Summary: Appears in 8th European Conference on Logic in Artificial Intelligence (JELIA '2002).
Interpolation Theorems for Nonmonotonic Reasoning
Systems
Eyal Amir
Computer Science Division
University of California at Berkeley
Berkeley, CA 94720­1776, USA
eyal@cs.berkeley.edu
Abstract. Craig's interpolation theorem [3] is an important theorem known for
propositional logic and first­order logic. It says that if a logical formula  logi­
cally follows from a formula , then there is a formula , including only symbols
that appear in both ; , such that  logically follows from and logically
follows from . Such theorems are important and useful for understanding those
logics in which they hold as well as for speeding up reasoning with theories in
those logics. In this paper we present interpolation theorems in this spirit for
three nonmonotonic systems: circumscription, default logic and logic programs
with the stable models semantics (a.k.a. answer set semantics). These results give
us better understanding of those logics, especially in contrast to their nonmono­
tonic characteristics. They suggest that some monotonicity principle holds despite
the failure of classic monotonicity for these logics. Also, they sometimes allow

Source: Amir, Eyal - Department of Computer Science, University of Illinois at Urbana-Champaign

Collections: Computer Technologies and Information Sciences