Wednesday
14.00 - 14.40 Hs. Guillaume Malod. Naming Worlds in Modal and Temporal Logic
In this talk we we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points): elements of the domain are names of possible worlds, and the quantifiers of first-order modal logic can then be used like the quantifiers of hybrid logics. We are thus able to express precise properties of the model or define new predicates such as D(x,y), which states that two time points are at the same distance from the root.

In classical logic we usually consider equality as a logical operation (i.e. it has a fixed interpretation as identity in all models). The reason to consider additional fixed connectives, especially equality, is their usefulness in applications, and their widespread and fundamental nature.

We will investigate similar additional predicates for modal and temporal logic and provide the systems studied with complete axiomatizations.

Relevant Material:

1.
D. Gabbay and Malod G. (2000). Naming worlds in modal and temporal logic. To appear in the Journal of Logic, Language and Information.
14.50 - 15.30 Hs. Carlos Areces. Hybrid Binders
Basic hybrid languages provides direct reference to elements in the domain. But once we have realized the potential provided by direct reference to specific points in the model, the way lies open for further enrichments. One of the most powerful being to regard nominals not as names but as variables over individual states, and to add quantifiers.

Hybrid languages with quantifiers display both modal and first-order characteristics: a Kripke semantis, and explicit variable binding apparatus.

In this talk, we will retrace the history, and examine the expressive power and meta-logical properties of hybrid quantifiers.

Relevant Material:

1.
The slides of the talk.
2.
P. Blackburn and J. Seligman. (1995). Hybrid languages. Journal of Logic, Language and Information, 4:251-272.
3.
C. Areces, P. Blackburn, and M. Marx (1998). Hybrid logics: Characterization, interpolation and complexity. To appear in the Journal of Symbolic Logic.

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