One of the hall marks of DLs is the separation of the knowledge available about a given situation into

• Terminological information (the T-Box): containing definitions of basic and derived notions, and of the ways they are inter-related. This information is ``generic'' or ``global,'' been true in every model of the situation and of every individual in the situation. And
• Assertional information (the A-Box): which records ``specific'' or ``local'' information, being true of certain particular individuals in the situation.

The formal languages used in description logics are very close to modal languages. But the link between basic modal logics and description logics can only be established at the level of concept satisfiability. Basic modal logic is not expressive enough to account for either A-Box reasoning or inference in the presence of definitions (non-empty T-Boxes). By using the extended expressive power of hibrid logics, we can neatly account for both A-Boxes and T-Boxes. In addition, we can take advantage of recent result to provide characterizations in terms of both complexity and expressive power.

Relevant Material:

1.

The slides of the talk.

2.

C. Areces (2000) Chapters 2 and 4, of ``Logic Engineering. The Case of Description and Hybrid Logics.'' PhD Thesis, ILLC, University of Amsterdam.

Hybrid languages are obtained from modal languages by extending the language with a new collection of symbols together with a restriction on the interpretation this symbols will receive on models. But the denotation of nominals (i.e., singletons) is probably just the most simple extension. What about exploring more complex sorts like paths, connected components, etc? And how do these sorts interact with one another? A neat example of sorted modal logics are the computational tree logics CTL and CTL*. In a very general perspective, hybrid logics as we know them today are just our first steps towards investigating the more general class of sorted modal logics.

In this talk we discuss a sorted language specially devised to capture Ockham conception of time. We introduce and axiomatize the basic Hybrid Ockhamist Temporal Logic with nominals over branches, and discuss some of its extensions.

Relevant Material:

1.

P. Blackburn and V. Goranko (2000). Hybrid Ockhamist Temporal Logic. (to be provided)