First Order Rewritability in Ontology-Mediated Querying in Horn Description Logics

Toman, David; Weddell, Grant E.

doi:10.1609/aaai.v36i5.20534

Cited by 4 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definite descriptions, like 'the smallest planet in the Solar System', are expressions having form 'the 𝑥 such that 𝜙'. Together with individual names, such as 'Mercury', they are used as referring expressions to identify objects in a given domain [1,2,3]. Definite description and individual names can also fail to denote any object at all, as in the cases of the definite description 'the planet between Mercury and the Sun' or the individual name 'Vulcan'.…”

Section: Introductionmentioning

confidence: 99%

On Free Description Logics with Definite Descriptions

Artale

Mazzullo

Ozaki

et al. 2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

Definite descriptions are phrases of the form ‘the x such that φ’, used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data over ontologies. We investigate free description logics with both individual names and definite descriptions as terms of the language, while also accounting for their possible lack of denotation. We focus on the extensions of ALC and, respectively, EL with nominals, the universal role, and definite descriptions. We show that standard reasoning in these extensions is not harder than in the original languages, and we characterise the expressive power of concepts relative to first-order formulas using a suitable notion of bisimulation. Moreover, we lay the foundations for automated support for definite descriptions generation by studying the complexity of deciding the existence of definite descriptions for an individual under an ontology. Finally, we provide a polynomial-time reduction of reasoning in other free description logic languages based on dual-domain semantics to the case of partial interpretations.

show abstract

Section: Introductionmentioning

confidence: 99%

On Free Description Logics with Definite Descriptions

Artale

Mazzullo

Ozaki

et al. 2021

Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning

View full text Add to dashboard Cite

show abstract

“…The BDP and PBDP have been used in ontology engineering to extract equivalent acyclic terminologies from ontologies (ten Cate et al 2006;ten Cate, Franconi, and Seylan 2013), they have been investigated in ontology-based data management to equivalently rewrite ontology-mediated queries (Seylan, Franconi, and de Bruijn 2009;Toman and Weddell 2020), and they have been proposed to support the construction of alignments between ontologies (Jiménez-Ruiz et al 2016). The CIP is often used as a tool to compute explicit definitions (ten Cate et al 2006;ten Cate, Franconi, and Seylan 2013;Toman and Weddell 2020). It is also the basic logical property that ensures the robust behaviour of ontology modules (Konev et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions

Artale

Jung

Mazzullo

et al. 2021

AAAI

View full text Add to dashboard Cite

The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP transform potentially hard existence problems into deduction problems in the underlying logic. Description Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but interpolants and explicit definitions have many potential applications in ontology engineering and ontology-based data management. In this article we show the following: even without Craig and Beth, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without Craig and Beth makes this problem harder than deduction: we prove that the existence problems become 2EXPTIME-complete, thus one exponential harder than validity. The existence of explicit definitions is 2EXPTIME-hard even if one asks for a definition of a nominal using any symbol distinct from that nominal, but it becomes EXPTIME-complete if one asks for a definition of a concept name using any symbol distinct from that concept name.

show abstract

Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Heuer,

Wernhard

2024

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs P and Q and vocabulary V (set of predicates) the existence of a program R in V such that $$P \cup R$$ P ∪ R and $$P \cup Q$$ P ∪ Q are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program R can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, which we apply in reverse to extract programs from formulas. As a further perspective, this allows transforming logic programs via transforming their first-order encodings. In a prototypical implementation, the Craig interpolation is performed by first-order provers based on clausal tableaux or resolution calculi. Our work shows how definability and interpolation, which underlie modern logic-based approaches to advanced tasks in knowledge representation, transfer to answer set programming.

show abstract

First Order Rewritability in Ontology-Mediated Querying in Horn Description Logics

Cited by 4 publications

References 19 publications

On Free Description Logics with Definite Descriptions

On Free Description Logics with Definite Descriptions

Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions

Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Contact Info

Product

Resources

About