A tractable algorithm for the wellfounded model

In the area of general logic programming (negated atoms allowed in the bodies of rules) and reason maintenance systems, the wellfounded model (first defined by Van Gelder, Ross and Schlipf in 1988) is generally considered to be the declarative semantics of the program. In this paper we present the concise mathematical development of a quadratic-time algorithm for the wellfounded model of propositional general logic programs. This algorithm has essentially been developed by Witteveen in 1990, based on ideas and material by Goodwin (1982).

[1]  A. Visser,et al.  Evaluation, provably deductive equivalence in Heyting's arithmetic of substitution instances of propositional formulas , 1985 .

[2]  Catholijn M. Jonker,et al.  On the semantics of conflict resolution in truth maintenance systems , 1991 .

[3]  Teodor C. Przymusinski.  Every logic program has a natural stratification and an iterated least fixed point model , 1989, PODS.

[4]  Frans Voorbraak,et al.  Generalized Kripke Models for Epistemic Logic , 1991, TARK.

[5]  H. van Ditmarsch.  Abstractie in wiskunde, expertsystemen en argumentatie , 1986 .

[6]  Frans Voorbraak,et al.  A Preferential Model Semantics For Default Logic , 1991, ECSQARU.

[7]  Georg Kreisel,et al.  HILBERT'S PROGRAMME , 1958 .

[8]  Jos L. M. Vrancken.  Parallel Object-Oriented Term Rewriting , 1988, ADT.

[9]  Craig Smorynski,et al.  Arithmetic analogues of McAloon's unique Rosser sentences , 1989, Archive for Mathematical Logic.

[10]  Michiel Doorman.  The existence property in the presence of function symbols , 1988 .

[11]  Marcus Kracht,et al.  Splittings and the finite model property , 1991, Journal of Symbolic Logic.

[12]  P. Rodenburg,et al.  Specification of the Fast Fourier Transform algorithm as a term rewriting system , 1987 .

[13]  J.L.M. Vrancken.  Parallel Object Oriented Terms Rewriting : a first implementation in Pool2 , 1989 .

[14]  Albert Visser.  Kunnen wij elke machine verslaan?: Beschouwingen rondom Lucas' Argument , 1986 .

[15]  M.F.J. Drossaers.  A perceptron network theorem prover for the propositional calculus , 1989 .

[16]  Kenneth A. Ross,et al.  Unfounded sets and well-founded semantics for general logic programs , 1988, PODS.

[17]  P. H. Rodenburg,et al.  Manufacturing a cartesian closed category with exactly two objects out of a C-monoid , 1989, Stud Logica.

[18]  J. C. Mulder,et al.  A modular approach to protocol verification using process algebra , 1986 .

[19]  F. D. Vries,et al.  Applications of constructive logic to sheaf constructions in toposes , 1987 .

[20]  Jan A. Bergstra,et al.  Put and get, primitives for synchronous unreliable message passing , 1985 .

[21]  Teodor C. Przymusinski.  The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics , 1990, Fundam. Inform..

[22]  G. R. Renardel de Lavalette,et al.  Choice in applicative theories , 1989 .

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

[24]  C. F. M. Vermeulen,et al.  Sequence semantics for dynamic predicate logic , 1993, J. Log. Lang. Inf..

[25]  Marcus Kracht,et al.  Prefinitely Axiomatizable Modal and Intermediate Logics , 1993, Math. Log. Q..

[26]  G. R. Renardel de Lavalette,et al.  Strictness analysis for POLYREC, a language with polymorphic and recursive types , 1988 .

[27]  COUNTEREXAMPLES IN APPLICATIVE THEORIES WITH CHOICE , 2022 .

[28]  Albert Visser,et al.  Peano's Smart Children: A Provability Logical Study of Systems with Built-in Consistency , 1986, Notre Dame J. Formal Log..

[29]  Bezem,et al.  Ramsey's theorem and the pigeonhole principle in intuitionistic mathematics , 1993 .

[30]  Edith Hemaspaandra,et al.  Query Optimization Using Rewrite Rules , 1990, RTA.

[31]  Albert Visser,et al.  Explicit Fixed Points in Interpretability Logic , 1989, Stud Logica.

[32]  Frans Voorbraak,et al.  A Computationally Efficient Approximation of Dempster-Shafer Theory , 1988, Int. J. Man Mach. Stud..

[33]  Frans Voorbraak,et al.  The logic of actual obligation. An alternative approach to deontic logic , 1989 .

[34]  G. R. D. Lavalette,et al.  Normalisation of database expressions involving calculations , 1989 .

[35]  Charles Elkan,et al.  Logical Characterizations of Nonmonotonic TMSs , 1989, MFCS.

[36]  Jan A. Bergstra,et al.  Process algebra semantics for queues , 1983 .

[37]  Albert Visser,et al.  Preliminary notes on interpretability logic , 1988 .

[38]  Albert Visser,et al.  A descending hierarchy of reflection principles , 1988 .

[39]  D. van Dalen,et al.  The war of frogs and mice, or the crisis of the Mathematische Annalen , 1987 .

[40]  J. Vrancken,et al.  Parallel object-oriented term rewriting : the booleans , 1988 .

[41]  F. Voorbraak,et al.  Redeneren met onzekerheid in expertsystemen , 1987 .

[42]  Frans Voorbraak,et al.  A Simplification of the Completeness Proofs for Guaspari and Solovay's R , 1986, Notre Dame J. Formal Log..

[43]  E. Barendsen,et al.  Bar recursion versus polymorphism : extended abstract , 1991 .

[44]  F.-J. de Vries,et al.  A functional program for Gaussian Elimination , 1987 .

[45]  Gerard R. Renardel de Lavalette.  Strictness Analysis via Abstract Interpretation for Recursively Defined Types , 1992, Inf. Comput..

[46]  Fer-Jan de Vries.  A functional program for the fast Fourier transform , 1988, ACM SIGPLAN Notices.

[47]  G. R. Renardel de Lavalette,et al.  Inductive definitions in COLD-K , 1989 .

[48]  Frans Voorbraak,et al.  The Logic of Objective Knowledge and Rational Belief , 1990, JELIA.

[49]  J. A. Bergstra,et al.  Module algebra for relational specifications , 1986 .

[50]  Marc Bezem,et al.  Strong Termination of Logic Programs , 1991, J. Log. Program..

[51]  F. Voorbraak.  Conditionals, probability, and belief revision , 1989 .

[52]  Albert Visser,et al.  The formalization of Interpretability , 1991, Stud Logica.

[53]  Fer-Jan de Vries,et al.  Intuitionistic Free Abelian Groups , 1988, Math. Log. Q..

[54]  Teodor C. Przymusinski,et al.  Semantic Issues in Deductive Databases and Logic Programs , 1990 .

[55]  Frans Voorbraak,et al.  On the Justification of Dempster's Rule of Combination , 1988, Artif. Intell..

[56]  G. R. Renardel de Lavalette,et al.  Interpolation in natural fragments of intuitionistic propositional logic , 1986 .

[57]  D. van Dalen,et al.  The War of the frogs and the mice, or the crisis of themathematische annalen , 1990 .

[58]  F. Voorbraak,et al.  Tensed intuitionistic logic , 1987 .

[59]  Gerard R. Renardel de Lavalette,et al.  Interpolation in fragments of intuitionistic propositional logic , 1987, Journal of Symbolic Logic.

[60]  Albert Visser.  The unprovability of small inconsistency , 1993, Arch. Math. Log..

[61]  Erik C. W. Krabbe.  Naess's Dichotomy of Tenability and Relevance , 1986 .

[62]  Jan A. Bergstra,et al.  A process creation mechanism in process algebra , 1985 .