Beth Definability in Expressive Description Logics

Cate, Balder ten; Franconi, Enrico; Seylan, Inanç

doi:10.1613/jair.4057

Cited by 21 publications

(3 citation statements)

References 28 publications

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“…It is known that in general there is no upper bound on the complexity of explicit definitions in first-order logic [11,36] and computing them is usually harder than entailment in FOL fragments (see e.g. [44]). On the other hand, one can take control over the growth of the component sizes by carefully choosing which signature ∆ can be shared between the components.…”

Section: Basic Facts About Decomposability and Inseparabilitymentioning

confidence: 99%

Progression of Decomposed Local-Effect Action Theories

Soutchanski¹

2023

Preprint

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<p>In many tasks related to reasoning about consequences of a logical theory, it is desirable to decompose the theory into a number of weakly related or independent components. However, a theory may represent knowledge that is subject to change, as a result of executing actions that have effects on some of the initial properties mentioned in the theory. Having once computed a decomposition of a theory, it is advantageous to know whether a decomposition has to be computed again in the newly changed theory (obtained from taking into account changes resulting from execution of an action). In this article, we address this problem in the scope of the situation calculus, where a change of an initial theory is related to the notion of progression. Progression provides a form of forward reasoning; it relies on forgetting values of those properties, which are subject to change, and computing new values for them. We consider decomposability and inseparability, two component properties known from the literature, and contribute by studying the conditions (1) when these properties are preserved and (2) when they are lost wrt progression and the related operation of forgetting. To show the latter, we demonstrate the boundaries using a number of negative examples. To show the former, we identify cases when these properties are preserved under forgetting and progression of initial theories in local-effect basic action theories of the situation calculus. Our article contributes to bridging two different communities in knowledge representation, namely, research on modularity and research on reasoning about actions. </p>

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Section: Basic Facts About Decomposability and Inseparabilitymentioning

confidence: 99%

Progression of Decomposed Local-Effect Action Theories

Soutchanski¹

2023

Preprint

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“…In addition to the theorems of Beth and Segoufin-Vianu mentioned in the introduction, there are numerous works on effective Bethstyle results for other logics. Some concern fragments of classical first-order logic, such as the guarded fragment [5,18]; others deal with non-classical logics such as description logics [36]. The Segoufin-Vianu result is closely related to variations of Beth's theorem and Craig interpolation for relativized quantification, such as Otto's interpolation theorem [30].…”

Section: Related Workmentioning

confidence: 99%

Synthesizing Nested Relational Queries from Implicit Specifications

Benedikt

Cécilia

Wernhard

2023

Proceedings of the 42nd ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Derived datasets can be defined implicitly or explicitly. An implicit definition (of dataset 𝑂 in terms of datasets ì 𝐼 ) is a logical specification involving the source data ì 𝐼 and the interface data 𝑂. It is a valid definition of 𝑂 in terms of ì 𝐼 , if any two models of the specification agreeing on ì 𝐼 agree on 𝑂. In contrast, an explicit definition is a query that produces 𝑂 from ì 𝐼 . Variants of Beth's theorem [6] state that one can convert implicit definitions to explicit ones. Further, this conversion can be done effectively given a proof witnessing implicit definability in a suitable proof system. We prove the analogous effective implicit-to-explicit result for nested relations: implicit definitions, given in the natural logic for nested relations, can be effectively converted to explicit definitions in the nested relational calculus (NRC). As a consequence, we can effectively extract rewritings of NRC queries in terms of NRC views, given a proof witnessing that the query is determined by the views.

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“…In order to get an idea about the size of the reformulations, for the ALCF I description logic there is a tableau-based algorithm computing explicit definitions of at most double exponential size (ten Cate et al, 2011;ten Cate, Franconi, & Seylan, 2013); this algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox.…”

Section: A Complete Proceduresmentioning

confidence: 99%

Exact Query Reformulation over Databases with First-order and Description Logics Ontologies

Franconi

Kerhet

Ngo

2013

jair

Self Cite

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We study a general framework for query rewriting in the presence of an arbitrary first-order logic ontology over a database signature. The framework supports deciding the existence of a safe-range first-order equivalent reformulation of a query in terms of the database signature, and if so, it provides an effective approach to construct the reformulation based on interpolation using standard theorem proving techniques (e.g., tableau). Since the reformulation is a safe-range formula, it is effectively executable as an SQL query. At the end, we present a non-trivial application of the framework with ontologies in the very expressive ALCHOIQ description logic, by providing effective means to compute safe-range first-order exact reformulations of queries.

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Beth Definability in Expressive Description Logics

Cited by 21 publications

References 28 publications

Progression of Decomposed Local-Effect Action Theories

Progression of Decomposed Local-Effect Action Theories

Synthesizing Nested Relational Queries from Implicit Specifications

Exact Query Reformulation over Databases with First-order and Description Logics Ontologies

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