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Computing Maximally Satisfiable Terminologies for the Description Logic ALC with Cyclic Definitions

Kevin Lee, Thomas Andreas Meyer, Jeff Z. Pan, Richard Booth
2006 International Workshop on Description Logics  
Note that clash-detection is not a condition for termination. Also, we assume that all concept assertions are in negation normal form.  ...  To compute the A-MSSs, simply find the prime implicants of the clash-resolve formula.  ... 
dblp:conf/dlog/LeeMPB06 fatcat:45jdvnwkyfcvlnc66fayswfwze

Concept Implicate Tree for Description Logics

Tingting Zou, Ansheng Deng
2015 Open Cybernetics and Systemics Journal  
In this paper, we first introduced the concept implicate tree for the ALC concept.  ...  Then, we present an algorithm, which can transform an ALC concept into an equivalent concept implicate tree, and proved that each branch of the tree is an implicate of this concept.  ...  Moreover, Bienvenu proposed the prime implicate normal form for ALC concepts, and concluded that the queries of such forms are based on polynomial time [25] .  ... 
doi:10.2174/1874110x01509012545 fatcat:4ihrid3zirayppy4toj73bbpoq

Explaining Subsumption by Optimal Interpolation [chapter]

Stefan Schlobach
2004 Lecture Notes in Computer Science  
We provide definitions for optimal interpolation and an algorithm based on Boolean minimisation of concept-names in a tableau proof for ALC-satisfiability.  ...  For the explanation of subsumption we search for particular concepts because of their syntactic and semantic properties.  ...  This research was supported by the Netherlands Organization for Scientific Research (NWO) under project number 220-80-001. Thanks to the anonymous referees for some valuable comments.  ... 
doi:10.1007/978-3-540-30227-8_35 fatcat:l5mhzxyxxvbqfgay4f57tfrg5i

Clinical Use of Benzodiazepines and Decreased Memory Activation in Anxious Problem Drinkers

Martin Zack, Tony Toneatto, Colin M. MacLeod
1999 Alcoholism: Clinical and Experimental Research  
All Ss had normal or corrected-to-normal vision. Ss knew that the study was not a part of their treatment and that they would be paid $10 for their participation.  ...  Stimulus Conditions for the Lexical Decision Task There were five prime-target test conditions [Negative Affective- Alcohol (NEG-ALC), ALC-NEG, ALC-ALC, NEG-NEG, Categorical- Categorical (CAT-CAT-matched  ... 
doi:10.1111/j.1530-0277.1999.tb04041.x pmid:10029221 fatcat:xuzqxvf7tbeezfww5cw3ogtc4q

Linkless Normal Form for $\mathcal{ALC}$ Concepts and TBoxes [chapter]

Claudia Schon
2011 Lecture Notes in Computer Science  
In this paper we introduce a normal form for ALC concepts and TBoxes called linkless normal form.  ...  We further show a way to approximate a TBox by a concept in linkless normal form, which allows us to check certain subsumptions efficiently.  ...  Recently, [5] introduced a normal form called prime implicate normal form for ALC concepts which allows a polynomial subsumption check.  ... 
doi:10.1007/978-3-642-24455-1_29 fatcat:ggzlzdxtmvcptoavemmq2mvtya

Non-Standard Reasoning Services for the Debugging of Description Logic Terminologies

Stefan Schlobach, Ronald Cornet
2003 International Joint Conference on Artificial Intelligence  
We provide complete algorithms for unfoldable ACC-TBoxes based on minimisation of axioms using Boolean methods for minimal unsatisfiability-presening sub-TBoxes, and an incomplete bottom-up method for  ...  Current Description Logic reasoning systems provide only limited support for debugging logically erroneous knowledge bases.  ...  The idea is to use prime implicants of A prime implicant is the smallest conjunction of literals 5 implying [Quine, 1952] .  ... 
dblp:conf/ijcai/SchlobachC03 fatcat:mpgu3bmt6zh5veevzndwqzip4q

Nonmonotonic Reasoning in Description Logic by Tableaux Algorithm with Blocking

Jaromir Malenko, Petr Stepánek
2012 International Workshop on Description Logics  
We discuss the problems with representation of a model for an MKNF-DL theory.  ...  This blocking technique allows for reasoning about a larger class of MKNF-DL theories than previous approaches.  ...  However the difference between the definitions has no implications for the tableaux algorithm, since the algorithm considers the flatten normal forms of formulae (created in preprocessing stage).  ... 
dblp:conf/dlog/MalenkoS12 fatcat:xl3gjrqx3fh7zl3r77vax4bebq

Interpretability assessment of fuzzy knowledge bases: A cointension based approach

C. Mencar, C. Castiello, R. Cannone, A.M. Fanelli
2011 International Journal of Approximate Reasoning  
Linguistic representation of knowledge is a major issue when fuzzy rule based models are acquired from data by some form of empirical learning.  ...  Implicit semantics calls for a representation of user's knowledge which is difficult to externalise.  ...  For each prime implicant in the PRIME-set, we select the implicant covering the greatest number of rows of the ON-set.  ... 
doi:10.1016/j.ijar.2010.11.007 fatcat:t6ctdrtd55extbeohcs4nfewxq

Prime Implicates and Prime Implicants: From Propositional to Modal Logic

M. Bienvenu
2009 The Journal of Artificial Intelligence Research  
While the paper focuses on the logic K, all of our results hold equally well for multi-modal K and for concept expressions in the description logic ALC.  ...  To this end, we provide sound and complete algorithms for generating and recognizing prime implicates, and we show the prime implicate recognition task to be PSPACE-complete.  ...  A natural idea would be to use our selected definition of prime implicate to define in an analogous manner a notion of prime implicate normal form for K formulae.  ... 
doi:10.1613/jair.2754 fatcat:ny3t7nartrdtbaac4azohasmvu

Connection-minimal Abduction in EL via Translation to FOL – Technical Report [article]

Fajar Haifani, Patrick Koopmann, Sophie Tourret, Christoph Weidenbach
2022 arXiv   pre-print
Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates.  ...  We consider TBox abduction in the lightweight description logic EL, where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions.  ...  Since T is not in normal form, we must normalize it before the translation.  ... 
arXiv:2205.08449v2 fatcat:3wssdt57erbjjhk3bdpqrrueou

Towards Constructive DL for Abstraction and Refinement

Michael Mendler, Stephan Scheele
2009 Journal of automated reasoning  
We introduce a constructive version of ALC, called cALC, for which we give a sound and complete Hilbert axiomatisation and a Gentzen tableau calculus showing finite model property and decidability.  ...  Acknowledgements We would like to thank the anonymous reviewers for their helpful comments. We also acknowledge the support by the German Research Council (DFG).  ...  On the other hand it is easy to show that concepts in negation normal form (NNF) coincide in ALC and cALC.  ... 
doi:10.1007/s10817-009-9151-8 fatcat:e7hdit7wsbb7fpl6n3l6se7rvm

Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability

Liangda Fang, Kewen Wang, Zhe Wang, Ximing Wen
One technique of tackling the intractability is to identify a fragment called a normal form of multiagent logics such that it is expressive but tractable for reasoning tasks such as entailment checking  ...  In this paper, we first introduce a notion of logical separability and then define a novel disjunctive normal form SDNF for the multiagent logic Kn, which overcomes some shortcomings of existing approaches  ...  Acknowledgments We are grateful to Yongmei Liu, Dacheng Wen and Fang Lv for their helpful discussions on the paper.  ... 
doi:10.1609/aaai.v33i01.33012817 fatcat:4f6dwrvdfnbwtmn5zyt6qmsozy

Knowledge Compilation in Multi-Agent Epistemic Logics [article]

Liangda Fang and Kewen Wang and Zhe Wang and Ximing Wen
2018 arXiv   pre-print
In this paper, by employing logical separability, we propose an approach to knowledge compilation for the logic Kn by defining a normal form SDNF.  ...  The property of logical separability allows to decompose a formula into some of its subformulas and thus modular algorithms for various reasoning tasks can be developed.  ...  Bienvenu (2008) introduced prime implicate normal forms (PINFs) for ALC.  ... 
arXiv:1806.10561v2 fatcat:rdzrkai5qjhqpje7t5r35gakzm

Debugging Incoherent Terminologies

Stefan Schlobach, Zhisheng Huang, Ronald Cornet, Frank van Harmelen
2007 Journal of automated reasoning  
We define a number of new non-standard reasoning services to explain incoherence through pinpointing, and we present algorithms for all of these services.  ...  For one of the core tasks of debugging, the calculation of minimal unsatisfiability preserving sub-terminologies, we developed two different algorithms, one implementing a bottom-up approach using support  ...  Acknowledgements We would like to thank the anonymous referees for their detailed, knowledgable and thus very valuable comments.  ... 
doi:10.1007/s10817-007-9076-z fatcat:omgqaeni75hbzdynu3ldkdq7ae

Simplifying Description Logic Ontologies [chapter]

Nadeschda Nikitina, Sven Schewe
2013 Lecture Notes in Computer Science  
classes of concepts.  ...  While this looks like a bad news result, we also provide a heuristic technique for minimizing TBoxes.  ...  One of such normal forms proposed in description logics is the prime implicates normal form for ALC ontologies [4] .  ... 
doi:10.1007/978-3-642-41335-3_26 fatcat:ckohynbxzfgfbctukwsee7vace
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