Ciclo di seminari
What it needs to be conservative
Abstract dell'evento
Kuroda's double negation shift (DNS) is indispensable for the generalisation to first-order logic of Glivenko's theorem for propositional logic: modulo double negation, classical predicate logic is conservative over intuitionistic logic, with DNS added to the latter in the predicate case. Related conservation theorems have turned out to hinge upon the corresponding variants of DNS, which made us perceive a general phenomenon in the borderland of classical and constructive reasoning. Abstracting Glivenko's theorem from double negation and provability to a nucleus over an inductively generated entailment relation requires that all generating rules of the latter remain admissible in the Kleisli extension, i.e. when the nucleus is applied to the succedent of every premiss and the conclusion. This conservation criterion clearly is automatic for every rule which is right invariant, i.e. all premisses and the conclusion of which have in common the very same succedent. For example, axioms put as premissless rules are trivially right invariant. The rules of the single-succedent calculi for propositional, infinitary and first-order minimal logic can be expressed as right invariant rules with the exceptions of the right rules for implication, infinite conjunction and the universal quantifier, respectively. As a matter of fact the conservation criteria for these critical right rules have proved to be counterparts of DNS.
Programma
“What it needs to be conservative” joint work with Giulio Fellin, University of Brescia, and Sara Negri, University Genoa
Relatori/Relatrici
Peter Schuster (University of Verona)
Dettagli sull'evento
Data e luogo
Inizio: 30/05/2024
alle ore 16:00
Fine: 30/05/2024
alle ore 18:00
Palazzo Albani (Urbino, Via Viti, 10) Aula C1
Organizzato e promosso da:
Dipartimento di Scienze Pure e Applicate
Scuola di Scienze, Tecnologie e Filosofia dell'Informazione
LM-78 - Classe delle lauree magistrali in scienze filosofiche - Filosofia dell'informazione. Teoria e gestione della conoscenza
Modalità di partecipazione
Altre informazioni utili
Ingresso libero. Per informazioni: pierluigi.graziani@uniurb.it
