Unification in the Description Logic EL

The Description Logic EL has recently drawn considerable attention since, on the one hand, important inference problems such as the subsumption problem are polynomial. On the other hand, EL is used to define large biomedical ontologies. Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The main result of this paper is that unification in EL is decidable. More precisely, EL-unification is NP-complete, and thus has the same complexity as EL-matching. We also show that, w.r.t. the unification type, EL is less well-behaved: it is of type zero, which in particular implies that there are unification problems that have no finite complete set of unifiers.Comment: 31page

Formal representation of complex SNOMED CT expressions

<p>Abstract</p> <p>Background</p> <p>Definitory expressions about clinical procedures, findings and diseases constitute a major benefit of a formally founded clinical reference terminology which is ontologically sound and suited for formal reasoning. SNOMED CT claims to support formal reasoning by description-logic based concept definitions.</p> <p>Methods</p> <p>On the basis of formal ontology criteria we analyze complex SNOMED CT concepts, such as "Concussion of Brain with(out) Loss of Consciousness", using alternatively full first order logics and the description logic <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1472-6947-8-S1-S9-i1"><m:semantics><m:mrow><m:mi>ℰ</m:mi><m:mi>ℒ</m:mi></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8hmHuKae8NeHWeaaa@37B1@</m:annotation></m:semantics></m:math></inline-formula>.</p> <p>Results</p> <p>Typical complex SNOMED CT concepts, including negations or not, can be expressed in full first-order logics. Negations cannot be properly expressed in the description logic <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1472-6947-8-S1-S9-i1"><m:semantics><m:mrow><m:mi>ℰ</m:mi><m:mi>ℒ</m:mi></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaWenfgDOvwBHrxAJfwnHbqeg0uy0HwzTfgDPnwy1aaceaGae8hmHuKae8NeHWeaaa@37B1@</m:annotation></m:semantics></m:math></inline-formula> underlying SNOMED CT. All concepts concepts the meaning of which implies a temporal scope may be subject to diverging interpretations, which are often unclear in SNOMED CT as their contextual determinants are not made explicit.</p> <p>Conclusion</p> <p>The description of complex medical occurrents is ambiguous, as the same situations can be described as (i) a complex occurrent <it>C </it>that has <it>A </it>and <it>B </it>as temporal parts, (ii) a simple occurrent <it>A' </it>defined as a kind of A followed by some <it>B</it>, or (iii) a simple occurrent <it>B' </it>defined as a kind of <it>B </it>preceded by some <it>A</it>. As negative statements in SNOMED CT cannot be exactly represented without a (computationally costly) extension of the set of logical constructors, a solution can be the reification of negative statments (e.g., "Period with no Loss of Consciousness"), or the use of the SNOMED CT context model. However, the interpretation of SNOMED CT context model concepts as description logics axioms is not recommended, because this may entail unintended models.</p

Optimising Description Logic Subsumption

Effective optimisation techniques can make a dramatic difference in the performance of knowledge representation systems based on expressive description logics. With currently-available desktop computers, systems that incorporate these techniques can effectively reason in description logics with intractable inference. Because of the correspondence between description logics and propositional modal logic, difficult problems in propositional modal logic can be effectively solved using the same techniques