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.

Guram Bezhanishvili	John Harding	Pat Morandi (Emeritus)	Joel Lucero-Bryan	Ilya Shapirovskiy

News

• In 2023, our group received a 5-year NSF grant for a Research Training Group in Logic and its Application
• John Harding was a co-organizer of AMS Special Session on Algebraic Structures in Topology, Logic, and Arithmetic I, AMS Sectional Meeting, University of Texas at El Paso, September 17-18, 2022. 
• Fall 2021: new weekly seminar in Foundations.
• On June 9-13, the BLAST 2021 international online conference was held in our Department. We had about one hundred talks and more than 250 registered participants from 30+ countries.
  
• In May 2021, Luca Carai received his PhD.
  
  

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

For prospective graduate students 

• Logic and Set Theory
• Mathematical Structures in Logic 
• Universal Algebra and Model Theory 

Events and Associations

• We hold a weekly Foundations seminar and are also involved in a weekly Algebra Seminar.
• We 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 the journals Advanced Studies: Euro-Tbilisi Mathematical Journal, Bulletin of Symbolic Logic, Mathematica Slovaca (adv. board), Order, Proyecciones, the Rocky Mountain Journal of Math.
• John Harding is the treasurer of the International Quantum Structures Association.

Students

Points of contact