Dynamic reasoning with qualified syllogisms

摘要

A qualified syllogism is a classical Aristotelean syllogism that has been “qualified” through the use of fuzzy quantifiers, likelihood modifiers, and usuality modifiers, e.g., “Most birds can fly; 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 nonmonotonic 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 multiple-inheritance hierarchy. The hierarchy duplicates some of the information recorded in the path logic, but additionally provides an extralogical specificity 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 frame problem.