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Description Logics with Concrete Domains and General Concept Inclusions Revisited (Extended Abstract)

Franz Baader, Jakub Rydval
2020 International Workshop on Description Logics  
Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability [4, 13] .  ...  Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons  ... 
dblp:conf/dlog/BaaderR20 fatcat:jmaxibremrg4vajv7jxljkbvua

Description Logics with Concrete Domains and General Concept Inclusions Revisited [chapter]

Franz Baader, Jakub Rydval
2020 Lecture Notes in Computer Science  
Concrete domains have been introduced in the area of Description Logic to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons  ...  Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability.  ...  We generalize this notion and the decidability result from concrete domains with only binary predicates as in [33] to concrete domains with predicates of arbitrary arity.  ... 
doi:10.1007/978-3-030-51074-9_24 fatcat:qmi3hjmyrjegpkt6d2eozmqaka

Reasoning About General TBoxes with Spatial and Temporal Constraints: Implementation and Optimizations

Matthias Hengel, Sefan Wölfl, Bernhard Nebel
2016 International Workshop on Description Logics  
Indeed, Lutz and Miličic (2007) showed that for the description logic ALC(C) with ω-admissible constraint systems, concept satsifiability with respect to general TBoxes can be decided by an extension of  ...  A feasible approach to this is to consider spatial or temporal constraint systems on concrete domains.  ...  We thank the anonymous reviewers for helpful suggestions and comments. This work was supported by DFG (Transregional Collaborative Research Center SFB/TR 8 Spatial Cognition, project R4-[LogoSpace]).  ... 
dblp:conf/dlog/HengelWN16 fatcat:ld6tlxc3graatf67lg47qycqoq

Matching Semantic Service Descriptions with Local Closed-World Reasoning [chapter]

Stephan Grimm, Boris Motik, Chris Preist
2006 Lecture Notes in Computer Science  
In this paper, we present a framework for annotating Web Services using description logics (DLs), a family of knowledge representation formalisms widely used in the Semantic Web.  ...  We investigate the use of epistemic operators of ADLs in service descriptions, and show how they affect DL inferences in the context of semantic matchmaking.  ...  of capability descriptions and domain ontologies.  ... 
doi:10.1007/11762256_42 fatcat:khyc5yisebcxdhv3fws4gliptm

Pushing the EL Envelope Further

Franz Baader, Carsten Lutz, Sebastian Brandt
2008 W3C Web Ontology Language (OWL) Experiences and Directions Workshop (OWLED)  
We extend the description logic EL ++ with reflexive roles and range restrictions, and show that subsumption remains tractable if a certain syntactic restriction is adopted.  ...  We are grateful to Meng Suntisrivaraporn for discussions and suggestions.  ...  Formally, a TBox is a finite set of constraints, which can be general concept inclusions (GCIs), role inclusions (RIs), domain restrictions (DRs) and range restrictions (RRs).  ... 
dblp:conf/owled/BaaderLB08 fatcat:cb7zz6bb6bdjll5ik2xwiqpl6i

The Description Logic ALCNH R + Extended with Concrete Domains: A Practically Motivated Approach [chapter]

Volker Haarslev, Ralf Möller, Michael Wessel
2001 Lecture Notes in Computer Science  
Prominent language features beyond ALC are number restrictions, role hierarchies, transitively closed roles, generalized concept inclusions and concrete domains.  ...  The paper introduces the description logic ALCN H R + (D) − .  ...  Acknowledgments We would like to thank Carsten Lutz and Ulrike Sattler for thoughtful comment on an earlier version of this report. All deficiencies are due to our own faults, of course.  ... 
doi:10.1007/3-540-45744-5_4 fatcat:lbwx5enntnfqrhuyx5utbiofd4

Absorption for ABoxes

Jiewen Wu, Alexander Hudek, David Toman, Grant Weddell
2014 Journal of automated reasoning  
We present a novel method of evaluating instance queries over description logic knowledge bases that derives from binary absorption.  ...  The method significantly improves the performance of instance checking, and particularly so in cases where a large number of concrete feature values are included.  ...  Concrete domain concepts such as f < k are considered to be a shorthand for (f < g) (g = k), which, together with f = k, may be generalized as (t 1 op t 2 ), where t 1 and t 2 refer to either a concrete  ... 
doi:10.1007/s10817-014-9304-2 fatcat:4zoa6huvqbhcjfl3hmcpfizy2q

A Description Logic Primer [article]

Markus Krötzsch, Frantisek Simancik, Ian Horrocks
2013 arXiv   pre-print
The main concepts and features are explained with examples before syntax and semantics of the DL SROIQ are defined in detail.  ...  This paper provides a self-contained first introduction to description logics (DLs).  ...  This can also be introduced in DLs by so-called concrete domains, i.e., pre-defined interpretation domains.  ... 
arXiv:1201.4089v3 fatcat:nxtgzmacyfgbtfivjhn3iaave4

Web Ontology Reasoning with Datatype Groups [chapter]

Jeff Z. Pan, Ian Horrocks
2003 Lecture Notes in Computer Science  
When providing reasoning services for ontology languages such as DAML+OIL and OWL, it is necessary for description logics to deal with "concrete" datatypes (strings, integers, etc.) as well as "abstract  ...  " concepts and relationships.  ...  Concrete Domains and Datatype Groups As mentioned in Section 1, Description Logic researchers have been working on combining DLs and datatypes for quite a long time, although they might not always have  ... 
doi:10.1007/978-3-540-39718-2_4 fatcat:74fvfgljq5asdjvotoauzrxuim

Semantic DMN: Formalizing Decision Models with Domain Knowledge [chapter]

Diego Calvanese, Marlon Dumas, Fabrizio M. Maggi, Marco Montali
2017 Lecture Notes in Computer Science  
We then consider the case where background knowledge is expressed as an ALC description logic ontology equipped with datatypes, and show that in this setting, all reasoning tasks can be actually decided  ...  In this paper, we overcome these issues, by proposing decision knowledge bases (DKBs), where decisions are modeled in DMN, and domain knowledge is captured by means of first-order logic with datatypes.  ...  supported by the Euregio IPN12 project Knowledge-Aware Operational Support (KAOS), funded by the "European Region Tyrol-South Tyrol-Trentino" (EGTC) under the first call for basic research projects, and  ... 
doi:10.1007/978-3-319-61252-2_6 fatcat:2fghe7afp5do3hcoz7excqrk3a

Revisiting Default Description Logics – and Their Role in Aligning Ontologies [chapter]

Kunal Sengupta, Pascal Hitzler, Krzysztof Janowicz
2015 Lecture Notes in Computer Science  
This work improves upon the previously established results on integrating defaults with description logics (DLs), which were shown to be decidable only when the application of defaults is restricted to  ...  of ontology alignment and ontology-based systems.  ...  This work was supported by the National Science Foundation under award 1017225 "III: Small: TROn-Tractable Reasoning with Ontologies" and award 1440202 "EarthCube Building Blocks: Collaborative Proposal  ... 
doi:10.1007/978-3-319-15615-6_1 fatcat:lxtlcx6rbbanlircy5folrhrom

The Double Move in Meaningful Teaching Revisited [chapter]

Bert van Oers
2019 Cultural-Historical Approaches to Studying Learning and Development  
Although Hedegaard gradually changed her descriptions of the ascendance from the abstract to the concrete into formulations focussing on the interaction between the general (scientific concepts) and the  ...  Therefore, we revisited the idea of ascending from the abstract to the concrete, or shifting from the general to the particular, as starting points for everyday classroom practices.  ... 
doi:10.1007/978-981-13-6826-4_8 fatcat:oqw4n3suancajcg7pasusesjf4

The theory of descriptions revisited

Alberto Peruzzi
1988 Notre Dame Journal of Formal Logic  
Fourman and D. Scott, is presented with reference to sheaves.  ...  An excursus is carried out through the principal steps in the development of the theory of descriptions (TD) from B.  ...  Here one can find a class of formal systems to which pertain both "inclusive" logics (for empty domains) and logics with terms which do not presuppose a denotation.  ... 
doi:10.1305/ndjfl/1093634997 fatcat:ehi3lr73fbhr7aiwzy3tmtugdu

Concept-oriented programming: from classes to concepts and from inheritance to inclusion [article]

Alexandr Savinov
2015 arXiv   pre-print
In this paper, we describe a novel approach to programming, called concept-oriented programming (COP), which generalizes classes and inheritance by introducing concepts and inclusion, respectively.  ...  For the past several decades, programmers have been modeling things in the world with trees using hierarchies of classes and object-oriented programming (OOP) languages.  ...  A concept can be thought of as a border between the internal domain consisting of its sub-concepts and the external domain consisting of all other concepts.  ... 
arXiv:1501.00720v1 fatcat:4ylftqjol5aftpstd2oi6tuxei

Fusions of Description Logics and Abstract Description Systems

F. Baader, C. Lutz, H. Sturm, F. Wolter
2002 The Journal of Artificial Intelligence Research  
To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results  ...  in this general setting.  ...  Then R(a, b) ∈ Γ 1 and thus W, A |= R(a, b). Similarly, Q(a, b) ∈ Γ implies Q(a, b) ∈ Γ 2 and W, A |= Q(a, b). Suppose (a : t) ∈ Γ. Then (a : sur 1 (t)) ∈ Γ 1 and so A 1  ... 
doi:10.1613/jair.919 fatcat:mwax3cm22ffldbvigjgf62tum4
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