Results 1  10
of
83
Hypertableau Reasoning for Description Logics
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 2007
"... We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning ca ..."
Abstract

Cited by 132 (25 self)
 Add to MetaCart
(Show Context)
We present a novel reasoning calculus for the description logic SHOIQ + —a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableaubased reasoning calculi used in stateoftheart reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions—a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over stateoftheart reasoners on several wellknown ontologies.
A FirstOrder Logic DavisPutnamLogemannLoveland Procedure
"... The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early ..."
Abstract

Cited by 38 (6 self)
 Add to MetaCart
The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early
Knowledge Representation with Logic Programs
 DEPT. OF CS OF THE UNIVERSITY OF KOBLENZLANDAU
, 1996
"... In this tutorialoverview, which resulted from a lecture course given by the authors at ..."
Abstract

Cited by 38 (6 self)
 Add to MetaCart
(Show Context)
In this tutorialoverview, which resulted from a lecture course given by the authors at
FDPLL – A FirstOrder DavisPutnamLogemanLoveland Procedure
 CADE17 – The 17th International Conference on Automated Deduction, volume 1831 of Lecture Notes in Artificial Intelligence
, 2000
"... Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and comp ..."
Abstract

Cited by 37 (12 self)
 Add to MetaCart
(Show Context)
Abstract. FDPLL is a directly lifted version of the wellknown DavisPutnamLogemanLoveland (DPLL) procedure. While DPLL is based on a splitting rule for case analysis wrt. ground and complementary literals, FDPLL uses a lifted splitting rule, i.e. the case analysis is made wrt. nonground and complementary literals now. The motivation for this lifting is to bring together successful firstorder techniques like unification and subsumption to the propositionally successful DPLL procedure. At the heart of the method is a new technique to represent firstorder interpretations, where a literal specifies truth values for all its ground instances, unless there is a more specific literal specifying opposite truth values. Based on this idea, the FDPLL calculus is developed and proven as strongly complete. 1
Characterizations of the Disjunctive Wellfounded Semantics: Confluent Calculi and Iterated GCWA
 Journal of Automated Reasoning
, 1997
"... . Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a non ..."
Abstract

Cited by 37 (9 self)
 Add to MetaCart
. Recently Brass and Dix have introduced the semantics DWFS for general disjunctive logic programs. The interesting feature of this approach is that it is both semantically and prooftheoretically founded. Any program \Phi is associated a normalform res(\Phi), called the residual program, by a nontrivial bottomup construction using least fixpoints of two monotonic operators. We show in this paper, that the original calculus, consisting of some simple transformations, has a very strong and appealing property: it is confluent and terminating. This means that all the transformations can be applied in any order: we always arrive at an irreducible program (no more transformation is applicable) and this program is already uniquely determined. Moreover, it coincides with the normalform res(\Phi) of the program we started with. The semantics DWFS can be read off from res(\Phi) immediately. No proper subset of the calculus has these properties  only when we restrict to certain subclasse...
Incremental closure of free variable tableaux
 Proc. Intl. Joint Conf. on Automated Reasoning IJCAR
, 2001
"... Abstract. This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee complete ..."
Abstract

Cited by 35 (6 self)
 Add to MetaCart
Abstract. This paper presents a technique for automated theorem proving with free variable tableaux that does not require backtracking. Most existing automated proof procedures using free variable tableaux require iterative deepening and backtracking over applied instantiations to guarantee completeness. If the correct instantiation is hard to find, this can lead to a significant amount of duplicated work. Incremental Closure is a way of organizing the search for closing instantiations that avoids this inefficiency. 1
Enhancing the MagicSet Method for Disjunctive Datalog Programs
 In Proc. 20th International Conference on Logic Programming (ICLP 04), Springer LNCS 3132
, 2004
"... Abstract. We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the MagicSet optimization technique (originally defined for nondisjunctive programs) to the disjunctive ca ..."
Abstract

Cited by 33 (10 self)
 Add to MetaCart
(Show Context)
Abstract. We present a new technique for the optimization of (partially) bound queries over disjunctive datalog programs. The technique exploits the propagation of query bindings, and extends the MagicSet optimization technique (originally defined for nondisjunctive programs) to the disjunctive case, substantially improving on previously defined approaches. MagicSettransformed disjunctive programs frequently contain redundant rules. We tackle this problem and propose a method for preventing the generation of such superfluous rules during the MagicSet transformation. In addition, we provide an efficient heuristic method for the identification of redundant rules, which can be applied in general, even if MagicSets are not used. We implement all proposed methods in the DLV system – the stateoftheart implementation of disjunctive datalog – and perform some experiments. The experimental results confirm the usefulness of MagicSets for disjunctive datalog, and they highlight the computational gain obtained by our method, which outperforms significantly the previously proposed MagicSet method for disjunctive datalog programs. 1
Representing Ontologies Using Description Logics, Description Graphs, and Rules
 Artificial Intelligence
"... Description logics (DLs) are a family of stateoftheart knowledge representation languages, and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems. Recent ex ..."
Abstract

Cited by 30 (8 self)
 Add to MetaCart
(Show Context)
Description logics (DLs) are a family of stateoftheart knowledge representation languages, and their expressive power has been carefully crafted to provide useful knowledge modeling primitives while allowing for practically effective decision procedures for the basic reasoning problems. Recent experience with DLs, however, has shown that their expressivity is often insufficient to accurately describe structured objects—objects whose parts are interconnected in arbitrary, rather than treelike ways. DL knowledge bases describing structured objects are therefore usually underconstrained, which precludes the entailment of certain consequences and causes performance problems during reasoning. To address this problem, we propose an extension of DL languages with description graphs—a knowledge modeling construct that can accurately describe objects with parts connected in arbitrary ways. Furthermore, to enable modeling the conditional aspects of structured objects, we also extend DLs with rules. We present an indepth study of the computational properties of such a formalism. In particular, we first identify the sources of undecidability of the general, unrestricted formalism. Based on that analysis, we then investigate several restrictions of the general formalism that make reasoning decidable. We present practical evidence that such a logic can be used to model nontrivial structured objects. Finally, we present a practical decision procedure for our formalism, as well as tight complexity bounds. Key words: knowledge representation, description logics, structured objects, ontologies ⋆ This is an extended version of two papers published at WWW 2008 [29] and KR 2008 [28], respectively. ∗ Corresponding author.
Simplification  A general constraint propagation technique for propositional and modal tableaux
, 1998
"... . Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
. Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than DavisPutnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cutrule) but there is another source of inefficiency: the lack of constraint propagation mechanisms. This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the DavisPutnam procedure. The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableauxlike calculi such as DPLL, KE, HARP, hypertableaux, BCP, KSAT. We show its practical impact with experimental results for random 3SAT and the industrial IFIP benchmarks for hardware ve...
Prolegomena to Logic Programming for NonMonotonic Reasoning
"... The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, b ..."
Abstract

Cited by 25 (16 self)
 Add to MetaCart
The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the