Description logics of context

We introduce Description Logics of Context (DLCs)—an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify and express first-order properties. DLCs are founded in two-dimensional possible world semantics, where one dimension represents a usual object domain and the other a domain of contexts, and accommodate two interacting DL languages—the object and the context language—interpreted over their respective domains. Effectively, DLCs comprise a family of two-sorted , two-dimensional combinations of pairs of DLs. We argue that this setup ensures a well-grounded, generic framework for capturing and studying mechanisms of contextualization in the DL paradigm. As the main technical contribution, we prove 2ExpTime-completeness of the satisfiability problem in the maximally expressive DLC, based on the DL forumla . As an interesting corollary, we show that under certain conditions this result holds also for a range of two-dimensional DLs, including the prominent forumla

Description Logics of Context with Rigid Roles Revisited

To represent and reason about contextualized knowledge often two-dimensional Description Logics (DLs) are employed, where one DL is used to describe contexts (or possible worlds) and the other DL is used to describe the objects, i.e. the relational structure of the specific contexts. Previous approaches for DLs of context that combined pairs of DLs resulted in undecidability in those cases where so-called rigid roles are admitted, i.e. if parts of the relational structure are the same in all contexts. In this paper, we present a novel combination of pairs of DLs and show that reasoning stays decidable even in the presence of rigid roles. We give complexity results for various combinations of DLs involving ALC, SHOQ, and EL

Matching Concept Descriptions with Existential Restrictions

Matching of concepts with variables (concept patterns) is a relatively new operation that has been introduced in the context of description logics, originally to help filter out unimportant aspects of large concepts appearing in industrial-strength knowledge bases. Previous work has concentrated on (sub-)languages of CLASSIC, which in particular do not allow for existential restrictions. In this work, we present sound and complete decision algorithms for the solvability of matching problems and for computing sets of matchers for matching problems in description logics with existential restrictions

Tailoring temporal description logics for reasoning over temporal conceptual models

Temporal data models have been used to describe how data can evolve in the context of temporal databases. Both the Extended Entity-Relationship (EER) model and the Unified Modelling Language (UML) have been temporally extended to design temporal databases. To automatically check quality properties of conceptual schemas various encoding to Description Logics (DLs) have been proposed in the literature. On the other hand, reasoning on temporally extended DLs turn out to be too complex for effective reasoning ranging from 2ExpTime up to undecidable languages. We propose here to temporalize the ‘light-weight’ DL-Lite logics obtaining nice computational results while still being able to represent various constraints of temporal conceptual models. In particular, we consider temporal extensions of DL-Lite^N_bool, which was shown to be adequate for capturing non-temporal conceptual models without relationship inclusion, and its fragment DL-Lite^N_core with most primitive concept inclusions, which are nevertheless enough to represent almost all types of atemporal constraints (apart from covering)

Two-dimensional description logics of context

Description Logics (DLs) provide a clear and broadly accepted paradigm for rea- soning about terminological knowledge. Under the standard Kripkean semantics, a DL ontology forces a unique, global view on the represented world, in which the ontology axioms are interpreted as universally true. This philosophy is well- suited as long as everyone can share the same conceptual perspective on the domain or there is no need for considering alternative viewpoints. Alas, this is hardly ever the case since a domain can be modeled dierently depending on the intended use of an ontology. Consequently, eective representation and reasoning about knowledge pertaining to such multiple, heterogenous viewpoints becomes the primary objective for many practical applications [1,2]. The challenges above resemble clearly those problems that originally inspired J. McCarthy to introduce a theory of formalizing contexts in knowledge repre- sentation systems, as a way of granting them more generality [3,4]. The gist of his proposal is to replace logical formulas ', as the basic knowledge carriers, with assertions ist(c; ') stating that ' is true in c, where c denotes an abstract first- order entity called a context, which on its own can be described in a first-order language