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.
Current research topics: Ordered algebraic structures, lattices 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 and modal logics; and formal concept analysis. For more details, see our homepages at Guram, John, Pat, or our researchgate pages at Guram, John, Pat.
For prospective graduate students: We offer a good range of graduate courses in areas of foundations including courses on Logic, Lattice Theory, Axiomatic Set Theory, and Universal Algebra. Special topics classes are also offered. Foundations is one of the course sequences for our PhD comprehensive exam. We continue to have a fine group of Master’s and PhD students working in various areas of foundations.
Events and Associations: We hold a weekly Algebra/Lattice Theory Seminar and are involved in the organization and/or scientific committees of a good number of conferences held in the local area, regionally, and internationally. These include AiML, BLAST, IQSA, QPL, TACL, and TOLO. Our group has members on the editorial boards of Order and Studia Logica (two of the main specialist journals in the field) as well as Mathematica Slovaca (adv. board), the Tbilisi Journal of Mathematics, the Journal of Language, Logic, and Computation, the Rocky Mountain Journal of Math, and on the Council of the International Quantum Structures Association.
Students: In May 2019, Maria Cruz and Kristina Brantley received their PhDs. Luca Carai hopes to be next.
- Our dept has a tenure-track position in Foundations. See Mathjobs.
- Our dept is creating an undergraduate concentration in Foundations with philosophy.