Applied logic for…the United Nations

I am proud to announce my logical contribution to the “United Nations Convention against Transnational Organized Crime and the Protocols thereto ” (UNTOC), in particular concerning its Review Mechanism.

The Convention represents the only global treaty instrument to fight transnational organized crime, as it counts 190 States parties.

An important obligation for the parties to the Convention is the participation in a peer review mechanism, through which States review each other, on how they implemented the measures requested by the Convention (or its Protocols).

This means that, according to the relevant resolution, each State party should be assigned some reviewers in a random fashion,  subject to  a series of constraints, such as, for instance:

“ (a) States shall not undertake mutual reviews;

(b) For each instrument, a State party under review shall not be reviewed by States which are not parties to the same instrument; in the case that a drawn reviewing State is not party to all the instruments to which the State under review is party, an additional drawing of lots shall be carried out so as to select an additional reviewing State only for those instruments;

(c) The total number of reviewing States for all instruments shall not exceed four unless the State under review decides otherwise…. ”

I was involved at this point, in devising a fair, random procedure for the assignment of reviewers, complying with all the relevant constraints.

After realizing that, due to the intricacies of the requirements, a standard physical procedure, consisting in drawing of lots, would have requested a forbidding amount of time for preparation and material execution, we opted for an automated procedure.

In this task, logic played an essential part. I encoded the legal constraints  into a logical language, and  developed a program, based on the Answer Set Programming paradigm, to find optimal random solutions for the problem at hand.
The program was accepted by the State parties, and is finally to be used on November 23rd, in a plenary meeting with the delegates of all the States for the official assignment of reviewers.

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.