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Computing Least Common Subsumers in Description Logics with Existential Restrictions
, 1999
"... Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottomup " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal va ..."
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Cited by 89 (24 self)
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Computing the least common subsumer (lcs) is an inference task that can be used to support the "bottomup " construction of knowledge bases for KR systems based on description logics. Previous work on how to compute the lcs has concentrated on description logics that allow for universal value restrictions, but not for existential restrictions. The main new contribution of this paper is the treatment of description logics with existential restrictions. Our approach for computing the lcs is based on an appropriate representation of concept descriptions by certain trees, and a characterization of subsumption by homomorphisms between these trees. The lcs operation then corresponds to the product operation on trees.
Least Common Subsumers and Most Specific Concepts in a Description Logic with Existential Restrictions and Terminological Cycles
, 2003
"... Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottomup construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attenti ..."
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Cited by 72 (17 self)
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Computing least common subsumers (Ics) and most specific concepts (msc) are inference tasks that can support the bottomup construction of knowledge bases in description logics. In description logics with existential restrictions, the most specific concept need not exist if one restricts the attention to concept descriptions or acyclic TBoxes. In this paper, we extend the notions les and msc to cyclic TBoxes. For the description logic EC (which allows for conjunctions, existential restrictions, and the topconcept), we show that the les and msc always exist and can be computed in polynomial time if we interpret cyclic definitions with greatest fixpoint semantics.
Polynomial time reasoning in a description logic with existential restrictions
 Proc. of the 16th Eur. Conf. on Artificial Intelligence (ECAI
"... Abstract. In the area of Description Logic (DL) based knowledge representation, research on reasoning w.r.t. general terminologies has mainly focused on very expressive DLs. Recently, though, it was shown for the DL EL, providing only the constructors conjunction and existential restriction, that th ..."
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Cited by 40 (2 self)
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Abstract. In the area of Description Logic (DL) based knowledge representation, research on reasoning w.r.t. general terminologies has mainly focused on very expressive DLs. Recently, though, it was shown for the DL EL, providing only the constructors conjunction and existential restriction, that the subsumption problem w.r.t. cyclic terminologies can be decided in polynomial time, a surprisingly low upper bound. In this paper, we show that even admitting general concept inclusion (GCI) axioms and role hierarchies in EL terminologies preserves the polynomial time upper bound for subsumption. We also show that subsumption becomes coNP hard when adding one of the constructors number restriction, disjunction, and ‘allsome’, an operator used in the DL KREP. One implication of the first result is that reasoning over the widely used medical terminology SNOMED is possible in polynomial time. 1
Towards A BroadCoverage Biomedical Ontology Based On Description Logics
, 2003
"... this paper. V 0 ! #"$ &' )* + , . / 0213 124 67 8 9: ;< => ?!@#AB DE F GH I J KL M NPOQORTSU2V X YZ [ \ ]_^ ` \ ]_^ ` aPbcbdfegh ifh jh k lTej dfmnh j_h k o ejdkj_h epfq r sdfm t um pjh u2e sdfm t um pjh ueruct r aPbQbdTeg2h v wx#y{z  }~x{ } wx#y{z ..."
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Cited by 18 (1 self)
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this paper. V 0 ! #"$ &' )* + , . / 0213 124 67 8 9: ;< => ?!@#AB DE F GH I J KL M NPOQORTSU2V X YZ [ \ ]_^ ` \ ]_^ ` aPbcbdfegh ifh jh k lTej dfmnh j_h k o ejdkj_h epfq r sdfm t um pjh u2e sdfm t um pjh ueruct r aPbQbdTeg2h v wx#y{z  }~x{ } wx#y{z  }~x } wx#y_z }~x{ }_ wx#y_z  }~nx } yz x !} y_z x  x{ }{{yw Q Q !# 2  !# _ _ 2Tnc  fcQ fQc #{ { #{ _{ 2 # _{ 2 # _{ 2 # _{ 2 # _{ 2 # Figure 2: Enabling/Disabling Role Propagation in a SEPEncoded Partonomy across partwhole hierarchies is disabled, in the second case it is enabled. As an example (cf. Figure 2), Enteritis is defined as haslocation Intestine , i.e., the range of the relation haslocation is restricted to the Enode of Intestine. This precludes, e.g., the classification of Appendicitis as Enteritis though the Appendix is related to the Intestine via an anatomicalpartof relation. In the `switchon' mode, however, Glomerulonephritis (haslocation Glomerulum ) is classified as Nephritis (has location Kidney ), with Glomerulum being an anatomicalpartof the Kidney. In the same way, PerforationofAppendix is classified as IntestinalPerforation (cf. Hahn et al. for an indepth analysis of these phenomena)
Computational ontologies of parthood, componenthood, and containment
 In: Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence 2005 (IJCAI05). Kaelbling
"... Parthood, componenthood, and containment relations are commonly assumed in biomedical ontologies and terminology systems, but are not usually clearly distinguished from another. This paper contributes towards a unified theory of parthood, componenthood, and containment relations. Our goal in this is ..."
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Cited by 10 (0 self)
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Parthood, componenthood, and containment relations are commonly assumed in biomedical ontologies and terminology systems, but are not usually clearly distinguished from another. This paper contributes towards a unified theory of parthood, componenthood, and containment relations. Our goal in this is to clarify distinctions between these relations as well as principles governing their interrelations. We first develop a theory of these relations in first order predicate logic and then discuss how description logics can be used to capture some important aspects of the first order theory. 1
Restricted RoleValueMaps in a Description Logic with Existential Restrictions and Terminological Cycles
 In Proc. DL’03, http://CEURWS.org/Vol81
, 2003
"... In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usua ..."
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Cited by 9 (1 self)
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In a previous paper we have investigated subsumption in the presence of terminological cycles for the description logic which allows conjunctions, existential restrictions, and the top concept, and have shown that the subsumption problem remains polynomial for all three types of semantics usually considered for cyclic definitions in description logics.
Granular SpatioTemporal Ontologies
, 2003
"... We propose an ontological theory that is powerful enough to describe both complex spatiotemporal processes (occurrents) and the enduring entities (continuants) that participate therein. The theory is divided into two major categories of subtheories: (sub) theories of type SPAN and (sub)theor ..."
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Cited by 8 (6 self)
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We propose an ontological theory that is powerful enough to describe both complex spatiotemporal processes (occurrents) and the enduring entities (continuants) that participate therein. The theory is divided into two major categories of subtheories: (sub) theories of type SPAN and (sub)theories of type SNAP. These theories represent two complementary perspectives on reality and result in distinct though compatible systems of categories. In SNAP we have enduring entities such as substances, qualities, roles, functions; in SPAN we have perduring entities such as processes and their parts and aggregates. We argue that both kinds of ontological theory are required in order to give a nonreductionism account of complex domains of reality.
Subsumption in EL w.r.t. hybrid TBoxes
"... In the area of Description Logic (DL) based knowledge representation, two desirable features of DL systems have as yet been incompatible: firstly, the support of general TBoxes containing general concept inclusion (GCI) axioms, and secondly, nonstandard inference services facilitating knowledge en ..."
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Cited by 1 (0 self)
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In the area of Description Logic (DL) based knowledge representation, two desirable features of DL systems have as yet been incompatible: firstly, the support of general TBoxes containing general concept inclusion (GCI) axioms, and secondly, nonstandard inference services facilitating knowledge engineering tasks, such as buildup and maintenance of terminologies (TBoxes). In order to make nonstandard inferences available without sacrificing the convenience of GCIs, the present paper proposes hybrid TBoxes consisting of a pair of a general TBox F interpreted by descriptive semantics, and a (possibly) cyclic TBox T interpreted by fixpoint semantics. F serves as a foundation of T in the sense that the GCIs in F define relationships between concepts used as atomic concept names in the definitions in T. Our main technical result is a polynomial time subsumption algorithm for hybrid ELTBoxes based on a polynomial reduction to subsumption w.r.t. cyclic ELTBoxes with fixpoint semantics. By virtue of this reduction, all nonstandard inferences already available for cyclic ELTBoxes become available for hybrid ones.
Locality and subsumption testing in EL and
"... Abstract. We show that subsumption problems in EL and related description logics can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras to obtain uniform PTIME decision procedures for ..."
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Abstract. We show that subsumption problems in EL and related description logics can be expressed as uniform word problems in classes of semilattices with monotone operators. We use possibilities of efficient local reasoning in such classes of algebras to obtain uniform PTIME decision procedures for CBox subsumption in EL and extensions thereof. These locality considerations allow us to present a new family of logics which extend EL and EL + with nary roles and/or numerical domains. 1
The Projection Problem for EL Actions
"... Classical action formalisms form a dichotomy regarding their expressive power and computational properties: they are either based on firstorder logic (FOL) and undecidable like the Situation Calculus [13], or decidable but only propositional like STRIPS [8, 7]. In [3, 11], it was proposed to integr ..."
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Classical action formalisms form a dichotomy regarding their expressive power and computational properties: they are either based on firstorder logic (FOL) and undecidable like the Situation Calculus [13], or decidable but only propositional like STRIPS [8, 7]. In [3, 11], it was proposed to integrate description