Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion. Though description logics are closely related to modal logics, they are not necessarily normal. In addition, ABox reasoning in description logics is not covered by the results from modal logics. In this paper, we extend the decidability transfer results from normal modal logics to a large class of description logics. To cover different description logics in a uniform way, we introduce abstract description systems, which can be seen as a common generalization of description and modal logics, and show the transfer results in this general setting.

We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C^2, the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C^2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals. Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisfiability for ALCQI with nominals is NExpTime-complete. Without nominals, this problem is known to be PSpace-complete.

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.

Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the possibility of defining a class, i.e., providing a set of properties that precisely characterize the instances of the class. Many recent articles point out that there are several ways of assigning a meaning to a class definition containing some sort of recursion. In this paper, we argue that, instead of choosing a single style of semantics, we achieve better results by adopting a formalism that allows for different semantics to coexist. We demonstrate the feasibility of our argument, by presenting a knowledge representation formalism, the description logic muALCQ, with the above characteristics. In addition to the constructs for conjunction, disjunction, negation, quantifiers, and qualified number restrictions, muALCQ includes special fixpoint constructs to express (suitably interpreted) recursive definitions. These constructs enable the usual frame-based descriptions to be combined with definitions of recursive data structures such as directed acyclic graphs, lists, streams, etc. We establish several properties of muALCQ, including the decidability and the computational complexity of reasoning, by formulating a correspondence with a particular modal logic of programs called the modal mu-calculus.

This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in CLASSIC descriptions, the developers have had to use an algorithm that is incomplete with respect to the standard, model-theoretic semantics for description logics. We provide a variant semantics for descriptions with respect to which the current implementation is complete, and which can be independently motivated. The soundness and completeness of the polynomial-time subsumption algorithm is established using description graphs, which are an abstracted version of the implementation structures used in CLASSIC, and are of independent interest.

KL-ONE is a system for representing knowledge in Artificial Intelligence programs. It has been developed and refined over a long period and has been used in both basic research and implemented knowledge-based systems in a number of places in the AI community. Here we present the kernel ideas of KL-ONE, emphasizing its ability to form complex structured descriptions. In addition to detailing all of KL-ONE's description-forming structures, we discuss a bit of the philosophy underlying the system, highlight notions of taxonomy and classification that are central to it, and include an extended example of the use of KL-ONE and its classifier in a recognition task. This research was supported in part by the Defense Advanced Research Projects Agency under Contract N00014-77-C-0378. Views and conclusions contained in this paper are the authors' and should not be interpreted as representing the official opinion or policy of DARPA, the U.S. Government, or any person or agency connected with them.

KL-ONE lets one define and use a class of descriptive terms called Concepts, where each Concept denotes a set of objects A subsumption relation between Concepts is defined which is related to set inclusion by way of a semantics for Concepts. This subsumption relation defines a partial order on Concepts, and KL-ONE organizes all Concepts into a taxonomy that reflects this partial order. Classification is a process that takes a new Concept and determines other Concepts that either subsume it or that it subsumes, thereby determining the location for the new Concept within a given taxonomy. We discuss these issues and demonstrate some uses of the classification algorithm. KL-ONE is a knowledge representation system developed at Bolt Beranek and Newman over the past few years (see [Brachman 77, Brachman 79, Schmolze 82. Sidner 81]), that grew out of semantic network formalisms. The primary unit of information in KL-ONE is called a Concept, which denotes a set of objects. A Concept has a set of (syntactic) components, each denoting a property that must be true of each member of the set denoted by the Concept.

The second KL-One workshop was held over a five-day period in October, 1981. The workshop included a general conference session, wherein people could report on activies at their own institutions, and a two day working research session.

Amidst the beautiful foliage in Jackson, N.H., the each session circulated a position paper to the group, Second KL-ONE Workshop was held over a five-day raising the questions he wanted to see addressed at the period this past October. Not only did "KloneTalk" (a version of KL-ONE implemented in we have a general conference session, wherein people SmaiiTa k at Xerox PARC -- this inchrded a videotaped could report on activities at their own institutions, discuss demonstration of the system's interface), prototypes in issues of general interest, etc., we also had a knowledge representation, translation of INTERLISP two-and-a-half day working research session. KL-ONE to FranzLisp, a calculus of Structural The technieai discussion part of the Workshop Descriptions, and the KL-ONE Classifier, not to mention several others. We also had the larger group break up preceded the general conference, so that we could report into smaller working groups to consider inference in on findings to the larger group of participants (forty-six KL-ONE, representing beliefs, some KL-ONE practice this year, from twenty-one institutions). Also, we planned to cover only a small extensive Proceedings of the Workshop.