Non-Standard Ways of Aggregating Formulas in Sequent Calculi

Non-Standard Ways of Aggregating Formulas in Sequent Calculi

Sala de Seminários do DMAT e online

2023-04-27 - 14:30

2023-04-27 - 15:30

Speakers: Camillo Fiore and Joaquín S. Toranzo Calderón
IIF-SADAF-CONICET, Universidad de Buenos Aires

Date: Thursday, 27 April 2023, 14:30
Venue: Sala de Seminários do DMAT 

Title: Non-Standard Ways of Aggregating Formulas in Sequent Calculi

Abstract: When Gentzen formulates his calculus LK for classical logic, he makes two key assumptions about the informal interpretation of a sequent: first, the commas in the antecedent are to be read as conjunctions, while the commas in the succedent are to read as disjunctions; second, an empty antecedent amounts to a logical truth, while an empty succedent amounts to a logical falsehood. In this talk, we present a number of sequent calculi that abandon one or both of Gentzen’s assumptions. More precisely, we study the family of sixteen systems that coincide with LK in the formula-formula fragment, but make a perhaps different choice about whether commas in the antecedent (succedent) should be read conjunctively or disjunctively, and whether an empty antecedent (succedent) should amount to a logical truth or a logical falsehood. We provide a sound and complete semantics for each of these systems. Also, we argue that our systems enjoy potential applications; for instance, they can be understood as applying the classical modes of reasoning to different epistemic contexts—where the relevant agents have specific goals and information at their disposal.