Dynamic Reasoning with Qualified Syllogisms

A gualij%e~ syllogism is a classical Aristoteiean syllogism that has been “qualified” through the use of fuzzy quantifiers, likelihood modifiers, and usuality modifiers, e.g., “Most birds can Ry; Tweety is a bird; therefore, it is likely that Tweety can fly.” This paper introduces a formal logic Q of such syllogisms and shows how this may be employed in a system of nonmonotonj~ reasoning. In process are defined the notions of path logic and dynamic reasoning system (DRS) The former is an adaptation of the conventional formal system which explicitly portrays reasoning as an activity that takes place in time. The latter consists of a path logic together with a multipleinhe~tance hierarchy. The hierarchy duplicates some of the info~ation recorded in the path logic, but additionally provides an extralogical spec#icity relation. The system uses typed predicates to formally distinguish between properties and kinds of things. The effectiveness of the approach is demonstrated through analysis of several “puzzles” that have appeared previously in the literature, e.g., Tweety the Bird, Clyde the Elephant, and the Nixon Diamond. It is also outlined how the DRS framework accommodates other reasoning techniques-in particular, predicate circumscription, a “localized” version of default logic, a variant of nonmonotonic logic, and reason maintenance. Furthermore it is seen that the same framework accomodates a new formulation of the notion of unless. A concluding section discusses the relevance of these systems to the well-known fiame problem. @ 1997 Elsevier Science B.V. ic;e?‘~~rds: Default reasoning; Dynamic reasoning systems; Fuzzy likelihood; Fuzzy probabilities; Fuzzy quanti~~rs; Multiple inheritance; Nonmonotoni~ reasoning; Qualified syllogisms; The frame problem; Unless ’ E-mail: [email protected]. 0~4.3702/97/$17.~ @ 1997 Elsevier Science E.V. All rights reserved. PIJ SOOO4-3702(97)00020-9 104 D.G. Sclwartz/Arfificial Intelligence 93 (1997) 103-167