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.Description Logic-Spatial Logic. A description logic L 1 (say, ALC or SHIQ [42]) talks about a domain D 1 of abstract objects. A spatial logic L 2 (say, qualitative S4 u [70,16,66,30] or quantitative MS [69,48]) talks about some spatial domain D 2 . An obvious E-connection is given by the relation E ⊆ D 1 ×D 2 defined by taking (x, y) ∈ E iff y belongs to the spatial extension of x-whenever x occupies some space. Then, given an L 1 -concept, say, river,
We investigate the expressive power and computational properties of two different types of languages intended for speaking about distances. First, we consider a first-order language FM the two-variable fragment of which turns out to be undecidable in the class of distance spaces validating the triangular inequality as well as in the class of all metric spaces. Yet, this two-variable fragment is decidable in various weaker classes of distance spaces. Second, we introduce a variable-free modal language MS that, when interpreted in metric spaces, has the same expressive power as the two-variable fragment of FM. We determine natural and expressive fragments of MS which are decidable in various classes of distance spaces validating the triangular inequality, in particular, the class of all metric spaces.
Abstract. There is a diversity of ontology languages in use, among them OWL, RDF, OBO, Common Logic, and F-logic. Related languages such as UML class diagrams, entity-relationship diagrams and object role modelling provide bridges from ontology modelling to applications, e.g. in software engineering and databases. Another diversity appears at the level of ontology modularity and relations among ontologies. There is ontology matching and alignment, module extraction, interpolation, ontologies linked by bridges, interpretation and refinement, and combination of ontologies. The Distributed Ontology, Modelling and Specification Language (DOL) aims at providing a unified meta language for handling this diversity. In particular, DOL provides constructs for (1) "as-is" use of ontologies formulated in a specific ontology language, (2) ontologies formalised in heterogeneous logics, (3) modular ontologies, and (4) links between ontologies. This paper sketches the design of the DOL language. DOL will be submitted as a proposal within the OntoIOp (Ontology Integration and Interoperability) standardisation activity of the Object Management Group (OMG).
This paper addresses questions of universality related to ontological engineering, namely aims at substantiating (negative) answers to the following three basic questions: (i) Is there a 'universal ontology' ?, (ii) Is there a 'universal formal ontology language' ?, and (iii) Is there a universally applicable 'mode of reasoning' for formal ontologies? To support our answers in a principled way, we present a general framework for the design of formal ontologies resting on two main principles: firstly, we endorse Rudolf Carnap's principle of logical tolerance by giving central stage to the concept of logical heterogeneity, i.e. the use of a plurality of logical languages within one ontology design. Secondly, to structure and combine heterogeneous ontologies in a semantically wellfounded way, we base our work on abstract model theory in the form of institutional semantics, as forcefully put forward by Joseph Goguen and Rod Burstall. In particular, we employ the structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining a general concept of heterogeneous, distributed, highly modular and structured ontologies, called hyperontologies. Moreover, we distinguish, on a structural and semantic level, several different kinds of combining and aligning heterogeneous ontologies, namely integration, connection, and refinement. We show how the notion of heterogeneous refinement can be used to provide both a general notion of sub-ontology as well as a notion of heterogeneous equivalence of ontologies, and finally sketch how different modes of reasoning over ontologies are related to these different structuring aspects.Mathematics Subject Classification (2010). Primary 68T30; Secondary 03C95.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.