A New Preprint

A New Preprint

[Amir Tabatabai]

Dear All,

I have recently posted my new preprint "Geometric Modality and Weak
Exponentials" on arxiv whose link is attached in the following.
Corrections, comments and suggestions are all welcome.

https://arxiv.org/abs/1711.01736

Abstract:

The intuitionistic implication and hence the notion of function space in
constructive disciplines is both non-geometric and impredicative. In this
paper we try to solve both of these problems by first introducing weak
exponential objects as a formalization for predicative function spaces and
then by proposing modal spaces as a way to introduce a natural family of
geometric predicative implications based on the interplay between the
concepts of time and space. This combination then leads to a brand new
family of modal propositional logics with predicative implications and then
to topological semantics for these logics and some weak modal and
sub-intuitionistic logics, as well. Finally, we will lift these notions and
the corresponding relations to a higher and more structured level of modal
topoi and modal type theory.

Best wishes,
Amir.


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