Speaker: Guillaume Massas (Chapman University) 

Time: 2025/09/30 (Tuesday) 10:00-12:00 

Zoom Meeting: http://us02web.zoom.us/j/87118074501?pwd=xXWcqAsNec7YTaRG01DhEwEQvmplo2.1

Meeting ID: 871 1807 4501

Passcode: 652685

Abstract:

Recently introduced by Wes Holliday, fundamental logic is a propositional logic that captures all and only those properties of conjunction, disjunction and negation that follow from their introduction and elimination rules in Fitch's natural deduction system. The resulting logic is strictly weaker than orthointuitionistic logic, the intersection of orthologic with the implication-free fragment of intuitionisitic logic. Fundamental logic has a natural algebraic semantics, given in terms of fundamental lattices (lattices equipped with a dually self-adjoint unary operation), and a natural concrete semantics, given in terms of closure operators induced by relations on sets.

In this talk, I will present four recent results that shed some new light on the relationship between fundamental logic, orthologic and (the implication-free fragment of) intuitionistic logic. The first two results, based on some joint work with Wes Holliday, are full and faithful translations of fundamental logic into modal orthologic and modal intuitionistic logic. These translations generalize the Gödel-McKinsey-Tarski and Goldblatt translations of intuitionistic logic and orthologic into S4 and KTB respectively. The last two results, based on some joint work with Juan P. Aguilera, are about extensions of fundamental logic. We provide a simple axiomatization of orthointuitionistic logic and show that the lattice of super-orthointuitionistic logics is isomorphic to the product of the lattice of intermediate logics and the lattice of quantum logics.