Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory


This paper is a contribution to the study of two distinct kinds of logics for modelling uncertainty. Both approaches use logics with a two-layered modal syntax, but while one employs classical logic on both levels and infinitely-many multimodal operators, the other involves a suitable system of fuzzy logic in the upper layer and only one monadic modality. We take two prominent examples of the former approach, the probability logics Plin and Prpol (whose modal operators correspond to all possible linear/polynomial inequalities with integer coefficients), and three logics of the latter approach: PrŁ, PrŁΔ and PrΔ (given by the Łukasiewicz logic and its expansions by the Baaz–Monteiro projection connective Δ and also by the product conjunction). We describe the relation between the two approaches by giving faithful translations of Prlin and Prpol into, respectively, PrŁΔ and PrΔ, and vice versa. We also contribute to the proof theory of two-layered modal logics of uncertainty by introducing a hypersequent calculus HPrŁ for the logic PrŁ. Using this formalism, we obtain a translation of Prlin into the logic PrŁ, seen as a logic on hypersequents of relations, and give an alternative proof of the axiomatization of Prlin.

P. Baldi, P.Cintula, C.Noguera. Classical and Fuzzy Two-Layered Modal Logics for Uncertainty: Translations and Proof-Theory, International Journal of Computational Intelligence Systems,
https://doi.org/10.2991/ijcis.d.200703.001

Online Seminar Series

After the first talk by Pere Pardo, our online seminar series continues!

All the talks will take place via Microsoft Teams, starting at 17:00.

Here is the schedule for the semester:

22/04 – Ofer Arieli   (Academic College of Tel Aviv)

07/05 – Jonathan Lawry (University of Bristol)

14/05 – Marcelo Finger (University of Sao Paulo )

21/05 – Nina Gierasimczuk ( Danish Technical University )

27/05 – Anthia Solaki (University of Amsterdam)

11/06- Rasmus Rendsvig (University of Copenhagen)

SEMINARS ON 12/03 AND 19/03 CANCELED

Unfortunately, due to the precautionary measures for the Coronavirus outbreak, we have to cancel yet two seminars in our series: the one scheduled for 12/03, to be held by Pere Pardo (Unimi) and the one scheduled for 19/03, to be held by Anthia Solaki (University of Amsterdam).

We will do our best to have all the canceled seminars rescheduled at a later time this year.