An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics

Baader, Franz; Rydval, Jakub

doi:10.1007/978-3-030-75775-5_14

Cited by 3 publications

(8 citation statements)

References 21 publications

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“…Unfortunately, the definition of convexity given in [11] was ambiguous, and what is really needed in the setting considered in [11] is what we call guarded convexity in [8]. However, in the setting considered in the present paper, where equality is always available in concrete domain restrictions, we will see that convexity rather than guarded convexity is the adequate notion.…”

Section: P-admissible Concrete Domainsmentioning

confidence: 81%

“…In each of these papers, two examples of concrete domains satisfying the respective restrictions were given. To the best of our knowledge, no other ω-admissible or p-admissible concrete domains had been exhibited in the literature before our investigations in [6] and [8]. This appears to be mainly due to the fact that it is not easy to show the conditions required by ω-admissibility or p-admissibility "by hand".…”

Section: Discussionmentioning

confidence: 92%

“…In [11], two p-admissible concrete domains were exhibited, where one of them is based on Q with unary predicates = p , > p and binary predicates + p , =. To the best of our knowledge, since then no other p-admissible concrete domains have been described in the literature before our work in [8]. Similarly, after the publication of [65] and before our work in [6], no new ω-admissible concrete domains were exhibited.…”

Section: Introductionmentioning

confidence: 83%

“…The main contribution of this paper is to develop such tools based on a model-theoretic analysis of the conditions required by these two notions of admissibility. It is based on the conference publications [6] and [8], but differs from them w.r.t. some details and also presents additional results.…”

Section: Introductionmentioning

confidence: 99%

“…To increase readability of the main text, some of the technical proofs have been moved to an appendix. Due to space constraints, some of the results of [6,8] are only cited without proof here.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Baader

Rydval

2022

J Autom Reasoning

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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) when defining concepts. 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. To regain decidability of the DL $$\mathcal {ALC}$$ ALC in the presence of GCIs, quite strong restrictions, in sum called $$\omega $$ ω -admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of $$\omega $$ ω -admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate $$\omega $$ ω -admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield $$\omega $$ ω -admissible concrete domains. This allows us to show $$\omega $$ ω -admissibility of concrete domains using existing results from model theory. When integrating concrete domains into lightweight DLs of the $$\mathcal {EL}$$ EL family, achieving decidability is not enough. One wants reasoning in the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although $$\omega $$ ω -admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into $$\mathcal {ALC}$$ ALC yields decidable DLs.

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Section: P-admissible Concrete Domainsmentioning

confidence: 81%

Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Baader

Rydval

2022

J Autom Reasoning

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First Steps Towards Taming Description Logics with Strings

Demri,

Quaas

2023

Lecture Notes in Computer Science

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We consider the description logic ALCF P pDΣq over the concrete domain DΣ " pΣ ˚, ă, ", p"wq wPΣ ˚q, where ă is the strict prefix order over finite strings in Σ ˚. Using an automata-based approach, we show that the concept satisfiability problem w.r.t. general TBoxes for ALCF P pDΣq is ExpTime-complete for all finite alphabets Σ. As far as we know, this is the first complexity result for an expressive description logic with a nontrivial concrete domain on strings.‹ The second author is supported by the Deutsche Forschungsgemeinschaft (DFG), project 504343613.

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Universal Horn Sentences and the Joint Embedding Property

Bodirsky¹,

Rydval²,

Schrottenloher³

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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The finite models of a universal sentence $\Phi$ in a finite relational signature are the age of a structure if and only if $\Phi$ has the joint embedding property. We prove that the computational problem whether a given universal sentence $\Phi$ has the joint embedding property is undecidable, even if $\Phi$ is additionally Horn and the signature of $\Phi$ only contains relation symbols of arity at most two.

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An Algebraic View on p-Admissible Concrete Domains for Lightweight Description Logics

Cited by 3 publications

References 21 publications

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains

First Steps Towards Taming Description Logics with Strings

Universal Horn Sentences and the Joint Embedding Property

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