A Temporal Description Logic for Reasoning over Conceptual Schemas and Queries [chapter]

Alessandro Artale, Enrico Franconi, Frank Wolter, Michael Zakharyaschev
2002 Lecture Notes in Computer Science  
This paper introduces a new logical formalism, intended for temporal conceptual modelling, as a natural combination of the well-known description logic DLR and point-based linear temporal logic with Since and Until. We define a query language (where queries are non-recursive Datalog programs and atoms are complex DLRUS expressions) and investigate the problem of checking query containment under the constraints defined by DLRUS conceptual schemas-i.e., DLRUS knowledge bases-as well as the
more » ... s of schema satisfiability and logical implication. DLR is not only a very powerful language for conceptual modelling. The problem of view-based query processing under DLR constraints has also been studied [9] . Viewbased query answering requires to answer a query over a virtual database (constrained by a DLR theory playing the role of the conceptual schema and of the integrity constraints) for which the only information comes from a set of materialised views over the same database; this problem with non-recursive Datalog queries and views is a co-NPcomplete problem (in data complexity) under the closed world assumption. Checking query containment of non-recursive Datalog queries under DLR constraints is decidable in 2EXPTIME [9] . Given all these nice features of DLR, it is natural to try to extend it with a temporal dimension, to understand the expressive power of the resulting hybrid with respect to the needs of temporal conceptual modelling and view based query processing, and to investigate its computational properties. This paper reports the results of such an attempt. We construct DLR U S as an organic combination of DLR and the propositional linear temporal logic with Since and Until (which usually serves as the temporal component in the first-order approach) by allowing applications of temporal operators to all syntactical terms of DLR: classes, relations, and formulas. We then investigate computational properties of reasoning with DLR U S by analysing schema, class, and relation satisfiability, logical implication, and query containment for non-recursive Datalog queries under DLR U S constraints. The full DLR U S turns out to be undecidable. The main reason for this is the possibility to postulate that a binary relation does not vary in time-a very small fragment of DLR U S (say, DLR augmented with a single time invariant binary relation) can encode the undecidable tiling problem (cf. [26, 19] ). The fragment DLR − U S of DLR U S deprived of the ability to talk about temporal persistence of n-ary relations, for n ≥ 2, is still very expressive, as is illustrated by examples in this paper, but its computational behaviour is much better. We obtain the following non-trivial novel complexity results: (1) reasoning in DLR − U S with atomic formulas is EXPTIME-complete, (2) satisfiability and logical implication of arbitrary DLR − U S formulas is EXPSPACE-complete, and (3) the problem of checking query containment of non-recursive Datalog queries under DLR − U S constraints is decidable in 2EXPTIME with an EXPSPACE lower bound. The results obtained in this paper are novel for several reasons. Previous approaches to temporal description logics considered much weaker languages having only binary relations (i.e., roles), without the cardinality constructs, without the inverse construct (which DLR U S implicitly is able to express by considering only binary relations), and without ever considering the ability to express queries [21, 25, 28, 23] . In this paper for the first time an upper bound for the complexity of reasoning in a temporal description logic with both future and past operators is proved, leading to a tight EXPSPACE-completeness result which automatically holds for the weaker basic temporal description logic ALC − U S as well. In this paper for the first time non trivial decidability and complexity results are presented for the problem of temporal query containment under complex constraints. For a survey of the previous various approaches to temporal description logics see [4] .
doi:10.1007/3-540-45757-7_9 fatcat:4vgmyrocprg5tfcxebna63xny4