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Negation by default and unstratifiable logic programs

Nicole Bidoít, Christine Froidevaux
1991 Theoretical Computer Science  
85 rams Bidoit, N. and C. Froidevaux, Negation by default and unstratifiable logic programs, Theoretical Computer Science 78 (1991) 85-112.  ...  The default approach to the theory of logic programs (and deductive databases) is based on the interpretation of negation by default rules.  ...  Acknowledgment Many thanks to Serge Abiteboul, Serenella Cerrito, Stephane Grumbach, Evangelos Paschos and Victor Vianu for useful suggestions and discussions. Work performed by N.  ... 
doi:10.1016/0304-3975(51)90004-7 fatcat:upeitsmbgrazpovrpt63tjakai

Page 4558 of Mathematical Reviews Vol. , Issue 92h [page]

1992 Mathematical Reviews  
Peter Bachmann (Dresden) 92h:68053 68Q55 68T27 Bidoit, Nicole (F-PARIS11-RI); Froidevaux, Christine (F-PARIS1 1-RI) Negation by default and unstratifiable logic programs.  ...  Summary: “The default approach to the theory of logic programs (and deductive databases) is based on the interpretation of nega- tion by default rules.  ... 

Answer Set Programming: A Declarative Approach to Solving Challenging Search Problems

Ilkka Niemelä
2011 2011 41st IEEE International Symposium on Multiple-Valued Logic  
of atoms (i) which satisfies the rules and (ii) where each atom is justified by the rules (negation by default; CWA) The set {b, eb} is not a stable model of P but {b, f } is the (unique) stable  ...  Normal Programs Encoding of choices A key point in ASP Choices can be encoded using normal rules with unstratified negation a ← not a , b, not c a ← not a Choice rules, however, provide a much  ... 
doi:10.1109/ismvl.2011.61 dblp:conf/ismvl/Niemela11 fatcat:evdlcs7bobg6dp25oovr6egv5a

An overview of nonmonotonic reasoning and logic programming

Jack Minker
1993 The Journal of Logic Programming  
Work in logic programming and nonmonotonic reasoning deals with the handling of negation. We consider two types of negation in logic programs: negation by rules of default and logical negation.  ...  Negation based on hxpoint techniques, three-valued logic, and nonmonotonic logics are presented for positive logic programs, (locally) stratified logic programs, and unstratifiable logic programs.  ... 
doi:10.1016/0743-1066(93)90028-f fatcat:zs5h4ximffdfvapevyr6rvs4fm

Logic programming and knowledge representation—The A-Prolog perspective

Michael Gelfond, Nicola Leone
2002 Artificial Intelligence  
In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning.  ...  PII: S 0 0 0 4 -3 7 0 2 ( 0 2 ) 0 0 2 0 7 -2 The A-Prolog language We start with a description of syntax and semantics of A-Prolog (also called Answer Set Programming [81])-a logic programming language  ...  The program is not head-cycle free, transforming disjunction to unstratified negation would alter the semantics of the program.  ... 
doi:10.1016/s0004-3702(02)00207-2 fatcat:3s6q45zj5zab5bp2ce36igl66q

SILK: Higher Level Rules with Defaults and Semantic Scalability [chapter]

Benjamin N. Grosof
2009 Lecture Notes in Computer Science  
. */ /* If an administrator controls a privilege and states at a time (t) that a user has a privilege, / If an administrator controls a privilege and states at a time (t) that a user has a privilege, then  ...  s Bob and Cara make conflicting statements over time about Al's printing */ Cara[states(2007) -> print(Al)].  ...  E-Commerce Ex. of Causal Process More SILK Expressive Requirements, continued • Closed-World [For defaults, numerical, collections, and meta-reasoning] • Unstratified (not just stratified) negation-as-failure  ... 
doi:10.1007/978-3-642-05082-4_2 fatcat:macyrt2hzva6jlzoj4svq52nf4

Answer Set Programming: A Primer [chapter]

Thomas Eiter, Giovambattista Ianni, Thomas Krennwallner
2009 Lecture Notes in Computer Science  
It looks into positive programs over stratified programs to arbitrary programs, and then proceeds to extensions with two kinds of negation (named weak and strong negation), and disjunction in rule heads  ...  This article is a gentle introduction to the subject; it starts with motivation and follows the historical development of the challenge of defining a semantics for logic programs with negation.  ...  Acknowledgments We thank Minh Dao-Tran, Wolfgang Faber and Gerald Pfeifer for their valuable comments and corrections.  ... 
doi:10.1007/978-3-642-03754-2_2 fatcat:au2bnpvk25awbja73itqqex5ni

NP Datalog: a Logic Language for Expressing NP Search and Optimization Problems [article]

Sergio Greco, Cristian Molinaro, Irina Trubitsyna, Ester Zumpano
2009 arXiv   pre-print
Specifically, first a language obtained by extending (positive) Datalog with intuitive and efficient constructs (namely, stratified negation, constraints and exclusive disjunction) is introduced.  ...  This language, called NP Datalog, captures the power of Datalog with unstratified negation in expressing search and optimization problems. A system prototype implementing NP Datalog is presented.  ...  of unstratified negation.  ... 
arXiv:0911.2785v1 fatcat:seapr5odo5flxmdmkm5lmd25ly

Nonmonotonic Description Logic Programs: Implementation and Experiments [chapter]

Thomas Eiter, Giovambattista Ianni, Roman Schindlauer, Hans Tompits
2005 Lecture Notes in Computer Science  
By virtue of their design, dl-programs fully support encapsulation and privacy of the description logic knowledge base, in the sense that logic programming and description logic inference are technically  ...  These are similar to usual rules in logic programs with negation as failure, but they may also contain queries to L in their bodies.  ...  Roughly speaking, stratified dl-programs are composed of hierarchic layers of positive dl-programs that are linked via default negation (for a formal definition, we refer the reader to [6] ).  ... 
doi:10.1007/978-3-540-32275-7_34 fatcat:7erye4xn5ffrvmgyp3gwlkzj7y

Rules and Ontologies for the Semantic Web [chapter]

Thomas Eiter, Giovambattista Ianni, Thomas Krennwallner, Axel Polleres
2008 Lecture Notes in Computer Science  
The next section provides some preliminaries, including RDF/RDF Schema and Description Logics as well as OWL.  ...  In Section 5, first general issues that come up in combining logic-based rules and ontologies are revisited in more detail; after that, three different generic settings for  ...  As shown in Table 4 , support for (unstratified) negation as failure (NAF) is typical for descendants of logic programming systems and hybrid combination approaches.  ... 
doi:10.1007/978-3-540-85658-0_1 fatcat:x75rrerlzvelbh7vpo6subgzru

Logic programming revisited: logic programs as inductive definitions

Marc Denecker, Maurice Bruynooghe, Victor Marek
2001 ACM Transactions on Computational Logic  
Another line of research developed the view of logic programming as a non-monotonic reasoning formalism strongly related to Default Logic and Auto-epistemic Logic.  ...  In particular, logic programs with negation represent non-monotone inductive definitions.  ...  The first author also wants to thank Danny De Schreye and Eugenia Ternovska for support and comments on earlier versions of the paper.  ... 
doi:10.1145/383779.383789 fatcat:ndazuobvzvfzjf53wm5fnswj2y

Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity [chapter]

Wolfgang Faber, Nicola Leone, Gerald Pfeifer
2004 Lecture Notes in Computer Science  
It is defined by a natural variant of the Gelfond-Lifschitz transformation, and treats aggregate and non-aggregate literals in a uniform way.  ...  This semantics is a fully declarative, genuine generalization of the answer set semantics for disjunctive logic programming (DLP).  ...  Acknowledgements We would like to thank the anonymous reviewers and Michael Gelfond and Vladimir Lifschitz for their useful comments.  ... 
doi:10.1007/978-3-540-30227-8_19 fatcat:mgzdt5pw5nf4fovr3iq5uuhh6u

Combining answer set programming with description logics for the Semantic Web

Thomas Eiter, Giovambattista Ianni, Thomas Lukasiewicz, Roman Schindlauer, Hans Tompits
2008 Artificial Intelligence  
Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies.  ...  For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the  ...  This work was partially supported by the Austrian Science Fund projects P17212-N04 and Z29-N04, by the German Research Foundation under the Heisenberg Programme, the Marie Curie Individual Fellowship HPMF-CT  ... 
doi:10.1016/j.artint.2008.04.002 fatcat:6ljwvnzkkrec3martvmac4cdua

The Web Service Modeling Language WSML: An Overview [chapter]

Jos de Bruijn, Holger Lausen, Axel Polleres, Dieter Fensel
2006 Lecture Notes in Computer Science  
This core language is extended in the directions of Description Logics and Logic Programming in a principled manner with strict layering.  ...  Services, starting from the intersection of Datalog and the Description Logic SHIQ.  ...  This work was funded by the European Commission under the projects ASG, DIP, KnowledgeWeb, and SEKT; by Science Foundation Ireland under Grant No.  ... 
doi:10.1007/11762256_43 fatcat:ae5ffg45lffhzjmgcwfjzhnxz4

Abductive logic programs with penalization: semantics, complexity and implementation

SIMONA PERRI, FRANCESCO SCARCELLO, NICOLA LEONE
2005 Theory and Practice of Logic Programming  
We define a formal model for abduction with penalization over logic programs, which extends the abductive framework proposed by Kakas and Mancarella.  ...  To this end, we design a translation from abduction problems with penalties into logic programs with weak constraints. We prove that this approach is sound and complete.  ...  This work was supported by the European Commission under projects IST-2002-33570 INFOMIX, IST-2001-32429 ICONS, and IST-2001  ... 
doi:10.1017/s1471068404002224 fatcat:pnrzhrek4jddbavuhyslmbprce
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