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19
NonStandard Reasoning Services for the Debugging of Description Logic Terminologies
, 2003
"... Current Description Logic reasoning systems provide only limited support for debugging logically erroneous knowledge bases. In this paper we propose new nonstandard reasoning services which we designed and implemented to pinpoint logical contradictions when developing the medical terminology DICE. ..."
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Cited by 106 (5 self)
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Current Description Logic reasoning systems provide only limited support for debugging logically erroneous knowledge bases. In this paper we propose new nonstandard reasoning services which we designed and implemented to pinpoint logical contradictions when developing the medical terminology DICE. We provide complete algorithms for unfoldable ACCTBoxes based on minimisation of axioms using Boolean methods for minimal unsatisfiabilitypresening subTBoxes, and an incomplete bottomup method for generalised incoherencepreserving terminologies. 1
DEBUGGING AND REPAIR OF OWL ONTOLOGIES
, 2006
"... With the advent of Semantic Web languages such as OWL (Web Ontology Language), the expressive Description Logic SHOIN is exposed to a wider audience of ontology users and developers. As an increasingly large number of OWL ontologies become available on the Semantic Web and the descriptions in the on ..."
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Cited by 38 (0 self)
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With the advent of Semantic Web languages such as OWL (Web Ontology Language), the expressive Description Logic SHOIN is exposed to a wider audience of ontology users and developers. As an increasingly large number of OWL ontologies become available on the Semantic Web and the descriptions in the ontologies become more complicated, finding the cause of errors becomes an extremely hard task even for experts. The problem is worse for newcomers to OWL who have little or no experience with DLbased knowledge representation. Existing ontology development environments, in conjunction with a reasoner, provide some limited debugging support, however this is restricted to merely reporting errors in the ontology, whereas bug diagnosis and resolution is usually left to the user. In this thesis, I present a complete endtoend framework for explaining, pinpointing and repairing semantic defects in OWLDL ontologies (or in other words, a SHOIN knowledge base). Semantic defects are logical contradictions that manifest as either inconsistent ontologies or unsatisfiable concepts. Where possible, I show extensions to handle related defects such as unsatisfiable roles, unintended entailments and nonentailments,
Certifying solutions to permutation group problems
 In F. Baader, ed, CADE19, LNAI 2741
, 2003
"... Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to pr ..."
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Cited by 13 (0 self)
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Abstract. We describe the integration of permutation group algorithms with proof planning. We consider eight basic questions arising in computational permutation group theory, for which our code provides both answers and a set of certificates enabling a user, or an intelligent software system, to provide a full proof of correctness of the answer. To guarantee correctness we use proof planning techniques, which construct proofs in a humanoriented reasoning style. This gives the human mathematician the necessary insight into the computed solution, as well as making it feasible to check the solution for relatively large groups. 1
Experiments with an Agentoriented Reasoning System
 In In Proc. of KI 2001, volume 2174 of LNAI
, 2001
"... Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise a ..."
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Cited by 12 (8 self)
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Abstract. This paper discusses experiments with an agent oriented approach to automated and interactive reasoning. The approach combines ideas from two subfields of AI (theorem proving/proof planning and multiagent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning agents over the internet. It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higherorder and firstorder theorem provers and computer algebra systems. 1
Proof Development with ΩMEGA
 PROCEEDINGS OF THE 18TH CONFERENCE ON AUTOMATED DEDUCTION (CADE–18), VOLUME 2392 OF LNAI
, 2002
"... ..."
Automatic learning of proof methods in proof planning
 L. J. of the IGPL
, 2002
"... Our research interests in this project are in exploring how automated reasoning systems can learn theorem proving strategies. In particular, we are looking into how a proof planning system (Bundy, 1988) can automatically learn ..."
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Cited by 8 (4 self)
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Our research interests in this project are in exploring how automated reasoning systems can learn theorem proving strategies. In particular, we are looking into how a proof planning system (Bundy, 1988) can automatically learn
English summaries of mathematical proofs
 Second International Joint Conference on Automated Reasoning — Workshop on ComputerSupported Mathematical Theory Development
, 2004
"... Automated theorem proving is becoming more important as the volume of applications in industrial and practical research areas increases. Due to the formalism of theorem provers and the massive amount of information included in machineoriented proofs, formal proofs are difficult to understand withou ..."
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Cited by 4 (0 self)
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Automated theorem proving is becoming more important as the volume of applications in industrial and practical research areas increases. Due to the formalism of theorem provers and the massive amount of information included in machineoriented proofs, formal proofs are difficult to understand without specific training. A verbalisation system, ClamNL, was developed to generate English text from formal representations of inductive proofs, as produced by the Clam proof planner. The aim was to generate natural language proofs that resemble the presentation of proofs found in mathematical textbooks and that contain only the mathematically interesting parts of the proof. 1
ΩMEGA: Computer supported mathematics
 IN: PROCEEDINGS OF THE 27TH GERMAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (KI 2004)
, 2004
"... The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated dedu ..."
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Cited by 3 (3 self)
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The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Classical theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited. The shift
Presenting Proofs with Adapted Granularity ⋆
"... Abstract. When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these prese ..."
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Cited by 3 (2 self)
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Abstract. When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of detail (also called granularity). Often these presentations are neither intended nor suitable for human use. A challenge therefore is to develop user and goaladaptive proof presentation techniques that obey common mathematical practice. We present a flexible and adaptive approach to proof presentation based on classification. Expert knowledge for the classification task can be handauthored or extracted from annotated proof examples via machine learning techniques. The obtained models are employed for the automated generation of further proofs at an adapted level of granularity.