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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 ..."
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Cited by 62 (19 self)
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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 ..."
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Cited by 38 (6 self)
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The DavisPutnamLogemannLoveland procedure (DPLL) was introduced in the early
Computing finite models by reduction to functionfree clause logic
 Journal of Applied Logic
, 2007
"... Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT sol ..."
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Cited by 21 (5 self)
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Recent years have seen considerable interest in procedures for computing finite models of firstorder logic specifications. One of the major paradigms, MACEstyle model building, is based on reducing model search to a sequence of propositional satisfiability problems and applying (efficient) SAT solvers to them. A problem with this method is that it does not scale well because the propositional formulas to be considered may become very large. We propose instead to reduce model search to a sequence of satisfiability problems consisting of functionfree firstorder clause sets, and to apply (efficient) theorem provers capable of deciding such problems. The main appeal of this method is that firstorder clause sets grow more slowly than their propositional counterparts, thus allowing for more space efficient reasoning. In this paper we describe our proposed reduction in detail and discuss how it is integrated into the Darwin prover, our implementation of the Model Evolution calculus. The results are general, however, as our approach can be used in principle with any system that decides the satisfiability of functionfree firstorder clause sets. To demonstrate its practical feasibility, we tested our approach on all satisfiable problems from the TPTP library. Our methods can solve a significant subset of these problems, which overlaps but is not included in the subset of problems solvable by stateoftheart finite model builders such as Paradox and Mace4.
A Survey of Decidable FirstOrder Fragments and Description Logics
 Journal of Relational Methods in Computer Science
, 2004
"... The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard tran ..."
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Cited by 9 (2 self)
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The guarded fragment and its extensions and subfragments are often considered as a framework for investigating the properties of description logics. There are also other, some less wellknown, decidable fragments of firstorder logic which all have in common that they generalise the standard translation of to firstorder logic. We provide a short survey of some of these fragments and motivate why they are interesting with respect to description logics, mentioning also connections to other nonclassical logics.
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...
Individual Reuse in Description Logic Reasoning
 In Proc. of the 4th Int. Joint Conf. on Automated Reasoning (IJCAR 2008
, 2008
"... Abstract. Tableau calculi are the stateoftheart for reasoning in description logics (DL). Despite recent improvements, tableaubased reasoners still cannot process certain knowledge bases (KBs), mainly because they end up building very large models. To address this, we propose a tableau calculus ..."
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Cited by 8 (5 self)
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Abstract. Tableau calculi are the stateoftheart for reasoning in description logics (DL). Despite recent improvements, tableaubased reasoners still cannot process certain knowledge bases (KBs), mainly because they end up building very large models. To address this, we propose a tableau calculus with individual reuse: to satisfy an existential assertion, our calculus nondeterministically tries to reuse individuals from the model generated thus far. We present two expansion strategies: one is applicable to the DL ELOH and gives us a worstcase optimal algorithm, and the other is applicable to the DL SHOIQ. Using this technique, our reasoner can process several KBs that no other reasoner can. 1
A Dynamic View on Model Construction for Discourse Interpretation
 In Proc. of ESSLLI '99, Student Session
, 1999
"... In this paper I take a dynamic view in the spirit of the update semantics by Veltman (1996) on the first–order model construction procedure presented by Manthey and Bry (1988). The motivation for this is twofold: Firstly, it turns out that the model construction procedure can be formulated very conc ..."
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Cited by 1 (0 self)
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In this paper I take a dynamic view in the spirit of the update semantics by Veltman (1996) on the first–order model construction procedure presented by Manthey and Bry (1988). The motivation for this is twofold: Firstly, it turns out that the model construction procedure can be formulated very concisely in a dynamic logic framework; and secondly, by a dynamic view on modelbased deduction we gain a method to incorporate reasoning about changes in first–order theorem proving. The dynamic specification of the model construction procedure is applied to a deductive task in computational semantics stated by Blackburn et al. (1998). 16.1
Presenting Herbrand Models with Linguistically Motivated Techniques
 In Proc. of CIMCA99
, 1999
"... Model generation refers to the automatic construction of models for firstorder logical theories and is used for instance to find solutions to logically encoded problem specifications. Handling these results may require an inspection of the generated models for crucial information, which is insuffic ..."
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Cited by 1 (1 self)
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Model generation refers to the automatic construction of models for firstorder logical theories and is used for instance to find solutions to logically encoded problem specifications. Handling these results may require an inspection of the generated models for crucial information, which is insufficiently supported by current simplistic presentation techniques. Improving these methods considerably, we adopt a number of linguistically motivated techniques for this purpose, including filtering out assertions considered inferable by the addressee, and aggregation of assertions sharing information. Through the incorporation of these techniques, presentations focus on interesting portions and differences across models, especially supporting the discovery of flaws in problem specifications. 1 Introduction Model generation refers to the automatic construction of models for firstorder logical theories. The motivation behind model generation is twofold: first, the existence of a model proves t...
Model Generation for NaturalLanguage Semantic Analysis
, 1999
"... . Semantic analysis refers to the analysis of semantic representations by inference on the basis of semantic information and world knowledge. I present some potential applications of model generators and model generation theorem provers in the construction and analysis of naturallanguage semantics ..."
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Cited by 1 (0 self)
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. Semantic analysis refers to the analysis of semantic representations by inference on the basis of semantic information and world knowledge. I present some potential applications of model generators and model generation theorem provers in the construction and analysis of naturallanguage semantics where both the process of model generation and the computed models are valuable sources of information. I discuss Bry and Torge's hyperresolution tableaux calculus EP as an approach to model generation for naturallanguage semantic analysis. 1 Introduction One goal of modern naturallanguage semantics has been to capture the conditions under which a sentence can be uttered truthfully. In logicbased semantic formalisms such as Discourse Representation Theory [17] or Montague Grammar [22], the representations constructed for naturallanguage sentences are logical formulas whose truthconditions are described by their models. The construction of semantic representations requires, amongst oth...