Journal of the ACM (JACM)
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning
Logic-based artificial intelligence
Fixpoint semantics for logic programming a survey
Theoretical Computer Science
Uniform semantic treatment of default and autoepistemic logics
Artificial Intelligence
Partial Evaluation and Relevance for Approximations of Stable Semantics
ISMIS '94 Proceedings of the 8th International Symposium on Methodologies for Intelligent Systems
Extending Classical Logic with Inductive Definitions
CL '00 Proceedings of the First International Conference on Computational Logic
Diagnostic reasoning with A-Prolog
Theory and Practice of Logic Programming
Splitting an operator: Algebraic modularity results for logics with fixpoint semantics
ACM Transactions on Computational Logic (TOCL)
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
SAT(ID): satisfiability of propositional logic extended with inductive definitions
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic Programming
Fundamenta Informaticae
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This paper studies the transformation of “predicate introduction”: replacing a complex formula in an existing logic program by a newly defined predicate. From a knowledge representation perspective, such transformations can be used to eliminate redundancy or to simplify a theory. From a more practical point of view, they can also be used to transform a theory into a normal form imposed by certain inference programs or theorems, e.g., through the elimination of universal quantifiers. In this paper, we study when predicate introduction is equivalence preserving under the stable and well-founded semantics. We do this in the algebraic framework of “approximation theory”; this is a fixpoint theory for non-monotone operators that generalizes all main semantics of various non-monotone logics, including Logic Programming, Default Logic and Autoepistemic Logic. We prove an abstract, algebraic equivalence result and then instantiate this abstract theorem to Logic Programming under the stable and well-founded semantics.