logic, a formal system for reasoning with defaults, developed by Raymond Reiter in 1980. Reiter’s defaults have the form ‘P:MQ1 , . . . , MQn/R’, read ‘If P is believed and Q1 . . . Qn are consistent with one’s beliefs, then R may be believed’. Whether a proposition is consistent with one’s beliefs depends on what defaults have already been applied. Given the defaults P:MQ/Q and R:M-Q/-Q, and the facts P and R, applying the first default yields Q while applying the second default yields -Q. So applying either default blocks the other. Consequently, a default theory may have several default extensions. Normal defaults having the form P:MQ/Q, useful for representing simple cases of nonmonotonic reasoning, are inadequate for more complex cases. Reiter produces a reasonably clean proof theory for normal default theories and proves that every normal default theory has an extension. See also DEFEASIBILITY, NON-MONOTONIC LOGI. D.N. defeasibility, a property that rules, principles, arguments, or bits of reasoning have when they might be defeated by some competitor. For example, the epistemic principle ‘Objects normally have the properties they appear to have’ or the normative principle ‘One should not lie’ are defeated, respectively, when perception occurs under unusual circumstances (e.g., under colored lights) or when there is some overriding moral consideration (e.g., to prevent murder). Apparently declarative sentences such as ‘Birds typically fly’ can be taken in part as expressing defeasible rules: take something’s being a bird as evidence that it flies. Defeasible arguments and reasoning inherit their defeasibility from the use of defeasible rules or principles. Recent analyses of defeasibility include circumscription and default logic, which belong to the broader category of non-monotonic logic. The rules in several of these formal systems contain special antecedent conditions and are not truly defeasible since they apply whenever their conditions are satisfied. Rules and arguments in other non-monotonic systems justify their conclusions only when they are not defeated by some other fact, rule, or argument. John Pollock distinguishes between rebutting and undercutting defeaters. ‘Snow is not normally red’ rebuts (in appropriate circumstances) the principle ‘Things that look red normally are red’, while ‘If the available light is red, do not use the principle that things that look red normally are red’ only undercuts the embedded rule. Pollock has influenced most other work on formal systems for defeasible reasoning. See also DEFAULT LOGIC, EPISTEMOLOGY, NON – MONOTONIC LOGI. D.N.