Table Of ContentLecture Notes in Artificial Intelligence 927
Subseries of Lecture Notes in Computer Science
Edited by iJ G. Carbonell and J. Siekmann
Lecture Notes in Computer Science
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Jtirgen Dix Louis Moniz Pereira
Teodor C. Przymusinski (Eds.)
Non-Monotonic
Extensions of
Logic gnimmargorP
ICLP '94 Workshop
Santa Margherita Ligure, Italy, June ,71 1994
Selected Papers
regnirpS
Series Editors
Jaime G. Carbonell
School of Computer Science
Carnegie Mellon University
Pittsburgh, AP 15213-3891, USA
J~rg Siekmann
University of Saarland
German Research Center forArtificial Intelligence (DFKI)
Stuhlsatzenhausweg 3, D-66123 Saarbriicken, Germany
Volume Editors
Jiirgen Dix
Institut fiir Informatik, Universit~it Koblenz-Landau
Rheinau ,1 D-56075 Koblenz, Germany
Louis Moniz Pereira
Departamento de Inform~ttica, Universidade Nova de Lisboa
P-2825 Monte da Caparica, Portugal
Teodor Przymusinski
Department of Computer Science, University of California
Riverside, CA 92521, USA
CR Subject Classification (1991): 1.2.3, F.4.1, D.1.6
ISBN 3-540-59467-1 Springer-Verlag Berlin Heidelberg New York
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Preface
This book is the outcome of an original compilation of extended and revised
versions of selected papers presented at the workshop on Non-Monotonic Exten-
sions of Logic Programming, held in Santa Margherita Ligure, Italy, on June ,71
1994. It also includes additional papers solicited from the participants. As some
workshop papers were published elsewhere, they do not appear in this volume.
The workshop on Non-Monotonic Extensions to Logic Programming was or-
ganized in conjunction with ICLP '94, the Eleventh International Conference on
Logic Programming. It was the fourth in a series of workshops held jointly with
logic programming conferences (NACLP'90, ILPS'91, and ILPS'93) and received
financial support from the ESPRIT Network of Excellence Compulog-Net and
the University of Koblenz.
The motivation for these workshops stems from the fact that during the
last decade a significant body of knowledge has been accumulated providing us
with a better understanding of the semantic issues in logic programming and
the theory of deductive databases. In particular, the class of perfect models for
(locally) stratified logic programs and two closely related extensions to normal,
non-disjunctive, logic programs were introduced and extensively investigated:
the well-founded models and the stable models.
Semantics of logic programs rely on a non-monotonic operator, often referred
to as negation-by-failure or negation-by-default. The non-monotonicity of this
operator allows us to view logic programs as special non-monotonic theories
and thus makes it possible to draw from the extensive research in the area of
non-monotonic reasoning and use it as a guidance in the search for a suitable
semantics for logic programs.
Furthermore, the problem of extending the well-founded and the stable mod-
els approaches, by defining a suitable semantics for normal and disjunctive pro-
grams extended with a second type of negation, turned out to be a difficult one,
as evidenced by a large number of papers devoted to the subject.
As a result, research work aimed at better understanding of the relation-
ships existing between logic programming (LP) and a variety of nonmonotonic
formalisms (NMF) has been mutually beneficial to both areas. NMFs help us
to determine suitable semantics for logic programs and they help us as well to
understand how they can be applied to express and solve various AI problems.
Conversely, the NMFs can utilize the wide body of knowledge already gathered
about LP and use logic programs as inference engines for query answering.
The 01 papers in this collection address the issues stemming from this out-
look. Because new semantics often require new computational procedures, the
papers can be naturally divided into two sections: Semantics 5( papers) and
Computation 5( papers). We give more specific comments about the papers
and their interrelationship in the Introduction (page .)1
IV
All contributions were refereed by the Program Committee members, who
are all to be thanked for their invaluable help and effort. Thanks are due as well
to the external reviewers (see next page).
Last but not least, let us congratulate all the authors, whose high quality
research and text formatting abilities made this book a reality. We are sure it
will spur on further research into this exciting and open field.
March 1995 Jfirgen Dix, Koblenz
Luis Moniz Pereira, Lisboa
Teodor C. Przymusinski, Riverside
Previous Workshops
0991 WS at NACLP '90, U.S.A. 1991 WS at ILPS '91, U.S.A.
3991 WS at ILPS '93, U.S.A. 1994 WS at ICLP '94, Italy
Sponsors
Compulog Network of Excellence, University of Koblenz.
Organizing Committee
Jiirgen Dix University of Koblenz
Luls Moniz Universidade Nova di Lisboa
Teodor Przymusinski University of California at Riverside
Program Committee
Jiirgen Dix University of Koblenz, Germany
Michael Gelfond University of Texas at 1E Paso, U.S.A.
Jorge Lobo University of Illinois at Chicago, U.S.A.
Wiktor Marek University of Kentucky at Lexington, U.S.A.
Luis Moniz Pereira Universidade Nova di Lisboa, Portugal
Teodor Przymusinski University of California at Riverside, U.S.A.
Additional Referees
J.J. Alferes, C.V. Damasio, L. Degerstedt, A. Provetti, and Carlos Uzc~tegui.
Table of Contents
Introduction ............................................................... 1
Semantics
An Argumentation Theoretic Semantics Based on Non-Refutable Falsity .... 3
J.J. Alferes and L.M. Pereira
From Disjunctive Programs to Abduction ................................. 23
.V Lifschitz and .H Turner
Semantics of Normal and Disjunctive Logic Programs:
A Unifying Framework ................................................... 43
."7 .C Przymusinski
Every Normal Program has a Nearly-Stable Model ........................ 68
.C Witteveen
Logic Programming with Assumption Denial .............................. 85
J.-H. You and L.Y. Yuan
Computation
A Resolution-based Procedure for Default Theories with Extensions ...... 101
M.D. Barback and J. oboL
A General Approach to Bottom-Up Computation of
Disjunctive Semantics ................................................... 127
S. Brass and J. Dix
Static Semantics as Program Transformation and
Well-founded Computation .............................................. 156
S. Costantini and G.A. Lanzarone
Magic Computation for Well-founded Semantics ......................... 181
L. Degersledl and .U Nilsson
Computing Stable and Partial Stable Models
of Extended Disjunctive Logic Programs ................................ 205
C. Ruiz and J. Minker
Introduction
In order to facilitate reading this book, we now give a brief overview of the
contents of the presented papers. We follow our classification of papers into two
categories, one devoted to semantics and the other to computation.
Semantics: While Alferes/Pereira as well as Witteveen deal with extended
normal programs, all other papers in this section deal with extended disjunctive
programs.
The first paper, An argumentation theoretic semantics on based non-refutable
falsity by J. J. Alferes and L. M. Pereira, extends previous works of the authors
(O-semantics) by presenting a new semantics for extended logic programs. The
intuition behind is that the well-founded semantics often is overly careful in
deciding about the falsity of some atoms by leaving them undefined. Default
literals are viewed as arguments a rational agent can sustain along with the
program.
The second paper, From Disjunctive Programs to Abduction by V. Lifschitz
and H. Turner, deals with the problem of representing incomplete information
using different formalisms (classical negation and epistemic disjunction versus
two variants of abductive logic programming). Three formalisms are applied to
a particular action-domain (the Yale Shooting) and the presented results show
that they are very closely related (by simple syntactic transformations).
The third paper, Semantics of Normal and Disjunctive Logic Programs: A
unifying framework by T. Przymusinski, introduces a uniform semantic frame-
work that isomorphically contains the major semantics for normal, disjunctive
and extended logic programs. The framework is based on the Autoepistemic
Logic of Knowledge and beliefs, AELB, introduced recently by the author.
C. Witteveen's paper, Every Normal Program has a Nearly-Stable Model,
investigates the inconsistency-problem of the stable semantics: stable models
need not always exist. He presents two simple syntactic transformations, shifting
and condensation that allow to transform any program in another one having
at least one stable model.
The last paper in the Semantics group, Logic Programming with Assumption
Denial by J.-H. You and L.-Y. Yuan, deals with arbitrary extended disjunctive
programs. The authors define a framework which allows to explicitely represent
defeats of assumptions, so called assumption denials. Their method is related
to abduction and reveals interesting relationships between disjunctive and non-
disjunctive programs.
Computation: With the exception of the first, all remaining papers deal
with transformations. Different syntactical transformations are applied to the
originM program to obtain a certain normal form which is used to compute the
semantics more efficiently. While Degerstedt/Nilsson consider the well-founded
semantics, the other authors compute (partial) stable models or the static se-
mantics for disjunctive programs.
The first paper of this section, A Resolution-based Procedure for Default
Theories with Extensions by M. Barback and J. Lobo, deals with a problem
in general non-monotonic reasoning: to determine if a given formula is true
in all (sceptical entailment) or in some (credulous entailment) extensions of
a default theory. The authors relate this problem to logic programming, by
defining a sound and complete proof-procedure that is closely related to SLDNF
and abduction-like procedures for logic programs.
In the second paper, A General Approach to Bottom-Up Computation of
Disjunctive Semantics by St. Brass and J. Dix, a method for deriving bottom-
up query evaluation algorithms from the abstract properties of the underlying
negation semantics is described. An important ingredient is to derive first the
residual program (using partial evaluation and reductions). The authors argue
that this approach is applicable to a large class of disjunctive semantics, like the
stable, and the static semantics and its variants.
The next paper, Static Semantics as Program Transformation and Well-
founded Computation by S. Costantini and G. Lanzarone, describes a general
framework of computing semantics for disjunctive logic programs that are similar
to the static semantics. They distinguish between a program transformation
phase, which absorbs most of the complexity and a constructive phase, which is
similar to the well-founded computation for normal programs.
The paper by L. Degerstedt and U. Nilsson, Magic Computation for Well-
founded Semantics, deals with non-disjunctive semantics under the well-founded
semantics. The authors introduce a new magic templates transformation and
show a step-by-step correspondence between the naive bottom-up evaluation of
the transformed program and a class of top-down search strategies. They show
their method to be sound and complete.
Finally, the last paper of this book, Computing Stable and Partial Stable
Models of Extended Disjunctive Logic Programs by C. Ruiz and J. Minker, again
deals with extended disjunctive logic programs. The authors describe a proce-
dure to compute the collection of all partial stable models of a program. This
is done by transforming the program into a constrained disjunctive program
without any non-monotonic negation such that the classical minimal models of
the transformed program correspond to the set of partial stable models of the
original program.
An argumentation theoretic semantics based on
non-refutable falsity*
Jos~ 3dlio Alferes 1 and Luis Moniz Pereira 2
1 DMAT, Universidade de ~vora and CRIA, Uninova
2825 Monte da Caparica, Portugal
[email protected]
2 DCS, U. Nova de Lisboa and CR.IA, Uninova
2825 Monte da Caparica, Portugal
[email protected]
Abstract. We contend that the well-founded semantics (WFS), for nor-
mal program, and similarly the well-founded semantics with explicit ne-
gation (WFSX), for extended ones are, by design, overly careful in deci-
ding about the falsity of some atoms, by leaving them undefined.
We've dealt with this issue in normal programs and have previously
defined the O-semantics, one that extends WFS by addjoining to it more
negative assumptions, at the expense of undefined literals. The goal of
this paper is to generalize that work to extended programs, and define
a semantics for such programs that enlarges WFSX with more negative
assumptions.
To achieve this we view default literals as arguments a rational agent
can sustain along with the program. As our goal is to enlarge WFSX, we
consider the latter as the common reasoning ground and argumentation
of agents.
tool
With this basis, and in order to define the semantics, we first formalize
the concepts of consistent and non-refutable sets of arguments (or of
hypotheses). In general several such sets may exist. So, and in order to
define a unique semantics, given by a single set of additional assumpti-
ons, we introduce an additional non-refutability of arguments criterium
tenability - for always and finally preferring just one set of arguments
-
over another.
1 Introduction
The Well Founded Semantics (WFS) GRS91 has been proposed as a suitable
semantics for normal logic programs. Unlike other semantics, WFS gives mea-
ning to every normal program, is cumulative Dix91, and can be obtained by
a bottom-up fixpoint construction. Because it is a relevant semantics Dix92 it
is susceptible of top-down existencial query procedures. However, as argued in
KM91, PAA92a, PAA93, the WFS is by design overly careful in deciding about
the falsity of some atoms, leaving them undefined.
* We thank Esprit BR project Compulog 2 (no. 6810) for its support.
