Theory and Practice of Logic Programming



Regular Papers

Embedding defeasible logic into logic programming


GRIGORIS ANTONIOU a1, DAVID BILLINGTON a2, GUIDO GOVERNATORI a3 and MICHAEL J. MAHER a4
a1 Institute of Computer Science, FORTH, Greece (e-mail: antoniou@ics.forth.gr)
a2 School of ICT, Griffith University, Australia (e-mail: d.billington@griffith.edu.au)
a3 School of ITEE, University of Queensland, Australia (e-mail: guido@itee.uq.edu.au)
a4 National ICT Australia, c/o UNSW, Australia (e-mail: mmaher@cse.unsw.edu.au)

Article author query
antoniou g   [Google Scholar] 
billington d   [Google Scholar] 
governatori g   [Google Scholar] 
maher mj   [Google Scholar] 
 

Abstract

Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of defeasible reasoning methods. So far no relationship has been established between defeasible logic and mainstream nonmonotonic reasoning approaches. In this paper we establish close links to known semantics of logic programs. In particular, we give a translation of a defeasible theory $D$ into a meta-program $P(D)$. We show that under a condition of decisiveness, the defeasible consequences of $D$ correspond exactly to the sceptical conclusions of $P(D)$ under the stable model semantics. Without decisiveness, the result holds only in one direction (all defeasible consequences of $D$ are included in all stable models of $P(D)$). If we wish a complete embedding for the general case, we need to use the Kunen semantics of $P(D)$, instead.

(Received September 20 2004)
(Revised October 12 2005)
(Accepted November 8 2005)


Key Words: Defeasible logic; stable semantics; Kunen semantics; non-monotonic logic.