Universal Algebra and Logic

Fall 2020 Seminars

Time: Monday, September 28, 2–3 PM (CDT, UTC -5)
Place: Zoom
Speaker: Bogdan Chornomaz
Title: Introduction to Möbius functions
Abstract: We will give a brief introduction to Möbius functions on lattices and discuss their basic properties. We will also prove that lattices with nonvanishing Möbius function are SSP and that geometric lattices have a nonvanishing (moreover, alternating) Möbius function.

Time: Monday, September 21, 2–3 PM (CDT, UTC -5)
Place: Zoom
Speaker: Bogdan Chornomaz
Title: SSP ?= RC
Slides: here
Preprint: here
Abstract: We will talk about SSP ?= RC conjecture, which states that a finite lattice satisfies an analogue of Sauer-Shelah-Perles lemma iff it is relatively complemented. In particular, we discuss one strategy of attacking the conjecture using certain colored bipartite graphs. We will hit the wall by constructing a “counterexample” in the language of those graphs. Then we will try to lift it to the counterexample to the general conjecture using some “pumping” constructions and will hit the wall again.

Time: Monday, September 14, 2–3 PM (CDT, UTC -5)
Place: Zoom
Speaker: Adam Prenosil
Title: Four-valued logics of truth, non-falsity, and material equivalence
Slides: here
Abstract: the purpose of this talk is to demonstrate how to work with quasivarieties (universal Horn classes) in a relational signature which consists of more than one predicate symbol. While universal algebraists work with the binary equality predicate, and algebraic logicians work with the unary truth predicate, the four-valued Belnap–Dunn logic provides a natural setting where two unary predicates arise (namely the truth and non-falsity predicates), as well as an equality predicate. We show how to axiomatize the logic of truth and non-falsity, as well as the logic of truth and equality, determined by the four-valued algebraic semantics of Belnap and Dunn.

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Contact Information

Department of Mathematics
Vanderbilt University
Stevenson Center 1326
Nashville, TN 37240

Phone: (615) 322-6672
Fax: (615) 343-0215