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A General Theory of Confluent Rewriting Systems for Logic Programming and its Applications
, 2001
"... Recently, Brass and Dix showed (Journal of Automated Reasoning 20(1), 1998) that the wellfounded semantics WFS can be defined as a conuent calculus of transformation rules. This lead not only to a simple extension to disjunctive programs (Journal of Logic Programming 38(3), 1999), but also to a new ..."
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Cited by 22 (13 self)
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Recently, Brass and Dix showed (Journal of Automated Reasoning 20(1), 1998) that the wellfounded semantics WFS can be defined as a conuent calculus of transformation rules. This lead not only to a simple extension to disjunctive programs (Journal of Logic Programming 38(3), 1999), but also to a new computation of the wellfounded semantics which is linear for a broad class of programs. We take this approach as a starting point and generalize it considerably by developing a general theory of Confluent LPSystems CS. Such a system CS is a rewriting system on the set of all logic programs over a fixed signature L and it induces in a natural way a canonical semantics. Moreover, we show four important applications of this theory: (1) most of the wellknown semantics are induced by confluent LPsystems, (2) there are many more transformation rules that lead to confluent LPsystems, (3) semantics induced by such systems can be used to model aggregation, (4) the new systems can be ...
The APOL System
"... Answer Set Programming (ASP) is a formalism widely used for knowledge representation since its introduction in 1988 by Gelfond and Lifschitz [4]. Nowadays there are powerful implementations of this paradigm, like DLV and Smodels . In order to increment the descriptive power of this tools, ..."
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Cited by 3 (1 self)
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Answer Set Programming (ASP) is a formalism widely used for knowledge representation since its introduction in 1988 by Gelfond and Lifschitz [4]. Nowadays there are powerful implementations of this paradigm, like DLV and Smodels . In order to increment the descriptive power of this tools, several extensions to their languages have been done. For example
A Decision Procedure for Monotone Functions Over . . .
"... This paper presents a practical decision procedure for the unquantified theory of lattices with monotone functions. Specifically, it considers the unquantified language Lmf with the predicates = and and with the operators inf and sup over terms which may involve also uninterpreted function sym ..."
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Cited by 2 (1 self)
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This paper presents a practical decision procedure for the unquantified theory of lattices with monotone functions. Specifically, it considers the unquantified language Lmf with the predicates = and and with the operators inf and sup over terms which may involve also uninterpreted function symbols. Additional predicates expressing increasing and decreasing monotonicity of functions are allowed as well as a predicate for pointwise functions comparison. For a restricted
Aggregation in Functional Query Languages ∗
, 2004
"... We consider the problem of improving the computational efficiency of a functional query language. Our focus is on aggregate operations which have proven to be of practical interest in database querying. Since aggregate operations are typically nonmonotonic in nature, recursive programs making use o ..."
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We consider the problem of improving the computational efficiency of a functional query language. Our focus is on aggregate operations which have proven to be of practical interest in database querying. Since aggregate operations are typically nonmonotonic in nature, recursive programs making use of aggregate operations must be suitably restricted in order that they have a welldefined meaning. In a recent paper we showed that partialorder clauses provide a wellstructured means of formulating such queries. The present paper extends earlier work in exploring the notion of declarative pruning. By “declarative pruning ” we mean that the programmer can specify declarative information about certain functions in the program without altering the meanings of these functions. Using this information, our proposed execution model provides for more efficient program execution. Essentially we require that certain domains must be totallyordered (as opposed to being partiallyordered). Given this information, we show how the search space of solutions can be pruned efficiently. The paper presents examples illustrating the language and its computation model, and also presents a formal operational semantics. 1
Computing Preferred Safe Beliefs
"... We recently proposed a definition of a language for nonmonotonic reasoning based on intuitionistic logic. Our main idea is a generalization of the notion of answer sets for arbitrary propositional theories. We call this extended framework safe beliefs. We present an algorithm, based on the Davis ..."
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We recently proposed a definition of a language for nonmonotonic reasoning based on intuitionistic logic. Our main idea is a generalization of the notion of answer sets for arbitrary propositional theories. We call this extended framework safe beliefs. We present an algorithm, based on the DavisPutnam (DP) method, to compute safe beliefs for arbitrary propositional theories. We briefly discuss some ideas on how to extend this paradigm to incorporate preferences.
1 Universidad de las Americas CENTIA
"... Abstract. The stable semantics has become a prime candidate for knowledge representation and reasoning. The rules associated with propositional logic programs and the stable semantics are not expressive enough to let one write concise optimization programs. We propose an extension to the language o ..."
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Abstract. The stable semantics has become a prime candidate for knowledge representation and reasoning. The rules associated with propositional logic programs and the stable semantics are not expressive enough to let one write concise optimization programs. We propose an extension to the language of logic programs that allows one to express optimization problems in a suitable well. In earlier work we dened the declarative semantics for partial order clauses. The main contribution of our paper is the following: First, we dene the language of our extended paradigm as well as its declarative semantics. Our declarative semantics is based on translating partial order clauses into normal programs and the using the stable semantics as the intended meaning of the original program. Second, we propose an operational semantics for our paradigm. Our experimental results show that our approach is more ecient than using the well known system SMODELS over the translated program. 1
Knowledge Representation Using HighLevel Nonmonotonic Reasoning
"... Abstract. We introduce the new paradigm of HighLevel NonMonotonic reasoning (HLNM). This paradigm is the consolidation of our recent results on disjunctions, sets, explicit and implicit negation, and partialorder clauses. We show how these concepts are integrated in a natural way into the standa ..."
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Abstract. We introduce the new paradigm of HighLevel NonMonotonic reasoning (HLNM). This paradigm is the consolidation of our recent results on disjunctions, sets, explicit and implicit negation, and partialorder clauses. We show how these concepts are integrated in a natural way into the standard logic programming framework. For this purpose, we present several well known examples from the literature that motivate the need of this new paradigm. Finally, we dene a declarative semantics for HLNM reasoning. 1