Combining knowledge representation and reasoning formalisms is an important and challenging task. It is important because non-trivial AI applications often comprise different aspects of the world, thus requiring suitable combinations of available formalisms modeling each of these aspects. It is challenging because the computational behavior of the resulting hybrids is often much worse than the behavior of their components. In this paper, we propose a new combination method which is computationally robust in the sense that the combination of decidable formalisms is again decidable, and which, nonetheless, allows non-trivial interactions between the combined components. The new method, called E-connection, is defined in terms of abstract description systems (ADSs), a common generalization of description logics, many logics of time and space, as well as modal and epistemic logics. The basic idea of E-connections is that the interpretation domains of n combined systems are disjoint, and that these domains are connected by means of n-ary ‘link relations. ’ We define several natural variants of E-connections and study in-depth the transfer of decidability from the component systems to their E-connections. Key words: description logics, temporal logics, spatial logics, combining logics, decidability.

Traditional rst order predicate logic is known to be designed for representing and manipulating static knowledge (e.g. mathematical theories). So are manyof its applications. Knowledge representation systems based on concept description logics are not exceptions.

Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building real-world applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...

In this paper we introduce a modal lan- guage L T for imposing constraints on trees, and an extension LT(L r) for imposing con- straints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously, and the paper illustrates this by showing how the leading ideas of arsa can be captured in LT(Lr).

A modal logic is developed to deal with finite ordered binary trees as they are used in (computational) linguistics. A modal language is introduced with operators for the `mother of', `first daughter of' and `second daughter of' relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which completeness is shown with respect to the class of finite ordered binary trees. A number of decidability results follow.

The paper considers the standard concept description language ALC augmented with various kinds of modal operators which can be applied to concepts and axioms. The main aim is to develop methods of proving decidability of the satisfiability problem for this language and apply them to description logics with most important temporal and epistemic operators, thereby obtaining satisfiability checking algorithms for these logics. We deal with the possible world semantics under the constant domain assumption and show that the expanding and varying domain assumptions are reducible to it. Models with both finite and arbitrary constant domains are investigated. We begin by considering description logics with only one modal operator and then prove a general transfer theorem which makes it possible to lift the obtained results to many systems of polymodal description logic.

We analyze the computational feasibility of checking temporal integrity constraints formulated in some sublanguages of first-order temporal logic. Our results illustrate the impact of the quantifier pattern on the complexity of this problem. The presence of a single quantifier in the scope of a temporal operator makes the problem undecidable. On the other hand, if no quantifiers are in the scope of a temporal operator and all the quantifiers are universal, temporal integrity checking can be done in exponential time. 1 Introduction As temporal databases become more widely used in practice [27, 28], the need arises to address database integrity issues that are specific to such databases. In particular, it is necessary to generalize the standard notion of static integrity (involving single database states) to temporal integrity (involving sequences of database states). This work is the first attempt to date to analyze the computational feasibility of checking temporal integrity constrain...

ABSTRACT: In this paper we describe a general way of formalizing reasoning behaviour. Such a behaviour may be described by all the patterns which are valid for the behaviour. A pattern can be seen as a sequence of information states which describe what has been derived at each time point. A transition from an information state at a point in time to the state at the (or a) next time point is induced by one or more inference steps. We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models. Using temporal logic one can define theories and look at all models of that theory. For a number of examples of reasoning behaviour we have been able to define temporal theories such that its (minimal) models correspond to the valid patterns of the behaviour. These theories prescribe that the inference steps which are possible, are "executed " in the temporal model. The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static ones in a clear fashion.

In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may contain both local (i.e., state-dependent) and global (i.e., state-independent) concepts, roles and objects. All this provides us with the most complete and natural means for re ecting the dynamic and intensional behaviour of application domains. We construct a satis ability checking (mosaic-type) algorithm for this language (based on ALC) in(i) arbitrary multimodal frames, (ii) frames with universal accessibility relations (for knowledge) and (iii) frames with transitive, symmetrical and euclidean relations (for beliefs). On the other hand, it is shown that the satisfaction problem becomes undecidable if the underlying frames are arbitrary strict linear orders, hN; <i, or the language contains the common knowledge operator for n 2 agents. 1

This paper is a continuation of the work started in [FG92] on combining temporal logics. In this work, four combination methods are described and studied with respect to the transference of logical properties from the component one-dimensional temporal logics to the resulting two-dimensional temporal logic. Three basic logical properties are analysed, namely soundness, completeness and decidability. Each combination method is composed of three submethods that combine the languages, the inference systems and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages with varying expressivity and varying degree of transference of logical properties. The temporalisation method and the independent combination method are shown to transfer all three basic logical properties. The method of full interlacing of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several...