Seminario
The Logic of Secrets, Somebody-Knows and Weak Forms of Conjunctive Distribution in Modal Logics
Abstract dell'evento
I will start with discussing formalising the notion of knowing a secret as a modality in modal logic, by combining standard notions of knowledge and ignorance from modal epistemic logic. Roughly speaking, Ann knows a secret if and only if she knows it and she knows that everyone else does not know it. The main aim is to study the properties of these secretly knowing modalities. It turns out that the modalities are non-normal, and are characterised by a derivation rule we call \emph {Interpolation} that is stronger than Equivalence but weaker than Monotonicity. We study the Interpolation rule and position it in the landscape of non-normal modal logics. We show that it, in combination with basic axioms, gives us a complete characterisation of the properties of the secretly knowing modalities under weak assumptions about the properties of individual knowledge, in the form of a sound and complete axiomatisation. This characterisation gives us the most basic and fundamental principles of secretly knowing.
In normal modal logics the modalities distribute over conjunction. Replacing Monotonicity with Interpolation results in weakening distribution over conjunction in one direction. Weakening the equivalence in the other direction we get non-adjunctive modal logics. I will look at a particular such weakening—"weak" conjunctive closure. I will present another application in epistemic logic: weak conjunctive closure characterises the notion of "somebody-knows". Again, I will present completeness and other meta-logical results.
Relatori/Relatrici
Thomas Ågotnes (University of Bergen)
Dettagli sull'evento
Data e luogo
Inizio: 12/03/2025
alle ore 11:00
Fine: 12/03/2025
alle ore 13:00
Palazzo Albani (Urbino, Via Viti, 10) Aula C5 - Sala Lauree
Organizzato e promosso da:
Dipartimento di Scienze Pure e Applicate
Scuola di Scienze, Tecnologie e Filosofia dell'Informazione
