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Fixpoint semantics for logic programming  a survey
, 2000
"... The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close para ..."
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Cited by 106 (0 self)
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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and manyvalued logic, lattice theory, game theory, and topology. One source of this richness is the inherent nonmonotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.
The Defining Power of Stratified and Hierarchical Logic Programs
"... We investigate the defining power of stratified and hierarchical logic programs. As an example for the treatment of negative information in the context of these structured programs we also introduce a stratified and hierarchical closedworld assumption. Our analysis tries to relate the defining powe ..."
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Cited by 14 (3 self)
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We investigate the defining power of stratified and hierarchical logic programs. As an example for the treatment of negative information in the context of these structured programs we also introduce a stratified and hierarchical closedworld assumption. Our analysis tries to relate the defining power of stratified and hierarchical programs (with and without an appropriate closedworld assumption) very precisely to notions and hierarchies in classical definability theory. Stratified and hierarchical logic programs are two wellknown and typical candidates of what one may more generally denote as structured programs. In both cases we have to deal with normal logic programs which satisfy certain syntactic conditions with respect to the occurrence of negative literals. Recently they have gained a lot of importance in connection with the search for nice declarative semantics for logic programs and the treatment of negative information in logic programming (e.g., Lloyd [10]). Stratified programs were introduced into logic programming by Apt, Blair, and Walker [2] and van Gelder [17] not long ago. In mathematical logic, however, theories of this kind have been studied for more than 20 years under the general theme of iterated inductive definability. Indeed, stratified programs can be understood as systems for (finitely) iterated inductive definitions where the definition clauses are of very low logical complexity. The notion of hierarchical program (e.g., Clark [6], Shepherdson [15]), on the other hand, is motivated by database theory and tries to reflect the idea of iterated explicit definability by simple principles. From a conceptual point of view we are interested in the relationship between logic programming, inductive definability and equational definability. By making u...
The Relative Complement Problem for HigherOrder Patterns
 Proceedings of the 1999 International Conference on Logic Programming (ICLP'99
, 1999
"... We address the problem of complementing higherorder patterns without repetitions of free variables. Differently from the firstorder case, the complement of a pattern cannot, in general, be described by a pattern, or even by a finite set of patterns. We therefore generalize the simplytyped calcul ..."
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Cited by 2 (2 self)
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We address the problem of complementing higherorder patterns without repetitions of free variables. Differently from the firstorder case, the complement of a pattern cannot, in general, be described by a pattern, or even by a finite set of patterns. We therefore generalize the simplytyped calculus to include an internal notion of strict function so that we can directly express that a term must depend on a given variable. We show that, in this more expressive calculus, finite sets of patterns without repeated variables are closed under complement and unification. Our principal application is the transformational approach to negation in higherorder logic programs. 1 Introduction In most functional and logic programming languages the notion of a pattern, together with the requisite algorithms for matching or unification, play an important role in the operational semantics. Besides unification other problems such as generalization or complement also arise frequently. In this paper w...