Speaker: EDWARD KROHNE (UNT)

Title: Gentzen's Ideas on Logic

Abstract: The first-order logic connectives ∧, ∨, ¬, →, ∀ and ∃ underpin almost all mathematics, and are worth studying in their own right. A variety of techniques exist for showing if statements, such as A→A or (A∧B)→B, are tautological (⊤, always true). We will review these logical connectives and then provide an elegant technique for proving tautologies. We will use a system called a Gentzen system. If time permits, we will discuss the relationship between Gentzen systems and truth valuation, and sketch an argument that absurdities like A∧¬A cannot be proven in the system.
This talk will require no specialized knowledge of logic or mathematics, though an existing familiarity with the connectives of first order logic will be helpful.