On an Algebraic Characterization of Default Reasoning

Helmut Thiele

Date: July 17th (Wednesday)
Time: ??.??
Abstract
This talk deals with non-monotonic logical consequence operators defined by default reasoning.
The aim is to consider and investigate such operators within the general framework of the theory of closure operators, in particular, topological and algebraic closure operators used in topology, algebra, logic and metamathematics.The main result of the paper is an appropriate generalization of the well-known theorem of G. Birkhoff, P. Hall and J. Schmidt, which gives an algebraic characterization of compact closure operators by universal algebras and also by classical, "monotonic", deductive systems.
For this p[urpose we introduce a new type of algebraic strusture generalizing the classical notion of universal algebra (introduced by G. Birkhoff) which we shall call regulated algebra. Furthermore, generalizing the concept of a classical monotonic deductive system which is closely asociated with the theorem of G. Birkhoff, P. Hall and J. Schmidt, we introduce Regulated Deductive Systems which include, for instance Reiter's default theories as special cases.
As we shall see in the sequel, many of the classical results in non-monotonic reasoning can be derived on the basis of this general axiomatic approach. Furthermore, this approach gives a deeper mathematical understanding of what default reasoning is and provides the starting point for further inverstigations of regulated algebras and regulated deductive systems.

______________
__________________________________________

Previous page RISC SWP Linz Austria