Calculi for Disjunctive Logic Programming

In this paper we investigate relationships between top-down and bottomup approaches to computation with disjunctive logic programs (DLPs). The bottom-up calculus considered, hyper tableaux, is depicted in its ground version and its relation to fixed point approaches from the literature is investigated. For the top-down calculus we use restart model elimination (RME) and show as our main result that hyper tableaux provide a bottom-up semantics for it. This generalizes the well-known result linking the T -operator to SLDresolution for definite programs towards disjunctive programs. Furthermore we discuss that hyper tableaux can be seen as an extension of SLO-resolution.

[1]  Chandrabose Aravindan.  An Abductive Framework for Negation in Disjunctive Logic Programming , 1996, JELIA.

[2]  Jürgen Ebert,et al.  A Declarative Approach to Graph Based Modeling , 1994, WG.

[3]  Peter Baumgartner,et al.  Hyper Tableaux , 1996, JELIA.

[4]  Ilkka Niemell.  A Tableau Calculus for Minimal Model Reasoning Ilkka Niemel a a Tableau Calculus for Minimal Model Reasoning , 1996 .

[5]  Donald W. Loveland,et al.  Near-Horn PROLOG , 1987, ICLP.

[6]  Lee Naish.  Calculi for Disjunctive Logic Programming , 1997 .

[7]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[8]  Peter Baumgartner,et al.  Model Elimination, Logic Programming and Computing Answers , 1995, IJCAI.

[9]  Harro Wimmel.  Fachberichte Informatik on Some Compositional Petri Net Semantics Universitt at Koblenz{landau on Some Compositional Petri Net Semantics , 1995 .

[10]  Donald W. Loveland,et al.  Automated theorem proving: a logical basis , 1978, Fundamental studies in computer science.

[11]  Jorge Lobo,et al.  Foundations of disjunctive logic programming , 1992, Logic Programming.

[12]  Walter Hower,et al.  Constraint Satisfaction - Algorithms and Complexity Analysis , 1995, Inf. Process. Lett..

[13]  F. Stolzenburg,et al.  Analyzing Rule Sets for the Calculation of Banking Fees by a Theorem Prover with Constraints , 1998 .

[14]  Jack Minker,et al.  A Fixpoint Semantics for Disjunctive Logic Programs , 1990, J. Log. Program..

[15]  Jürgen Dix,et al.  A Comparison of STATIC Semantics with D-WFS , 1996 .

[16]  Jürgen Ebert,et al.  Graph Based Modeling and Implementation with EER / GRAL , 1996, ER.

[17]  J. A. Robinson,et al.  Automatic Deduction with Hyper-Resolution , 1983 .

[18]  Ilkka Niemelä.  Implementing Circumscription Using a Tableau Method , 1996, ECAI.

[19]  Stefan Brass,et al.  D-wfs: a Connuent Calculus and an Equivalent Characterization , 1995 .

[20]  J. Minker,et al.  Semantics for disjunctive logic programs , 1989 .

[21]  Ilkka Niemelä,et al.  A Tableau Calculus for Minimal Model Reasoning , 1996, TABLEAUX.

[22]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[23]  NET CASE: Towards a Petri Net Based Technique for the Development of Expert/Database Systems , 1994 .

[24]  Jürgen Dix,et al.  Characterizations of the Stable Semantics by Partial Evaluation , 1994, LPNMR.

[25]  Jürgen Dix,et al.  A general Approach to Bottom-Up Computation of Disjunctive Semantics , 1994, NMELP.

[26]  Ulrich Furbach.  Theory Reasoning in First Order Calculi , 1994, IS/KI.

[27]  Stephan Philippi,et al.  Integration of Integrity Constraints into Object-Oriented Database Schema according to ODMG-93 , 1995 .

[28]  P. Simons.  Eecient Implementation of the Well- Founded and Stable Model Seman- Tics , 1996 .

[29]  Jürgen Dix,et al.  Characterizations and Implementation of Static Semantics of Disjunctive Programs , 1996 .

[30]  Jürgen Dix,et al.  Reducing Disjunctive to Non-Disjunctive Semantics by Shift-Operations , 1996, Fundam. Informaticae.

[31]  Jürgen Dix,et al.  A Disjunctive Semantics Bases on Unfolding and Bottom-Up Evaluation , 1994, GI Jahrestagung.

[32]  Carolina Ruiz,et al.  Model Generation and State Generation for Disjunctive Logic Programs , 1995, J. Log. Program..

[33]  Jürgen Dix,et al.  Logisches Programmieren mit Negation und Disjunktion , 1996, Künstliche Intell..

[34]  Martin Jung,et al.  GTU - A workbench for the development of natural language grammars , 1995 .

[35]  Frieder Stolzenburg,et al.  Membership-Constraints and Complexity in Logic Programming with Sets , 1996, FroCoS.

[36]  J. Ebert,et al.  Querying Graph Structures with GQL , 1996 .

[37]  Gottfried Vossen,et al.  I-Serializability: Generalized Correctness for Transaction-Based Environments , 1997, Inf. Process. Lett..

[38]  Jack Minker,et al.  Bottom-Up Evaluation of Hierarchical Disjunctive Deductive Databases , 1991, ICLP.

[39]  Dieter Zöbel,et al.  PROGRAM TRANSFORMATIONS FOR DISTRIBUTED CONTROL SYSTEMS , 1994 .

[40]  A. Winter.  Generic Support for Understanding Heterogeneous Software Generic Support for Understanding Heterogeneous Software , 1995 .

[41]  Thomas Marx,et al.  NetCASE -- a Petri Net based Method for Database Application Design and Generation , 1995 .

[42]  Peter Baumgartner,et al.  PROTEIN: A PROver with a Theory Extension INterface , 1994, CADE.

[43]  François Bry,et al.  SATCHMO: A Theorem Prover Implemented in Prolog , 1988, CADE.

[44]  Christoph Steigner,et al.  Modelling Timeouts in Protocol Design , 1995 .

[45]  Ulrich Furbach.  Computing Answers for Disjunctive Logic Programs , 1992, JELIA.

[46]  Ralf Hofestädt,et al.  Workshop Parallele Datenverarbeitung im Verbund von Hochleistungs-Workstations , 1994 .