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A Deduction Method Complete for Refutation and Finite Satisfiability
 In Proc. 6th European Workshop on Logics in Artificial Intelligence, LNAI
, 1998
"... . Database and Artificial Intelligence applications are briefly discussed and it is argued that they need deduction methods that are not only refutation complete but also complete for finite satisfiability. A novel deduction method is introduced for such applications. Instead of relying on Skolemiza ..."
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Cited by 20 (4 self)
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. Database and Artificial Intelligence applications are briefly discussed and it is argued that they need deduction methods that are not only refutation complete but also complete for finite satisfiability. A novel deduction method is introduced for such applications. Instead of relying on Skolemization, as most refutation methods do, the proposed method processes existential quantifiers in a special manner which makes it complete not only for refutation, but also for finite satisfiability. A main contribution of this paper is the proof of these results. Keywords: Artificial Intelligence, Expert Systems, Databases, Automated Reasoning, Finite Satisfiability. 1 Introduction For many applications of automated reasoning, the tableaux methods [32, 16, 34, 18] have the following advantages: They not only detect unsatisfiability but also generate models; they are close to common sense reasoning, hence easy to enhance with an explanation tool; and they are quite easy to adapt to the special...
Semantically Guided Theorem Proving for Diagnosis Applications
, 1997
"... In this paper we demonstrate how general purpose automated theorem proving techniques can be used to solve realistic modelbased diagnosis problems. For this ..."
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Cited by 20 (6 self)
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In this paper we demonstrate how general purpose automated theorem proving techniques can be used to solve realistic modelbased diagnosis problems. For this
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 ..."
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Cited by 19 (5 self)
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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.
Abductive Coreference by Model Construction
 JOURNAL OF LANGUAGE AND COMPUTATION
, 1999
"... In this paper, we argue that the resolution of anaphoric expressions in an utterance is essentially an abductive task following [HSAM93] who use a weighted abduction scheme on horn clauses to deal with reference. We give a semantic representation for utterances containing anaphora that enables us to ..."
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Cited by 16 (2 self)
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In this paper, we argue that the resolution of anaphoric expressions in an utterance is essentially an abductive task following [HSAM93] who use a weighted abduction scheme on horn clauses to deal with reference. We give a semantic representation for utterances containing anaphora that enables us to compute possible antecedents by abductive inference. We extend the disjunctive model construction procedure of hyper tableaux [BFN96, Kuh97] with a clause transformation turning the abductive task into a model generation problem and show the completeness of this transformation with respect to the computation of abuctive explanations. This abductive inference is applied to the resolution of anaphoric expressions in our general model constructing framework for incremental discourse representation [Kuh99] which we argue to be useful for computing information updates from natural language utterances [Vel96].
Hyperresolution for guarded formulae
 J. Symbolic Computat
, 2000
"... Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolutio ..."
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Cited by 15 (9 self)
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Abstract. This paper investigates the use of hyperresolution as a decision procedure and model builder for guarded formulae. In general hyperresolution is not a decision procedure for the entire guarded fragment. However we show that there are natural fragments which can be decided by hyperresolution. In particular, we prove decidability of hyperresolution with or without splitting for the fragment GF1 − and point out several ways of extending this fragment without loosing decidability. As hyperresolution is closely related to various tableaux methods the present work is also relevant for tableaux methods. We compare our approach to hypertableaux, and mention the relationship to other clausal classes which are decidable by hyperresolution. 1
User Profiles and Matchmaking on Mobile Phones
"... Abstract. During the past few years mobile phones have become an ubiquitous companion. In parallel the semantic web provides enabling technologies to annotate and match information with a user’s interests. In this paper the necessary definitions and optimizations of annotations and profiles are give ..."
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Cited by 10 (1 self)
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Abstract. During the past few years mobile phones have become an ubiquitous companion. In parallel the semantic web provides enabling technologies to annotate and match information with a user’s interests. In this paper the necessary definitions and optimizations of annotations and profiles are given to make the mobile phone a first class participant of a semantic environment rather than a mere displaying client of services running elsewhere. The implementation of the system – including a first order model generating theorem prover and a description logic interface – renders the idea viable in the real world and even enables explanations within the matchmaking process. The profile does not have to leave the personal device and ensures privacy by doing so. 1
Computing Answers with Model Elimination
, 1997
"... We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry ..."
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Cited by 9 (2 self)
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We demonstrate that theorem provers using model elimination (ME) can be used as answercomplete interpreters for disjunctive logic programming. More specifically, we introduce a mechanism for computing answers into the restart variant of ME. Building on this we develop a new calculus called ancestry restart ME. This variant admits a more restrictive regularity restriction than restart ME, and, as a side effect, it is in particular attractive for computing definite answers. The presented calculi can also be used successfully in the context of automated theorem proving. We demonstrate experimentally that it is more difficult to compute (nontrivial) answers to goals, instead of only proving the existence of answers. Keywords. Automated reasoning; theorem proving; model elimination; logic programming; computing answers. In first order automatic theorem proving one is interested in the question whether a given formula follows logically from a set of axioms. This is a rather artificial t...
Merge Path Improvements for Minimal Model Hyper Tableaux
 In Proc. TABLEAUX’99
, 1999
"... . We combine techniques originally developed for refutational firstorder theorem proving within the clause tree framework with techniques for minimal model computation developed within the hyper tableau framework. This combination generalizes wellknown tableaux techniques like complement split ..."
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Cited by 9 (0 self)
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. We combine techniques originally developed for refutational firstorder theorem proving within the clause tree framework with techniques for minimal model computation developed within the hyper tableau framework. This combination generalizes wellknown tableaux techniques like complement splitting and foldingup/down. We argue that this combination allows for efficiency improvements over previous, related methods. It is motivated by application to diagnosis tasks; in particular the problem of avoiding redundancies in the diagnoses of electrical circuits with reconvergent fanouts is addressed by the new technique. In the paper we develop as our main contribution in a more general way a sound and complete calculus for propositional circumscriptive reasoning in the presence of minimized and varying predicates. 1 Introduction Recently clause trees [6], a data structure and calculus for automated theorem proving, introduced a general method to close branches based on socalle...
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
 Journal of Automated Reasoning
, 2000
"... . Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate bec ..."
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Cited by 8 (0 self)
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. Minimal Herbrand models of sets of firstorder clauses are useful in several areas of computer science, e.g. automated theorem proving, program verification, logic programming, databases, and artificial intelligence. In most cases, the conventional model generation algorithms are inappropriate because they generate nonminimal Herbrand models and can be inefficient. This article describes an approach for generating the minimal Herbrand models of sets of firstorder clauses. The approach builds upon positive unit hyperresolution (PUHR) tableaux, that are in general smaller than conventional tableaux. PUHR tableaux formalize the approach initially introduced with the theorem prover SATCHMO. Two minimal model generation procedures are described. The first one expands PUHR tableaux depthfirst relying on a complement splitting expansion rule and on a form of backtracking involving constraints. A Prolog implementation, named MMSATCHMO, of this procedure is given and its performance on ben...
Tableaux for Diagnosis Applications
, 1997
"... . In [NF96] a very efficient system for solving diagnosis tasks has been described, which is based on belief revision procedures and uses first order logic system descriptions. In this paper we demonstrate how such a system can be rigorously formalized from the viewpoint of deduction by using the ca ..."
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Cited by 7 (0 self)
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. In [NF96] a very efficient system for solving diagnosis tasks has been described, which is based on belief revision procedures and uses first order logic system descriptions. In this paper we demonstrate how such a system can be rigorously formalized from the viewpoint of deduction by using the calculus of hyper tableaux [BFN96]. The benefits of this approach are twofold: first, it gives us a clear logical description of the diagnosis task to be solved; second, as our experiments show, the approach is feasible in practice and thus serves as an example of a successful application of deduction techniques to realworld applications. 1 Introduction In this paper we will demonstrate that model generation theorem proving is very well suited for solving consistencybased diagnosis tasks. According to Reiter ([Rei87]) a simulation model of the technical device under consideration is constructed and is used to predict its normal behavior. By comparing this prediction with the actual behavior ...