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Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm [chapter]

Uwe Keller, Stijn Heymans
2008 Lecture Notes in Computer Science  
We present FixIt(ALC), a novel procedure for deciding knowledge base (KB) satisfiability in the Fuzzy Description Logic (FDL) ALC.  ...  To the best of our knowledge it is the first fixpoint-based decision procedure for FDLs, hence introducing a new class of inference procedures into FDL reasoning.  ...  Fuzzy Description Logics (FDLs) [17] extend DLs to represent vague concepts and relations, and as such are very well suited to cover for representing and reasoning with uncertainty, a requirement that  ... 
doi:10.1007/978-3-540-92687-0_18 fatcat:evmugbmvbzgzze3izh7bsrjtyi

Deciding Fuzzy Description Logics by Type Elimination

Uwe Keller, Stijn Heymans
2008 International Semantic Web Conference  
We present a novel procedure FixIt(ALC) for deciding knowledge base satisfiability in the Fuzzy Description Logic (FDL) ALC.  ...  To the best of our knowledge it is the first fixpoint-based decision procedure for FDLs, hence introducing a new class of inference procedures into FDL reasoning.  ...  Fuzzy Description Logics (FDLs) [13] extend DLs to represent vague concepts and relations, and as such are very well suited to cover for representing and reasoning with uncertainty, a requirement that  ... 
dblp:conf/semweb/KellerH08 fatcat:zuvm24e7rvbv5k2dyyb75omnuq

Description logic programs under probabilistic uncertainty and fuzzy vagueness

Thomas Lukasiewicz, Umberto Straccia
2009 International Journal of Approximate Reasoning  
We also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity  ...  Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic Web applications.  ...  We thank the reviewers of this paper and its ECSQARU-2007 preliminary version for their useful and constructive comments, which have helped to improve this work.  ... 
doi:10.1016/j.ijar.2009.03.004 fatcat:yycaw6pcjvcz7j6xtqrv54fbqm

Description Logic Programs Under Probabilistic Uncertainty and Fuzzy Vagueness [chapter]

Thomas Lukasiewicz, Umberto Straccia
2007 Lecture Notes in Computer Science  
We also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity  ...  Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic Web applications.  ...  We thank the reviewers of this paper and its ECSQARU-2007 preliminary version for their useful and constructive comments, which have helped to improve this work.  ... 
doi:10.1007/978-3-540-75256-1_19 fatcat:5d3l2xuh5zdf3h4adltf6y4tjq

Probabilistic RDF

Octavian Udrea, V.S. Subrahmanian, Zoran Majkic
2006 2006 IEEE International Conference on Information Reuse & Integration  
In this paper, we develop a framework called Probabilistic RDF (pRDF for short) -we provide a syntax as well as a model theoretic and fixpoint semantics for acyclic pRDF theories.  ...  We then provide algorithms to efficiently answer queries posed to pRDF ontologies. We have developed a prototype implementation that shows that our algorithms work very well in practice.  ...  This is a reasonable assumption -the main argument is that the expressiveness of RDF is lower than that of most description logic frameworks (which can deal with cyclic ABoxes).  ... 
doi:10.1109/iri.2006.252408 dblp:conf/iri/UdreaSM06 fatcat:kxbuzqwtynbh7dc2mu5yzmkjyu

Computing minimal sets of descriptive conditions for binary data

Radim Belohlavek, Vilem Vychodil
2014 International Journal of General Systems  
We present an example demonstrating usefulness of discovering descriptive conditions and evaluate performance of the algorithm.  ...  In this sense, we look for minimal sets of descriptive conditions for a set of binary attributes.  ...  His academic interests are in the areas of uncertainty and information, fuzzy logic and fuzzy sets, applied algebra and logic, and data analysis and formal concept analysis.  ... 
doi:10.1080/03081079.2014.885166 fatcat:sajadgwp7bcejitg4qt4gkom4u

Reducing Fuzzy Answer Set Programming to Model Finding in Fuzzy Logics [article]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock
2011 arXiv   pre-print
In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.  ...  logics.  ...  Acknowledgment The authors would like to thank the anonymous reviewers for their useful suggestions and remarks.  ... 
arXiv:1104.5133v1 fatcat:aksfbu2tnzgntbwub465in7xhy

Reducing fuzzy answer set programming to model finding in fuzzy logics

JEROEN JANSSEN, DIRK VERMEIR, STEVEN SCHOCKAERT, MARTINE DE COCK
2011 Theory and Practice of Logic Programming  
In this paper, we show how this idea can be extended to fuzzy ASP, paving the wayto implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.  ...  logics.  ...  Acknowledgment The authors would like to thank the anonymous reviewers for their useful suggestions and remarks.  ... 
doi:10.1017/s1471068411000093 fatcat:unnwhgj5ejgyvihdh2oe3l6ibq

Optimal triangular decompositions of matrices with entries from residuated lattices

Radim Belohlavek
2009 International Journal of Approximate Reasoning  
We prove that fixpoints of particular operators associated with I, which are studied in formal concept analysis, are optimal factors for decomposition of I in that they provide us with decompositions I  ...  We describe optimal decompositions of an n m matrix I into a triangular product I ¼ A / B of an n k matrix A and a k m matrix B.  ...  This paper is an extended version of a contribution presented at ROGICS 2008. Support by research plan MSM 6198959214 and by Grant No. 1ET101370417 of GA AV Č R is gratefully acknowledged.  ... 
doi:10.1016/j.ijar.2009.05.006 fatcat:ujyrmzpffnd7xo6wopgathtdpi

Quantitative deduction and its fixpoint theory

M.H. Van Emden
1986 The Journal of Logic Programming  
Logic programming provides a model for rule-based reasoning in expert systems.  ...  The analog of the PROLOG interpreter for quantitative deduction becomes a search of the game tree (= proof tree) using the alpha-beta heuristic well known in game theory. a  ...  We have chosen the Horn clause subset of first-order predicate logic as a well-established, coherent method of world description and reasoning.  ... 
doi:10.1016/0743-1066(86)90003-8 fatcat:3hy3hyppmjg6xbtct6l6x6uhnm

Homogenizing multi-adjoint logic programs

Jesús Medina, Manuel Ojeda-Aciego
2003 European Society for Fuzzy Logic and Technology  
The concept of homogeneous multi-adjoint logic program is introduced, and a procedure to homogenize an arbitrary multi-adjoint logic program is presented.  ...  This procedure is used in [5] as a preprocessing step of the implementation of the fixpoint semantics of multiadjoint programs by using ideas borrowed from neural networks.  ...  a continuous fixpoint semantics was introduced.  ... 
dblp:conf/eusflat/MedinaO03 fatcat:6wb6bw7ttnczredecoxyczpz3m

Page 3188 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
Based on an appropriate stack machine, defined as an evolving algebra, and a functional description of a compiler for a sam- ple language, we give a complete proof of correctness for this technique using  ...  Summary: “A fuzzy Datalog program is a set of Horn formu- lae with uncertainty degrees. The meaning of a program is the fixpoint of consecutive deterministic or nondeterministic transfor- mations.  ... 

Probabilistic description logic programs

Thomas Lukasiewicz
2007 International Journal of Approximate Reasoning  
The main ideas behind it are to add a machine-readable meaning to Web pages, to use ontologies for a precise definition of shared terms in Web resources, to use KR technology for automated reasoning from  ...  Towards this goal, the works [12, 13] have proposed description logic programs (or simply dlprograms), which are of the form KB = (L, P ), where L is a knowledge base in a description logic and P is a  ...  An interesting topic of future research is to further enhance pdl-programs towards a possible use for Web Services.  ... 
doi:10.1016/j.ijar.2006.06.012 fatcat:uwt4uvjzszhula5jh5tzmewz4u

Probabilistic Description Logic Programs [chapter]

Thomas Lukasiewicz
2005 Lecture Notes in Computer Science  
The main ideas behind it are to add a machine-readable meaning to Web pages, to use ontologies for a precise definition of shared terms in Web resources, to use KR technology for automated reasoning from  ...  Towards this goal, the works [12, 13] have proposed description logic programs (or simply dlprograms), which are of the form KB = (L, P ), where L is a knowledge base in a description logic and P is a  ...  An interesting topic of future research is to further enhance pdl-programs towards a possible use for Web Services.  ... 
doi:10.1007/11518655_62 fatcat:2fkh2ijkubhslezjjurq2c3ak4

Practical RDF Schema Reasoning with Annotated Semantic Web Data [chapter]

Carlos Viegas Damásio, Filipe Ferreira
2011 Lecture Notes in Computer Science  
Semantic Web data with annotations is becoming available, being YAGO knowledge base a prominent example.  ...  In this paper we present an approach to perform the closure of large RDF Schema annotated semantic web data using standard database technology.  ...  logic [8] , obtaining the fuzzy RDFS framework in [21] .  ... 
doi:10.1007/978-3-642-25073-6_47 fatcat:o72xzqztfrc5jcx3veuctm5ibq
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