Michael Bukatin, Nokia Corporation, Cambridge, MA

"Progress report on partial inconsistency, bitopology, and vector semantics"

Joint work with Ralph Kopperman and Steve Matthews

Abstract:

In the first part of this talk, we review the partial inconsistency
landscape with the emphasis on the fact that Scott domains tend to
become embedded into vector spaces in presence of partial inconsistency,
revisit partially inconsistent interval numbers [R] which are obtained
by adjoining formal pseudosegments [a, b] with the contradictory
property that b < a to the ordinary interval numbers, and review the
Lawvere duality between generalized distances and multivalued predicates,
focusing on the case when these distances and predicates
are valued in the domain of arrows.

We revisit the isomophism between [R] with the added "infinity crust"
and the d-frame LU of the (lower, upper) bitopology on reals,
show that any (lower, upper)-valued bitopology can be understood as
a topology valued in LU, hence a topology valued in [R],
and revisit anti-monotonic group negation and
[R]-valued partial metrics in connection with
the role played by the domain of arrows.

In the second part of the talk, we focus on the linear models
of computations, and in particular on the situations when
linear combinations of actual computational processes are well
defined. We revisit sampling semantics and generalized animations,
discuss the links between probabilistic programming and evolutionary
algorithms, discuss hybrid computational architectures
between linear models and traditional programs, and review
the recent advances in generative models produced by generative
models ("sampling the samplers" paradigm).