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Register a new userDecidability of an Expressive Description Logic with Rational Grading
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Added by
Mitko Yanchev
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Authors
Mitko Yanchev
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In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part restrictions essentially enrich the expressive capabilities of DLs. We examine an extension of well-studied DL ALCQIHR+ with part restrictions, and prove that the reasoning in the extended logic is still decidable. The proof uses tableaux technique augmented with indices technique, designed for dealing with part restrictions.
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Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are undecidable, over many model classes. Over the years, only a few fragments (such as the monodic) have been shown to be decidable. In this paper, we study fragments that bundle quantifiers and modalities together, inspired by earlier work on epistemic logics of know-how/why/what. As always with quantified modal logics, it makes a significant difference whether the domain stays the same across worlds, or not. In particular, we show that the bundle $forall Box$ is undecidable over constant domain interpretations, even with only monadic predicates, whereas $exists Box$ bundle is decidable. On the other hand, over increasing domain interpretations, we get decidability with both $forall Box$ and $exists Box$ bundles with unrestricted predicates. In these cases, we also obtain tableau based procedures that run in PSPACE. We further show that the $exists Box$ bundle cannot distinguish between constant domain and increasing domain interpretations.
The paper introduces a knowledge representation language that combines the event calculus with description logic in a logic programming framework. The purpose is to provide the user with an expressive language for modelling and analysing systems that evolve over time. The approach is exemplified with the logic programming language as implemented in the Fusemate system. The paper extends Fusemates rule language with a weakly DL-safe interface to the description logic $cal ALCIF$ and adapts the event calculus to this extended language. This way, time-stamped ABoxes can be manipulated as fluents in the event calculus. All that is done in the frame of Fusemates concept of stratification by time. The paper provides conditions for soundness and completeness where appropriate. Using an elaborated example it demonstrates the interplay of the event calculus, description logic and logic programming rules for computing possible models as plausible explanations of the current state of the modelled system.
We study query containment in three closely related formalisms: monadic disjunctive Datalog (MDDLog), MMSNP (a logical generalization of constraint satisfaction problems), and ontology-mediated queries (OMQs) based on expressive description logics and unions of conjunctive queries. Containment in MMSNP was known to be decidable due to a result by Feder and Vardi, but its exact complexity has remained open. We prove 2NEXPTIME-completeness and extend this result to monadic disjunctive Datalog and to OMQs.
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for representing and handling uncertainty. A probabilistic extension of a light-weight DL was recently proposed for dealing with certain knowledge occurring in uncertain contexts. In this paper, we continue that line of research by introducing the Bayesian extension BALC of the propositionally closed DL ALC. We present a tableau-based procedure for deciding consistency, and adapt it to solve other probabilistic, contextual, and general inferences in this logic. We also show that all these problems remain ExpTime-complete, the same as reasoning in the underlying classical ALC.
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational problems for these logics have been studied for their computational complexity. However, essentially all complexity analyses of reasoning problems for description logics use the one-dimensional framework of classical complexity theory. The multi-dimensional framework of parameterized complexity theory is able to provide a much more detailed image of the complexity of reasoning problems. In this paper we argue that the framework of parameterized complexity has a lot to offer for the complexity analysis of description logic reasoning problems---when one takes a progressive and forward-looking view on parameterized complexity tools. We substantiate our argument by means of three case studies. The first case study is about the problem of concept satisfiability for the logic ALC with respect to nearly acyclic TBoxes. The second case study concerns concept satisfiability for ALC concepts parameterized by the number of occurrences of union operators and the number of occurrences of full existential quantification. The third case study offers a critical look at data complexity results from a parameterized complexity point of view. These three case studies are representative for the wide range of uses for parameterized complexity methods for description logic problems.
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