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
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
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
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)
Predicate Introduction for Logics with Fixpoint Semantics. Part II: Autoepistemic Logic
Fundamenta Informaticae
Predicate introduction under stable and well-founded semantics
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
A Classification Theory Of Semantics Of Normal Logic Programs: Ii. Weak Properties
Fundamenta Informaticae
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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We study the transformation of "predicate introduction" in non-monotonic logics. By this, we mean the act of replacing a complex formula 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. In this paper, we study predicate introduction in the algebraic framework of "approximation theory"; this is a fixpoint theory for nonmonotone operators that generalizes all main semantics of various non-monotonic logics, including logic programming, default logic and autoepistemic logic. We prove an abstract, algebraic equivalence result in this framework. This can then be used to show that, in logic programming, certain transformations are equivalence preserving under, among others, both the stable and well-founded semantics. Based on this result, we develop a general method of eliminating universal quantifiers in the bodies of rules. Our work is, however, also applicable beyond logic programming. In a companion paper, we demonstrate this, by using the same algebraic results to derive a transformation which reduces the nesting depth of the modal operator K in autoepistemic logic.