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Interpolation Theorems for Nonmonotonic Reasoning Systems

Summary: Interpolation Theorems for Nonmonotonic
Reasoning Systems
Eyal Amir
Computer Science Division,
University of California, at Berkeley
Berkeley, CA 94720
August 18, 2002
Craig's interpolation theorem [Craig, 1957] is an important theorem
known for propositional logic and rst-order logic. It says that if a logical
formula logically 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 impor-
tant 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 sta-
ble models semantics (a.k.a. answer set semantics). These results give us
better understanding of those logics, especially in contrast to their non-


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


Collections: Computer Technologies and Information Sciences