Query Conservative Extensions in Horn Description Logics with Inverse Roles

Jung, Jean Christoph; Lutz, Carsten; Martel, Mauricio; Schneider, Thomas

doi:10.24963/ijcai.2017/155

Cited by 6 publications

(8 citation statements)

References 11 publications

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“…We then consider uniform interpolant existence and conservative extension and show that both problems are undecidable for Q 1 S5 and S5 ALC u . The proof extends a reduction proving undecidability of conservative extensions for FO 2 (with and without equality) from (Jung et al 2017). As a corollary of our proof, we obtain that uniform interpolant existence is undecidable for FO 2 (with and without equality), settling an open problem from (Jung et al 2017).…”

Section: Introductionsupporting

confidence: 67%

“…If in the previous definition we require (b) to hold for all χ with sig(χ) ∩ sig(ϕ) ⊆ sig(ψ), then ϕ is called a strong L-conservative extension of ψ. As observed by (Jung et al 2017), the difference between conservative and strong conservative extensions is closely related to the failure of CIP: if L enjoys CIP, then L-conservative extensions coincide with strong L-conservative extensions. The problem of deciding whether a given ϕ is a (strong) conservative extension of a given ψ will be referred to as (S)CEP.…”

Section: Main Notions and Characterisationsmentioning

confidence: 82%

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Definitions and (Uniform) Interpolants in First-Order Modal Logic

Kurucz¹,

Wolter²,

Zakharyaschev³

2023

Preprint

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We first consider two decidable fragments of quantified modal logic S5: the one-variable fragment Q 1 S5 and its extension S5ALCu that combines S5 and the description logic ALC with the universal role. As neither of them enjoys Craig interpolation or projective Beth definability, the existence of interpolants and explicit definitions of predicateswhich is crucial in many knowledge engineering tasks-does not directly reduce to entailment. Our concern therefore is the computational complexity of deciding whether (uniform) interpolants and definitions exist for given input formulas, signatures and ontologies. We prove that interpolant and definition existence in Q 1 S5 and S5ALCu is decidable in CON2EXPTIME, being 2EXPTIME-hard, while uniform interpolant existence is undecidable. Then we show that interpolant and definition existence in the one-variable fragment Q 1 K of quantified modal logic K is nonelementary decidable, while uniform interpolant existence is undecidable.

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Section: Introductionsupporting

confidence: 67%

Section: Main Notions and Characterisationsmentioning

confidence: 82%

Definitions and (Uniform) Interpolants in First-Order Modal Logic

Kurucz¹,

Wolter²,

Zakharyaschev³

2023

Preprint

View full text Add to dashboard Cite

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“…We conjecture that extensions of our results to DLs with qualified number restrictions and role inclusions are rather straightforward (though proofs might become significantly less transparent). The addition of inverse roles, however, might lead to non-trivial modifications of the model-theoretic criteria, see also [68].…”

Section: Discussionmentioning

confidence: 99%

“…The method is purely model-theoretic and based on the close relationship between concept and query inseparability for EL. More recently, CQ inseparability has been investigated for HornALCHI and shown to be 2ExpTime-complete, using a subtle approach that combines a mosaic technique with automata [68]. The mentioned results are summarised in Table 5.…”

Section: Related Workmentioning

confidence: 99%

Query inseparability for ALC ontologies

Botoeva

Lutz

Ryzhikov

et al. 2019

Artificial Intelligence

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We investigate the problem whether two ALC ontologies are indistinguishable (or inseparable) by means of queries in a given signature, which is fundamental for ontology engineering tasks such as ontology versioning, modularisation, update, and forgetting. We consider both knowledge base (KB) and TBox inseparability. For KBs, we give modeltheoretic criteria in terms of (finite partial) homomorphisms and products and prove that this problem is undecidable for conjunctive queries (CQs), but 2ExpTime-complete for unions of CQs (UCQs). The same results hold if (U)CQs are replaced by rooted (U)CQs, where every variable is connected to an answer variable. We also show that inseparability by CQs is still undecidable if one KB is given in the lightweight DL EL and if no restrictions are imposed on the signature of the CQs. We also consider the problem whether two ALC TBoxes give the same answers to any query over any ABox in a given signature and show that, for CQs, this problem is undecidable, too. We then develop model-theoretic criteria for HornALC TBoxes and show using tree automata that, in contrast, inseparability becomes decidable and 2ExpTime-complete, even ExpTime-complete when restricted to (unions of) rooted CQs. module is extracted from an ontology. In ontology update or revision, the difference between the answers to queries over the updated or revised ontology and the original one should be minimised when constructing update or revision operators. Similarly, in forgetting, it is the answers to queries which should be preserved under appropriate forgetting operators. Thus, in the context of query answering, the fundamental relationship between ontologies is not whether they are logically equivalent (have the same models), but whether they give the same answers to any relevant query. To illustrate, consider the following simple TBox T = {Book ∃author.¬Book} saying that every book has an author who is not a book. Clearly, T is not logically equivalent to the TBoxwhich only states that every book has an author. However, if one takes as the query language the popular classes of conjunctive queries (CQs) or unions of CQs (UCQs), then no matter what the data is, every query will have the same answers independently of whether one uses T or T . Intuitively, the reason is that the 'positive' information given by T coincides with the 'positive' information given by T . If the main purpose of the ontology is answering UCQs, it is thus more important to know that T can be safely replaced by T without affecting the answers to UCQs than to establish that T and T are not logically equivalent.In most ontology engineering applications for ontology-based data access, the relevant class Q of queries can be further restricted to those given in a finite signature of relevant concept and role names. For example, to establish that a subset M of an ontology O is a module of O, one should not require that M and O give the same answers to all queries in Q, but only to those that are in the signature of M. Similarly, in the versioning ...

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“…For a more detailed introduction to description logics, we refer to [3,4]. For latest results on logical inseparability see [7,8,15], and for a survey on query inseparability, see [6]. Definition 1 (Logical Difference).…”

Section: Preliminariesmentioning

confidence: 99%

Computing Minimal Projection Modules for $$\mathcal{ELH}^{r}$$ -Terminologies

Chen¹,

Ludwig²,

Ma³

et al. 2019

Logics in Artificial Intelligence

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For the development of large-scale representations of knowledge, the application of methodologies and design principles becomes relevant. The knowledge may be organized in ontologies in a modular and hierarchical fashion. An upper-level (reference) ontology typically provides specifications of requirements, functions, design or standards that are to be complied with by domain ontologies for a specific task on a lower level (task ontology) in the hierarchy. Verifying whether and how specifications have been implemented by a task ontology becomes a challenge when relevant axioms of the domain ontology need to be inspected. We consider specifications to be defined using entailments of certain queries over a given vocabulary. For selecting the relevant axioms from task ontologies, we propose a novel module notion called projection module that entails the queries that follow from a reference ontology. We develop algorithms for computing minimal projection modules of Description Logic terminologies for subsumption, instance and conjunctive queries.This work is partially funded by the ANR project GoAsQ (ANR-15-CE23-0022).

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Query Conservative Extensions in Horn Description Logics with Inverse Roles

Cited by 6 publications

References 11 publications

Definitions and (Uniform) Interpolants in First-Order Modal Logic

Definitions and (Uniform) Interpolants in First-Order Modal Logic

Query inseparability for ALC ontologies

Computing Minimal Projection Modules for $$\mathcal{ELH}^{r}$$ -Terminologies

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