Logic and Foundations Group
The Logic and Foundations group in the Department of Mathematical Sciences conducts research in the application of algebraic and topological structures to logic and foundational issues.
Faculty: Guram Bezhanishvili, Mai Gehrke, John Harding, Pat Morandi
Emeritus Faculty: Joseph Kist, Art Kruse, Ray Mines, David
Muller, Carol Walker, Elbert Walker
PSL (A research laboratory on campus): Alex Pogel, Tim
Hannan
Current research topics: Lattices, distributive lattices,
and Boolean algebras with operators, and their applications
to logic; topological and order-topological models of
non-classical logics; algebraic aspects of fuzzy logic;
orthomodular structures and quantum logic, intuituionistic
ans modal logics.
Recently graduated students: Alex Pogel (Ph.D. 1998) currently
at PSL, Hideo Nagahashi (Ph.D. 2002) currently a Post-doctoral
Fellow at Arizona State, Barry Church (Masters 2000)
currently a Ph.D. student at Oregon State, Hailin Sang
(Masters 2003) currently a Ph.D. student at University
of Connecticut.
Current Students: Joel Lucero-Bryan (Ph.D.), Joel funded
through the Department of Mathematical Sciences.
Events: We hold a weekly Lattice Theory Seminar. We hosted
the 1999 Holiday Symposium with Wim Blok and Bjarni Jonsson
as main speakers. In cooperation
with PSL we hosted conferences in January 2000 and January
2001 on applications of logic to intelligent systems. With
support of a grant of Civil Research Development Fund (CRDF)
and Georgian Research Development Fund (GRDF) and in cooperation
with the Georgian Academy of Sciences we held a conference "Algebraic
and Topological Methods in non-Classical Logics" at
Tbilisi State University, Tbilisi, Georgia in the Summer
of 2003. We have been involved in organization of the past
two North American Summer Schools in Logic, Language, and
Information. Our group has members on the editorial boards
of Order and Studia Logica, two of the main specialist
journals in the field.
Points of contact: G. Bezhanishvilli, M. Gehrke, J. Harding.