Temporal Description Logics: A Survey <s> Introduction <s> An attempt is made to integrate three well-known formalisms of knowledge representation: terminological logic in the tradition of KL-ONE, the temporal logic of Shoham, and Allen's interval calculus. Drawing on each of these sources, a temporal terminological logic is proposed which combines structural with temporal abstraction. A formal semantics is provided, and some hints are given for exploring the computational properties of reasoning in the formalism. <s> BIB001 </s> Temporal Description Logics: A Survey <s> Introduction <s> We show how to add full first-order temporal expressiveness to terminological logics. This can be achieved by embedding point-based tense operators in propositionally closed concept languages like ALC. The resulting temporal terminological logics are fully expressive over linear, Dedekind complete time such as ℕ and ℝ in the sense that all first-order temporal formulae over these time structures are expressible. We then prove that augmenting ALC by future-oriented tense operators interpreted over linear, discrete, unbounded time like IN does not increase its computational complexity. To establish this complexity result we show that coherence in ALC augmented by functional roles and their transitive closure is computable in polynomial space. We finally show how to obtain directly an axiomatization and a tableau-based algorithm for the tenselogical extension of terminological logics. <s> BIB002 </s> Temporal Description Logics: A Survey <s> Introduction <s> Until now, interval-based temporal Description Logics (DLs) did-if at all-only admit TBoxes of a very restricted form, namely acyclic macro definitions. In this paper, we present a temporal DL that overcomes this deficieny and combines interval-based temporal reasoning with general TBoxes. We argue that this combination is very interesting for many application domains. An automata-based decision procedure is devised and a tight ExpTime-complexity bound is obtained. Since the presented logic can be viewed as being equipped with a concrete domain, our results can be seen from a different perspective: We show that there exist interesting concrete domains for which reasoning with general TBoxes in decidable. <s> BIB003 </s> Temporal Description Logics: A Survey <s> Introduction <s> 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 problems of schema satisfiability and logical implication. <s> BIB004 </s> Temporal Description Logics: A Survey <s> Introduction <s> This paper surveys the temporal extensions of description logics appearearing in the literature. The analysis considers a large spectrum of approaches appearearing in the temporal description logics area: from the loosely coupled approaches – which comprise, for example, the enhancement of simple description logics with a constraint based mechanism – to the most principled ones – which consider a combined semantics for the abstract and the temporal domains. It will be shown how these latter approaches have a strict connection with temporal logics. ::: ::: Advantages of using temporal description logics are their high expressivity combined with desirable computational properties – such as decidability, soundness and completeness of deduction procedures. In this survey the computational properties of various families of temporal description logics will be pointed out. <s> BIB005 </s> Temporal Description Logics: A Survey <s> Introduction <s> A class of interval-based temporal languages for uniformly representing and reasoning about actions and plans is presented. Actions are represented by describing what is true while the action itself is occurring, and plans are constructed by temporally relating actions and world states. The temporal languages are members of the family of Description Logics, which are characterized by high expressivity combined with good computational properties. The subsumption problem for a class of temporal Description Logics is investigated and sound and complete decision procedures are given. The basic language TL-F is considered first: it is the composition of a temporal logic TL -- able to express interval temporal networks -- together with the non-temporal logic F -- a Feature Description Logic. It is proven that subsumption in this language is an NP-complete problem. Then it is shown how to reason with the more expressive languages TLU-FU and TL-ALCF. The former adds disjunction both at the temporal and non-temporal sides of the language, the latter extends the non-temporal side with set-valued features (i.e., roles) and a propositionally complete language. <s> BIB006
Description Logics (DLs) are a well-known family of logic-based knowledge representation formalisms with a number of relevant applications. For example, DLs enjoy significant popularity as ontology languages, which has resulted in the standardization of a description logic as part of W3C's ontology language OWL. Other relevant applications of DLs include the representation of and reasoning about conceptual database models. Notably, extended entity-relation (EER) models and UML class diagrams can be embedded into DLs, and DL reasoners can be used to verify their consistency and to derive implicit consequences of the model  . In many applications of DLs, temporal aspects play an important role. For example, the description of a concept in an ontology often involves reference to temporal patternsconsider, e.g., the definition of Malaria in a bio-medical ontology. Likewise, time plays a crucial role when using DLs to represent conceptual models of temporal databases. These observations have resulted in a rather diverse literature on temporal description logic (TDLs). Proposals for TDLs include combinations of DLs with Halpern and Shoham's logic of time intervals  BIB001 , formalisms inspired by action logics BIB006 , and the treatment of time points and intervals as a datatype BIB003 . For more information, see the previous surveys BIB005  . In contrast to the existing surveys, we focus on combinations of standard DLs such as ALC with standard temporal logics (TLs) such as LTL (linear time temporal logic) and CTL (computational tree logic). Such combinations are based on a two-dimensional semantics, where one dimension is for time and the other for the DL domain. They were first proposed by Schild BIB002 in 1993, and since then have experienced constant development. Notably, TDLs of this kind are well-suited for capturing the temporal aspects of concepts in ontologies, and for encoding temporal EER models BIB004 . We mainly discuss complexity results and algorithms for satisfiability checking, which is the most important reasoning problem for DLs and TDLs. In particular, satisfiability can be used to decide concistency of (encoded) temporal EER models. For all TDLs considered in this paper, satisfiability is inter-reducible with subsumption in polynomial time. Thus, the covered results also apply to the latter problem, which is highly relevant for reasoning about ontologies. When constructing a two-dimensional TDL, a number of design decisions have to be made. For example, one has to choose a concrete DL and a TL to be combined. In this paper, we mainly use ALC for the DL part and LTL for the TL part. Another important decision is whether to apply the TL operators to DL concepts, roles, TBoxes, or ABoxes. The structure of this survey roughly reflects the available choices regarding this second issue. After some preliminaries in Section 2, in Section 3 we analyze the application of TL operators to concepts and roles. In Sections 4 and 5, we consider the application of these operators to TBoxes and ABoxes, respectively. Section 6 is devoted to TDLs whose DL component is the lightweight description logic DL-Lite, and Section 7 is concerned with TDLs whose TL component is CTL. Throughout the paper, we also discuss whether or not the choice of a different DL has an impact on the presented results.