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Elementary sets for logic programs
 In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI
, 2006
"... By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark’s completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the LinZhao theorem remains corr ..."
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Cited by 16 (12 self)
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correct even if we restrict loop formulas to a special class of loops called “elementary loops. ” In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop
Quantifier Elimination in Elementary Set Theory
, 2006
"... In the current paper we provide two methods for quantifier elimination applicable to a large class of formulas of the elementary set theory. The first one adapts the Ackermann method [1] and the second one adapts the fixpoint method of [20]. We show applications of the proposed techniques in the th ..."
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In the current paper we provide two methods for quantifier elimination applicable to a large class of formulas of the elementary set theory. The first one adapts the Ackermann method [1] and the second one adapts the fixpoint method of [20]. We show applications of the proposed techniques
Headelementarysetfree logic programs
 Proceedings of the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’07
, 2007
"... Abstract. The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose th ..."
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Cited by 7 (4 self)
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Abstract. The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose
Abstract A THEOREM PROVER FOR ELEMENTARY SET THEORY
"... We describe a theorem prover for elementary set theory which is based on truth value preserving transformations, and then give an example of the protocol produced by this system when trying to prove the theorem of set theory known as Cantor's Theorem. 1. ..."
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We describe a theorem prover for elementary set theory which is based on truth value preserving transformations, and then give an example of the protocol produced by this system when trying to prove the theorem of set theory known as Cantor's Theorem. 1.
On the complexity of identifying Head Elementary Set Free programs ∗
, 2009
"... Headelementarysetfree programs were proposed in (Gebser et al. 2007) and shown to generalize over headcyclefree programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying headelementarysetfree programs. Thi ..."
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Cited by 2 (0 self)
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Headelementarysetfree programs were proposed in (Gebser et al. 2007) and shown to generalize over headcyclefree programs while retaining their nice properties. It was left as an open problem in (Gebser et al. 2007) to establish the complexity of identifying headelementarysetfree programs
Option Pricing: A Simplified Approach
 Journal of Financial Economics
, 1979
"... This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated Blac ..."
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Cited by 1016 (10 self)
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This paper presents a simple discretetime model for valumg optlons. The fundamental econonuc principles of option pricing by arbitrage methods are particularly clear In this setting. Its development requires only elementary mathematics, yet it contains as a special limiting case the celebrated
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
, 1983
"... For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a patternr ..."
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Cited by 2096 (5 self)
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For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a pattern
Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
 in Conference Record of The TwentySeventh Asilomar Conference on Signals, Systems and Computers
, 1993
"... In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (199 ..."
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Cited by 637 (1 self)
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In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang
A Tableau Calculus for Integrating FirstOrder and Elementary Set Theory Reasoning
, 2000
"... . In this paper we describe an approach to integrate rstorder reasoning with stratied set theory reasoning, resulting into a technique which allows to lift decision procedures for ground theories to 98sentences and combine them also with elementary set constructs, such as union, intersection, n ..."
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Cited by 1 (0 self)
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. In this paper we describe an approach to integrate rstorder reasoning with stratied set theory reasoning, resulting into a technique which allows to lift decision procedures for ground theories to 98sentences and combine them also with elementary set constructs, such as union, intersection
Results 1  10
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4,703