[FOM] intuitionistic and modal logics: a valuable researcher
Vladik Kreinovich
vladik at cs.utep.edu
Fri Oct 31 10:40:35 EST 2003
Dear Friends,
On November 5, Larisa Maksimova will turn 60. She has done a lot
of very interesting research in different non-standard logics ranging
from intuitionistic to modal to temporal logics.
RELATION TO FOUNDATIONS OF MATHEMATICS
Many of these logics are very helpful in the foundations of
mathematics. Researchers from this mailing list are very familiar with
the numerous contributions of intuitionism ideas and results to the
foundations of mathematics - and, via its relation to constructive
mathematics, to the analysis of algorithmic solvability of different
mathematical problems.
Applications of modal logic are less
well-known, but there has been a fruitful research directed towards
"modal mathematics", in which, under uncertainty, we can distinguish
between properties that are guaranteed to be true and property that
may be true. A lot of this research was done in connection with
interval mathematics, a direction that Matiyasevich, the solver of
Hilbert's 10th problem and one of the champions of interval
computations, considers to be Applied Constructive Mathematics.
WHAT PROFESSOR MAKSIMOVA DID
Dr. Maksimova's forte is her ability to describe results and ideas
from each of the different non-standard logics - logics motivated
by drastically different intuitions - in algebraic form, and to
use this algebraic reformulation as a means of
extending these results to other non-standard logics -
where the intuition behind the original logic is no longer
applicable.
These extensions are not only interesting mathematical results, they
deepen our understanding of different logics and thus, deepen our
understanding of the commonsense intuitions behind these logics.
In her ability to describe logical properties in algebraic terms and
thus, use mathematical (algebraic) ideas in logic-related problems,
Professor Maksimova continues the tradition going back all the way to
Boole's "An Investigation of the Laws of Thought".
CONGRATULATIONS
I want to express our sincere congratulations to Dr. Maksimova!
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