A Semantic Similarity Measure for Expressive Description Logics

A totally semantic measure is presented which is able to calculate a similarity value between concept descriptions and also between concept description and individual or between individuals expressed in an expressive description logic. It is applicable on symbolic descriptions although it uses a numeric approach for the calculus. Considering that Description Logics stand as the theoretic framework for the ontological knowledge representation and reasoning, the proposed measure can be effectively used for agglomerative and divisional clustering task applied to the semantic web domain.Comment: 13 pages, Appeared at CILC 2005, Convegno Italiano di Logica Computazionale also available at http://www.disp.uniroma2.it/CILC2005/downloads/papers/15.dAmato_CILC05.pd

Decidable Reasoning in Terminological Knowledge Representation Systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.Comment: See http://www.jair.org/ for any accompanying file

Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery

Structural Subsumption for ALN

Aus der Einleitung: „In this paper, we reuse the representation formalism `description graph' in order to characterize subsumption of ALN-concepts. The description logic ALN allows for conjunction, valuerestrictions, number restrictions, and primitive negation. Since Classic allows for more constructors than ALN, e.g., equality restrictions an attribute chains by the constructor SAME-AS,we can confine the notion of description graphs from [BP94]. On the other hand, ALN explicitly allows for primitive negation which yields another possibility { besides conflicting number restrictions { to express inconsistency. Thus, we have to modify the notion of canonical description graphs in order to cope with inconsistent concepts in the structural characterization of subsumption. It turns out that the description graphs obtained from ALN-concepts are in fact trees. A canonical graph is a deterministic tree. The conditions required by the structural characterization of subsumption on these trees can be tested by an eficient algorithm, i.e., we obtain an algorithm deciding subsumption of C and D in time polynomial in the size of C and D. The report is structured as follows. In the preliminaries, we define syntax and semantics of the description logic ALN as well as the inference problem of subsumption. In Section 3, we introduce description graphs, the data structure our structural subsumption algorithm is working on. Besides syntax and semantics also an algorithm for translating ALN-concepts into description graphs is given. Thereafter, we present the main result of this report in Section 6, a characterization of subsumption of ALN-concepts by a structural comparison of corresponding description graphs. Furthermore, a structural subsumption algorithm can be found in Section 6.2. In the last section we summarize our results and give an outlook to further applications of structural subsumption in terminological knowledge representation systems

Semantics and Ontology:\ud On the Modal Structure of an Epistemic Theory of Meaning

In this paper I shall confront three basic questions.\ud First, the relevance of epistemic structures, as formalized\ud and dealt with by current epistemic logics, for a\ud general Theory of meaning. Here I acknowledge M. Dummett"s\ud idea that a systematic account of what is meaning of\ud an arbitrary language subsystem must especially take into\ud account the inferential components of meaning itself. That\ud is, an analysis of meaning comprehension processes,\ud given in terms of epistemic logics and semantics for epistemic\ud notions.\ud The second and third questions relate to the ontological\ud and epistemological framework for this approach.\ud Concerning the epistemological aspects of an epistemic\ud theory of meaning, the question is: how epistemic logics\ud can eventually account for the informative character of\ud meaning comprehension processes. "Information� seems\ud to be built in the very formal structure of epistemic processes,\ud and should be exhibited in modal and possibleworld\ud semantics for propositional knowledge and belief.\ud However, it is not yet clear what is e.g. a possible world.\ud That is: how it can be defined semantically, other than by\ud accessibility rules which merely define it by considering its\ud set-theoretic relations with other sets-possible worlds.\ud Therefore, it is not clear which is the epistemological status\ud of propositional information contained in the structural\ud aspects of possible world semantics. The problem here\ud seems to be what kind of meaning one attributes to the\ud modal notion of possibility, thus allowing semantical and\ud synctactical selectors for possibilities. This is a typically\ud Dummett-style problem.\ud The third question is linked with this epistemological\ud problem, since it is its ontological counterpart. It concerns\ud the limits of the logical space and of logical semantics for a\ud of meaning. That is, it is concerned with the kind of\ud structure described by inferential processes, thought, in a\ud fregean perspective, as pre-conditions of estentional\ud treatment of meaning itself. The second and third questions\ud relate to some observations in Wittgenstein"s Tractatus.\ud I shall also try to show how their behaviour limits the\ud explicative power of some semantics for epistemic logics\ud (Konolige"s and Levesque"s for knowledge and belief)