Semantics for Nute's Defeasible Logic


Dr. Fred Maier

A logic is called monotonic if its associated consequence relation |- satisfies the below property:

If A |- p, then A union B |- p.

If we can derive a statement p from a set A of premises, then we can also derive p from A plus any additional set B. It is sometimes thought that a logic intended to model aspects of common sense reasoning should not have this property. We often draw plausible conclusions from a set of premises only to later reject them when additional information is discovered. Defeasible logic is a family of simple nonmonotonic logics originally developed by Donald Nute. Knowledge is encoded in theories consisting of strict and defeasible rules, where strict rules represent statements like "bachelors are unmarried males", and defeasible rules represent statements like "Americans usually are English speakers".

The consequences of defeasible theories have traditionally been defined through the particular defeasible logics. In this talk, a fixpoint semantics for defeasible theories will be presented. Nute's most recent defeasible logic is sound with respect to this semantics, and for finite theories it is complete. The formal properties of the semantics, its relationship to semantics for logic programs, and problematic examples will be discussed.

Fred Maier will receive his PhD in Computer Science from the University of Georgia in December. His dissertation, under the supervision of Donald Nute and Robert Robinson, is an examination of Nute's defeasible logic. Originally from the Gulf Coast, Fred received a BA in philosophy from Spring Hill College in Mobile, AL and an MA in philosophy from Tulane University. His studies there mostly fall into the analytic tradition. He moved to UGA in 1999 to study artificial intelligence. He received an MS there in 2002.