Summary: Semantics for Reasoning with Contradictory Extended Logic
Anastasia Analyti & Sakti Pramanik
Department of Computer Science, Michigan State University, E. Lansing, MI 48824
E-mail: firstname.lastname@example.org, email@example.com
Extended programs are normal programs extended with classical negation. Because of the
classical negation in the head of the rules, an extended logic program can be contradictory.
Human reasoning is often based on conflicting evidence and on assumptions which are not
always valid. Our goal is to derive useful conclusions from programs that may be contradictory.
We consider rules to be defaults. Rule prioritization can be viewed as a tool to specify
confidence information about these defaults. We present a new semantics for extended
programs with rule prioritization, called contradiction-free semantics (CFS). CFS is defined as
the least fixpoint of a monotonic operator. Every extended program with rule prioritization has at
least one stable c-model. We show that the CFS of a program P coincides with the least stable
c-model of P. A sound and complete proof procedure to answer queries based on CFS is
Keywords: extended logic programs, rule prioritization, contradictions, declarative semantics,