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The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

S. Tobies
2000 The Journal of Artificial Intelligence Research  
We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts.  ...  This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals.  ... 
doi:10.1613/jair.705 fatcat:a6cemsgibfbaxnn75hdnzgt6fy

Parallelizing Algebraic Reasoning for the Description Logic SHOQ

Jocelyne Faddoul, Wendy MacCaull
2013 Canadian Semantic Web Symposium  
ACKNOWLEDGMENT The first author is an ACEnet Postdoctoral Fellow, and gratefully acknowledges support from Atlantic Canada's HPC Consortium; the second author acknowledges support from NSERC and ACOA.  ...  of complex ontologies relying on the use of nominals and qualified cardinality restrictions [16] , [7] .  ...  Hybrid algebraic reasoning has been investigated in the context of optimizing reasoning with ontologies where the expressivity is rich enough to include qualified cardinality restrictions and nominals.  ... 
dblp:conf/csws/FaddoulM13 fatcat:7skri2lxdfglppu4x4vselc34q

OWL DL vs. OWL flight

Jos de Bruijn, Rubén Lara, Axel Polleres, Dieter Fensel
2005 Proceedings of the 14th international conference on World Wide Web - WWW '05  
In this paper we present OWL Flight, which is loosely based on OWL, but the semantics is grounded in Logic Programming rather than Description Logics, and it borrows the constraint-based modeling style  ...  We analyze the modeling paradigms of OWL DL and OWL Flight, as well as reasoning tasks supported by both languages.  ...  Acknowledgement This work has been supported by the European Commission under the projects DIP, Knowledge Web, InfraWebs, SEKT, SWWS, ASG and Esperonto; by the Science Foundation Ireland under the DERI-Lion  ... 
doi:10.1145/1060745.1060836 dblp:conf/www/BruijnLPF05 fatcat:nijmne2rfbfgzh2srzanlkv2km

Reasoning about Relation Based Access Control

Alessandro Artale, Bruno Crispo, Fausto Giunchiglia, Fatih Turkmen, Rui Zhang
2010 2010 Fourth International Conference on Network and System Security  
of the underlying Description Logic.  ...  Under this model, we discuss in this paper how to formalize typical access control policies with Description Logics.  ...  THE DESCRIPTION LOGIC ALCQIBO The logic ALCQIBO extends the description logic ALC [7] with qualified cardinalities, inverse roles, nominals and Boolean for roles (see [8] , [9] , [10] for extensions  ... 
doi:10.1109/nss.2010.76 dblp:conf/nss/ArtaleCGTZ10 fatcat:m5axizilbfdqje5ljjekakgc7u

Inference in Probabilistic Ontologies with Attributive Concept Descriptions and Nominals

Rodrigo Bellizia Polastro, Fábio Gagliardi Cozman
2008 International Semantic Web Conference  
This paper proposes a probabilistic description logic that combines (i) constructs of the well-known ALC logic, (ii) probabilistic assertions, and (iii) limited use of nominals.  ...  We show how inference can be conducted in crALC and present examples with real ontologies that display the level of scalability of our proposals.  ...  Acknowledgements This work was partially funded by FAPESP (04/09568-0); the first author is supported by HP Brazil R&D.; the second author is partially supported by CNPq.  ... 
dblp:conf/semweb/PolastroC08 fatcat:glzo2fjiebfthadubs7ugeb47y

Optimizing Algebraic Tableau Reasoning for SHOQ: First Experimental Results

Jocelyne Faddoul, Volker Haarslev
2010 International Workshop on Description Logics  
Motivation Nominals play an important role in Description Logics (DLs) as they allow one to express the notion of identity and enumeration; nominals must be interpreted as singleton sets.  ...  The cardinality of Eye Color is restricted to have at most 5 instances, i.e., the abovementioned nominals.  ...  With SHOQ we distinguish and encode the following cardinalities: (i) Concepts of the form (≥ nR) and (≤ mR) in the label of a node x express cardinality bounds n and m, respectively, on the set FIL(R,  ... 
dblp:conf/dlog/FaddoulH10 fatcat:gu6j4oukzbdodds3fay3lxzlte

Towards Unveiling the Ontology Key Features Altering Reasoner Performances [article]

Nourhène Alaya and Sadok Ben Yahia and Myriam Lamolle
2015 arXiv   pre-print
Reasoning with ontologies is one of the core fields of research in Description Logics.  ...  A variety of efficient reasoner with highly optimized algorithms have been developed to allow inference tasks on expressive ontology languages such as OWL(DL).  ...  In the remainder, we first recall the basics of OWL language and the Description Logics and then, we remind the main concepts of reasoning with ontologies.  ... 
arXiv:1509.08717v1 fatcat:2blv2wcflbetzop7vnurd7ijuy

Classifying Ontologies

Fábio Natanael Kepler, Christian Paz-Trillo, Joselyto Riani, Márcio Moretto Ribeiro, Karina Valdivia Delgado, Leliane Nunes de Barros, Renata Wassermann
2006 Workshop on Ontologies and their Applications  
During the development of an ontology it may be important to know which is the logic underlying that particular ontology, so that the developer knows what the expected complexity of reasoning over it will  ...  In this paper, we first present an ontology that describes several description logics and then two different classifiers that were implemented using our ontology.  ...  Acknowledgements: We would like to thank André Casado Castaño, Andréia Machion and George Henrique Silva for helping with the development of the tools.  ... 
dblp:conf/wonto/KeplerPRRDBW06 fatcat:rnlsdnxetbeftpguizafm4ym3i

Using Description Logics in Relation Based Access Control

Rui Zhang, Alessandro Artale, Fausto Giunchiglia, Bruno Crispo
2009 International Workshop on Description Logics  
Under this model, we discuss in this paper how to formalize with Description Logics the typical authorization problems of access control together with the enforcement of an important security property:  ...  Separation of Duties (SoD) and some high level security policies about the composition of those subjects on which to separate the duties.  ...  The Description Logic ALCQIBO The logic ALCQIBO extends the description logic ALC [1] with qualified cardinalities, inverse roles, nominals and Boolean for roles (see [16, 14, 13] for extensions of  ... 
dblp:conf/dlog/ZhangAGC09 fatcat:icgmuwvzqral5dizxbeg7ofruq

Handling Non-determinism with Description Logics using a Fork/Join Approach

Jocelyne Faddoul, Wendy MacCaull
2015 International Journal of Networking and Computing  
The increasing use of Ontologies, formulated using expressive Description Logics, for time sensitive applications necessitates the development of fast (near realtime) reasoning tools.  ...  We implement a fork/join parallel framework into our tableau-based algebraic reasoner, which handles qualified cardinality restrictions and nominals using in-equation solving.  ...  We plan to extend this work to handle the full expressivity of the DL SHOQ, where the complexity of reasoning due to the interaction between nominals (O) and qualified cardinality restrictions (Q) might  ... 
doi:10.15803/ijnc.5.1_61 fatcat:mdnzhhm5qngrdiv6kz67f22grq

Hybrid Logics and Ontology Languages

Ian Horrocks, Birte Glimm, Ulrike Sattler
2007 Electronical Notes in Theoretical Computer Science  
Description Logics (DLs) are a family of logic based knowledge representation formalisms.  ...  However, recent work has shown that this feature could play a very useful role in query answering, where the syntactic structure of queries means that the occurrence of state variables is restricted in  ...  Reasoning with Nominals A key motivation for basing OWL DL on Description Logics was in order to exploit both theoretical results and implemented DL reasoning systems.  ... 
doi:10.1016/j.entcs.2006.11.022 fatcat:4p2bri54zfd75ewx6kqizy34cm

Expressive description logics via SAT

Francis Gasse, Volker Haarslev
2009 Proceedings of the 7th International Workshop on Satisfiability Modulo Theories - SMT '09  
Description logics are an expressive subset of first-order logic with high complexity reasoning that could benefit from this approach.  ...  In this paper, we present a SMT-based description logic reasoner, its reasoning techniques, architecture, and some first experimental results.  ...  Description Logics (DLs) [BCM + 03] are an expressive subset of first order logic.  ... 
doi:10.1145/1670412.1670417 fatcat:zdvnfgjwqvehpkze2y2ies4rni

Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints

Franz Baader, Bartosz Bednarczyk, Sebastian Rudolph
2019 International Workshop on Description Logics  
This shows that the more expressive number restrictions do not increase the complexity of reasoning since reasoning in ALCQ has the same complexity [17, 19] .  ...  We consider an expressive description logic (DL) in which the global and local cardinality constraints introduced in previous papers can be mixed.  ...  Acknowledgements Bartosz Bednarczyk was supported by the Polish Ministry of Science and Higher Education program "Diamentowy Grant" no. DI2017 006447.  ... 
dblp:conf/dlog/BaaderBR19 fatcat:tc2h7f4imjhtrnvel7zhbd6dcy

Syllogistic Knowledge Bases with Description Logic Reasoners

Ersin Cine
2018 2018 3rd International Conference on Computer Science and Engineering (UBMK)  
Firstly, we formally define a practical family of SLs with different levels of expressivity, including a logic which has recently been introduced for automated reasoning.  ...  Finally, we propose a framework for knowledge representation in SLs and link it to sound and complete DL reasoners for automated deduction.  ...  Our SLs are defined with syntactic restrictions applied on this logic. Table I shows definitions of these logics. B. Semantics Let C and D be complex terms.  ... 
doi:10.1109/ubmk.2018.8566535 fatcat:l2o2fpvxgjgnfovczzdoizhtsu

Reducing OWL Entailment to Description Logic Satisfiability [chapter]

Ian Horrocks, Peter F. Patel-Schneider
2003 Lecture Notes in Computer Science  
We show how to reduce ontology entailment for the OWL DL and OWL Lite ontology languages to knowledge base satisfiability in (respectively) the SHOIN (D) and SHIF(D) description logics.  ...  Because of the semantic restrictions in OWL DL, metaclasses and other notions that do not fit into the description logic semantic framework can be ignored.  ...  The abstract syntax for OWL DL has classes and data ranges, which are analogues of concepts and concrete datatypes in description logics, and axioms and facts, which are analogues of axioms in description  ... 
doi:10.1007/978-3-540-39718-2_2 fatcat:gdcjatae2vhixbmmfyyrru2h3u
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