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Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 281 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
An Overview of Rewrite Rule Laboratory (RRL)
 J. of Computer and Mathematics with Applications
, 1995
"... RRL (Rewrite Rule Laboratory) was originally developed as an environment for experimenting with automated reasoning algorithms for equational logic based on rewrite techniques. It has now matured into a fullfledged theorem prover which has been used to solve hard and challenging mathematical proble ..."
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Cited by 64 (25 self)
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RRL (Rewrite Rule Laboratory) was originally developed as an environment for experimenting with automated reasoning algorithms for equational logic based on rewrite techniques. It has now matured into a fullfledged theorem prover which has been used to solve hard and challenging mathematical problems in automated reasoning literature as well as a research tool for investigating the use of formal methods in hardware and software design. We provide a brief historical account of development of RRL and its descendants, give an overview of the main capabilities of RRL and conclude with a discussion of applications of RRL. Key words. RRL, rewrite techniques, equational logic, discrimination nets 1 Introduction The theorem prover RRL (Rewrite Rule Laboratory) is an automated reasoning program based on rewrite techniques. The theorem prover has implementations of completion procedures for generating a complete set of rewrite rules from an equational axiomatization, associativecommutative mat...
ELAN from a rewriting logic point of view
 Theoretical Computer Science
, 2002
"... ELAN implements computational systems, a concept that combines two first class entities: rewrite rules and rewriting strategies. ELAN can be used either as a logical framework or to describe and execute deterministic as well as nondeterministic rule based processes. With the general goal to make pr ..."
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Cited by 54 (5 self)
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ELAN implements computational systems, a concept that combines two first class entities: rewrite rules and rewriting strategies. ELAN can be used either as a logical framework or to describe and execute deterministic as well as nondeterministic rule based processes. With the general goal to make precise a rewriting logic based semantics of ELAN, this paper has three contributions: a presentation of the concepts of rules and strategies available in ELAN, an expression of rewrite rules with matching conditions in conditional rewriting logic, and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic.
Compiling Language Definitions: The ASF+SDF Compiler
, 1999
"... The ASF+SDF MetaEnvironment is an interactive language development environment... ..."
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Cited by 39 (7 self)
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The ASF+SDF MetaEnvironment is an interactive language development environment...
Promoting Rewriting to a Programming Language: A Compiler for NonDeterministic Rewrite Programs in AssociativeCommutative Theories
, 2001
"... Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation ..."
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Cited by 30 (6 self)
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Firstorder languages based on rewrite rules share many features with functional languages. But one difference is that matching and rewriting can be made much more expressive and powerful by incorporating some builtin equational theories. To provide reasonable programming environments, compilation techniques for such languages based on rewriting have to be designed. This is the topic addressed in this paper. The proposed techniques are independent from the rewriting language and may be useful to build a compiler for any system using rewriting modulo associative and commutative (AC) theories. An algorithm for manytoone AC matching is presented, that works efficiently for a restricted class of patterns. Other patterns are transformed to fit into this class. A refined data structure, namely compact bipartite graph, allows encoding all matching problems relative to a set of rewrite rules. A few optimisations concerning the construction of the substitution and of the reduced term are described. We also address the problem of nondeterminism related to AC rewriting and show how to handle it through the concept of strategies. We explain how an analysis of the determinism can be performed at compile time and we illustrate the benefits of this analysis for the performance of the compiled evaluation process. Then we briefly introduce the ELAN system and its compiler, in order to give some experimental results and comparisons with other languages or rewrite engines.
Term Rewriting for Sale
, 1998
"... Term rewriting has a large potential for industrial applications, but these applications are always larger than one could ever dream of: huge sets of rewrite rules and gigantic terms to rewrite pose interesting challenges for implementors and theoreticians alike. We give a brief overview of the gene ..."
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Cited by 21 (15 self)
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Term rewriting has a large potential for industrial applications, but these applications are always larger than one could ever dream of: huge sets of rewrite rules and gigantic terms to rewrite pose interesting challenges for implementors and theoreticians alike. We give a brief overview of the generation of termrewritingbased tools as done in the Asf+Sdf MetaEnvironment and then we sketch two major applications of term rewriting: transformation of legacy COBOL systems and compilation of Asf+Sdf to C. Based on these experiences we suggest the study of topics that could further advance the use of term rewriting in industrial applications: persistent term databases, generalized LR parsing versus parallel term rewriting, and coordination languages versus strategy languages. It will turn out that we have an "alien" view on research in term rewriting: properties like confluence and termination are of very limited use when selling term rewriting to industry.
Rewriting Extended Regular Expressions
, 1993
"... We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion ..."
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Cited by 19 (1 self)
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We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion of the algebra and develop some termrewriting techniques for constructing logical inferences of valid equations. A shorter version of this paper is to appear in the proceedings of Developments in Language Theory, Univ. of Turku, July 1993, published by World Scientific. The present version has been submitted for publication elsewhere. 1 Introduction In this paper we consider an extended algebra of regular events (languages) on a given alphabet with intersection besides the usual operations (union, concatenation, Kleene star, empty, and the regular unit). This algebra has the structure of a distributive lattice (join is union, meet is intersection) with only monotonic operations. The latte...
Programming with Equations, Subsets, and Relations
 Proceedings of NACLP89
, 1989
"... We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semant ..."
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Cited by 17 (6 self)
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We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semantics of subset assertions incorporate a collect all capability, which is expressed formally by the completion of the program. When used in conjunction with equational assertions, subset assertions serve to define setvalued functions, and the resulting paradigm is called subsetequational programming. We also present the class of stratified subsetequational programs for formalizing the class of closure functions, which are useful in defining various transitiveclosure sets. The declarative and operational semantics of simple and stratified subsetequational programs are the main focus of this paper. The operational semantics of closures is based on memotables (or extension tables). When sub...
Foundations of rulebased query answering
 IN REASONING WEB, INT. SUMMER SCHOOL, LNCS
, 2007
"... This survey article introduces into the essential concepts and methods underlying rulebased query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evalua ..."
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Cited by 15 (8 self)
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This survey article introduces into the essential concepts and methods underlying rulebased query languages. It covers four complementary areas: declarative semantics based on adaptations of mathematical logic, operational semantics, complexity and expressive power, and optimisation of query evaluation. The treatment of these areas is foundationoriented, the foundations having resulted from over four decades of research in the logic programming and database communities on combinations of query languages and rules. These results have later formed the basis for conceiving, improving, and implementing several Web and Semantic Web technologies, in particular query languages such as XQuery or SPARQL for querying relational, XML, and RDF data, and rule languages like the “Rule Interchange Framework (RIF) ” currently being developed in a working group of the W3C. Coverage of the article is deliberately limited to declarative languages in a classical setting: issues such as query answering in FLogic or in description logics, or the relationship of query answering to reactive rules and events, are not addressed.