|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
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.
|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
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.
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