Showing papers by "Franz Baader published in 1995"

Embedding defaults into terminological knowledge representation formalisms

Abstract: We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are applied only to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable. We describe an algorithm for computing extensions and show how the inference procedures of terminological systems can be modified to give optimal support to this algorithm.

Priorities on defaults with prerequisites, and their application in treating specificity in terminological default logic

Abstract: In a recent paper we have proposed terminological default logic as a formalism that combines means both for structured representation of classes and objects and for default inheritance of properties. The major drawback that terminological default logic inherits from general default logic is that it does not take precedence of more specific defaults over more general ones into account. This behavior has already been criticized in the general context of default logic, but it is all the more problematic in the terminological case where the emphasis lies on the hierarchical organization of concepts.

Terminological logics with modal operators

Abstract: Terminological knowledge representation formalisms can be used to represent objective, time-independent facts about an application domain. Notions like belief, intentions, time - which are essential for the representation of multi-agent environments - can only be expressed in a very limited way. For such notions, modal logics with possible worlds semantics provides a formally well-founded and well-investigated basis. This paper presents a framework for integrating modal operators into terminological knowledge representation languages. These operators can be used both inside of concept expressions and in front of terminological and assertional axioms. The main restrictions are that all modal operators are interpreted in the basic logic K, and that we consider increasing domains instead of constant domains. We introduce syntax and semantics of the extended language, and show that satisfiability of finite sets of formulas is decidable.

On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers

Abstract: When combining languages for symbolic constraints, one is typically faced with the problem of how to treat “mixed” constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a “free amalgamated product” as a possible solution to the first problem. Subsequently, we define so-called simply-combinable structures (SC-structures). For SC-structures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SC-structures yields the free amalgamated product. The combination technique of [BaS92, BaS94a] can be used to combine constraint solvers for (strong) SC-structures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SC-structures contains many solution structures that have been used in constraint logic programming, such as the algebra of rational trees, feature structures, and domains consisting of hereditarily finite (wellfounded or non-wellfounded) nested sets and lists.

A Multi-Dimensional Terminological Knowledge Representation Language

Abstract: An extension of the concept description language ALC used in KL-ONE-like terminological reasoning is presented. The extension includes multi-modal operators that either stand for the usual role quantifications or for modalities such as belief, time, etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an instance of a new kind of combination of modal logics where the modal operators of one logic may operate directly on the operators of the other logic. Different versions of this logic are investigated and various results about decidability and undecidability are presented. The main problem, however, decidability of the basic version of the logic, remains open.

Combination of Constraint Solving Techniques: An Algebraic POint of View

Abstract: In a previous paper we have introduced a method that allows one to combine decision procedures for unifiability in disjoint equational theories. Lately, it has turned out that the prerequisite for this method to apply—namely that unification with so-called linear constant restrictions is decidable in the single theories—is equivalent to requiring decidability of the positive fragment of the first order theory of the equational theories. Thus, the combination method can also be seen as a tool for combining decision procedures for positive theories of free algebras defined by equational theories. Complementing this logical point of view, the present paper isolates an abstract algebraic property of free algebras—called combinability—that clarifies why our combination method applies to such algebras. We use this algebraic point of view to introduce a new proof method that depends on abstract notions and results from universal algebra, as opposed to technical manipulations of terms (such as ordered rewriting, abstraction functions, etc.) With this proof method, the previous combination results for unification can easily be extended to the case of constraint solvers that also take relational constraints (such as ordering constraints) into account. Background information from universal algebra about free structures is given to clarify the algebraic meaning of our results.

Reasoning about structured objects - knowledge representation meets databases

Abstract: Structured objects are items with defined properties that are to be represented in a computer system. Research in Knowledge Representation (KR) and in Database Design (DB) has produced languages for describing structured objects. Although different in the particular means for defining properties, both areas share the goal of representing a part of the world in a structured way. Moreover, the rise of object-centred formalisms in the last decade has significantly influenced the convergence of languages.

Working notes of the KI'95 Workshop : KRDB-95 - Reasoning about structured objects : knowledge representation meets databases ; Bielefeld, Germany, Sept. 11-12, 1995

Abstract: Two different aspects of data management are addressed by description logics (DL) and databases (DB): the semantic organization of data and powerful reasoning services (by DL) and their efficient management and access (by DB). It is recently emerging that experiences from both DL and DB should profitably cross-fertilize each other, and a great interest is rising about this topic. In the present paper our technique, that allows uniform access by means of a DL-based query language to information distributed over knowledge bases and databases, is briefty reviewed. Our extended paradigm integrates the separately existing retrieving functions of description logics management systems (DLMS) and of database management systems (DBMS) in order to allow, via a query language grounded on a DL-based schema knowledge, uniformly formulating and ans wering queries, so that uniform retrieval from mixed knowledge/data bases is possible. In particular, some new developments extending those presented in [Bresciani, 1994] are introduced. By means of them the mapping between DL concepts and DB views is not more limited to primitive concepts, but also to some non-primitively defined ones.