An ExpTime Upper Bound for π’œβ„’π’ž with Integers (Extended Version)

06/03/2020
βˆ™
by   Nadia Labai, et al.
βˆ™
0
βˆ™

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called Ο‰-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of π’œβ„’π’ž with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of π’œβ„’π’ž with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard π’œβ„’π’ž. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
βˆ™ 05/04/2023

The complexity of Presburger arithmetic with power or powers

We investigate expansions of Presburger arithmetic, i.e., the theory of ...
research
βˆ™ 07/04/2012

Description Logics with Fuzzy Concrete Domains

We present a fuzzy version of description logics with concrete domains. ...
research
βˆ™ 01/10/2018

Worst-case Optimal Submodular Extensions for Marginal Estimation

Submodular extensions of an energy function can be used to efficiently c...
research
βˆ™ 02/10/2023

Constraint Automata on Infinite Data Trees: From CTL(Z)/CTL*(Z) To Decision Procedures

We introduce the class of tree constraint automata with data values in Z...
research
βˆ™ 02/28/2014

Nested Regular Path Queries in Description Logics

Two-way regular path queries (2RPQs) have received increased attention r...
research
βˆ™ 06/01/2011

The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

We study the complexity of the combination of the Description Logics ALC...

Please sign up or login with your details

Forgot password? Click here to reset