The IDP framework for declarative problem solving

The IDP framework is a declarative problem solving paradigm, in which the computational task is to expand a given finite interpretation of a set of symbols into a model of a given ID-logic theory, a classical logic theory extended with inductive definitions. This framework has been proposed as a general approach for solving finite domain problems. In this paper, we introduce a typed version of the IDP-language, illustrate the use of the framework through some prototypical examples and discuss theoretical and methodological aspects. We also compare the framework to SAT and ASP. Finally, we report on an implementation of IDP.

[1]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[2]  Eugenia Ternovska,et al.  Inductive situation calculus , 2004, Artif. Intell..

[3]  Miroslaw Truszczynski,et al.  Predicate-calculus-based logics for modeling and solving search problems , 2006, TOCL.

[4]  David G. Mitchell,et al.  A Framework for Representing and Solving NP Search Problems , 2005, AAAI.

[5]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[6]  Victor W. Marek,et al.  Logic programming revisited , 2001, ACM Trans. Comput. Log..

[7]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

[8]  Maarten Mariën,et al.  On the Relation Between ID-Logic and Answer Set Programming , 2004, JELIA.

[9]  Maurice Bruynooghe,et al.  Satisfiability Checking for PC(ID) , 2005, LPAR.

[10]  Eugenia Ternovska,et al.  Reducing Inductive Definitions to Propositional Satisfiability , 2005, ICLP.

[11]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[12]  Hector J. Levesque,et al.  Competence in Knowledge Representation , 1982, AAAI.

[13]  Ilkka Niemelä,et al.  Smodels: A System for Answer Set Programming , 2000, ArXiv.

[14]  Han Reichgelt Knowledge representation - an AI perspective , 1991, Tutorial monographs in cognitive science.

[15]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[16]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[17]  Marc Denecker,et al.  Extending Classical Logic with Inductive Definitions , 2000, Computational Logic.