Matching in the Description Logic FL0 with respect to General TBoxes

Baader, Franz; Gil, Oliver Fernández; Marantidis, Pavlos

doi:10.29007/q74p

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…While a negative result for ACUIG would have implied negative results for the two DLs, the methods used to show the positive results for ACUIG are too simple to be useful for FL 0 and EL. For EL, there are some positive results for the case where the TBox satisfies certain cycle-restrictions (Baader et al, 2012), while for FL 0 there are only positive results for matching in the presence of TBoxes (Baader et al, 2018), but none for unification.…”

Section: Resultsmentioning

confidence: 99%

Extensions of unification modulo ACUI

Baader

Marantidis

Mottet

et al. 2019

Math. Struct. Comp. Sci.

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The theory ACUI of an associative, commutative, and idempotent binary function symbol + with unit 0 was one of the first equational theories for which the complexity of testing solvability of unification problems was investigated in detail. In this paper, we investigate two extensions of ACUI. On one hand, we consider approximate ACUI-unification, where we use appropriate measures to express how close a substitution is to being a unifier. On the other hand, we extend ACUI-unification to ACUIG-unification, that is, unification in equational theories that are obtained from ACUI by adding a finite set G of ground identities. Finally, we combine the two extensions, that is, consider approximate ACUI-unification. For all cases we are able to determine the exact worst-case complexity of the unification problem.

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Section: Resultsmentioning

confidence: 99%

Extensions of unification modulo ACUI

Baader

Marantidis

Mottet

et al. 2019

Math. Struct. Comp. Sci.

Self Cite

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“…Finally, quite a number of non-standard reasoning tasks in 28 F. Baader et al FL 0 w.r.t. general TBoxes have recently been investigated (Baader et al 2016(Baader et al , 2018(Baader et al , 2018a(Baader et al , 2018b. The algorithms developed for solving these tasks usually depend on sub-procedures that perform subsumption tests or that use the least functional model directly.…”

Section: Discussionmentioning

confidence: 99%

Efficient TBox Reasoning with Value Restrictions using the wer Reasoner

Baader¹,

Koopmann²,

Michel³

et al. 2021

Theory and Practice of Logic Programming

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The inexpressive Description Logic (DL) ${\cal F}{{\cal L}_0}$ , which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in ${\cal F}{{\cal L}_0}$ w.r.t. general TBoxes is ExpTime-complete, that is, as hard as in the considerably more expressive logic ${\cal A}{\cal L}{\cal C}$ . In this paper, we rehabilitate ${\cal F}{{\cal L}_0}$ by presenting a dedicated subsumption algorithm for ${\cal F}{{\cal L}_0}$ , which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our ${\cal F}{{\cal L}_0}$ wer reasoner, compares very well with that of the highly optimized reasoners. ${\cal F}{{\cal L}_0}$ wer can also deal with ontologies written in the extension ${\cal F}{{\cal L}_ \bot }$ of ${\cal F}{{\cal L}_0}$ with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of ${\cal F}{{\cal L}_0}$ and ${\cal F}{{\cal L}_ \bot }$ .

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“…In rule conflict detection, the reasoning mainly covers two aspects: if the rule conflict arises from the hierarchy of attributes, the key is to validate the CIR that interprets the instance sub-model; if the rule conflict arises from RAR transfer, the key is to verify the consistency between the assertion sets of RAR action and instance sub-models. These reasoning problems are comparable to the satisfiability problem and the consistency detection problem in the DDL [19,20] Definition 10. If the two assertions ℱ 1 and ℱ 2 in instance sub-models ℳ 1 and ℳ 2 that transfer RAR results obey ℱ 1 ⊓ ℱ 2 = ∅, then the two instance sub-models are inconsistent, i.e.…”

Section: Ddl-based Reasoningmentioning

confidence: 99%

Detection of Conflicts Between Resource Authorization Rules in Extensible Access Control Markup Language Based on Dynamic Description Logic

Yang¹,

Tan²

2020

ISI

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For resources in an open environment, the access control rules (ACRs), which are described by extensible access control markup language (XACML), might have conflicts between each other. To improve the rule management, the root causes of rule conflicts must be identified. This paper firstly formally models the resource attributes by dynamic description logic (DDL), and then investigates inference problems like attribute consistency and rule satisfiability by setting up concept, instance and action knowledge bases. Next, DDL-based rule conflict detection algorithms were designed to identify possible rule conflicts. Finally, the feasibility and decidability of the proposed algorithms were verified through experiments on expanded Continue dataset. The research results provide new insights to the detection of conflicts between resource authorization rules (RARs).

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Matching in the Description Logic FL0 with respect to General TBoxes

Cited by 3 publications

References 9 publications

Extensions of unification modulo ACUI

Extensions of unification modulo ACUI

Efficient TBox Reasoning with Value Restrictions using the wer Reasoner

Detection of Conflicts Between Resource Authorization Rules in Extensible Access Control Markup Language Based on Dynamic Description Logic

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