A Multi-Agent Depth Bounded Boolean Logic

Recent developments in the formalization of reasoning, especially in computational settings, have aimed at defining cognitive and resource bounds to express limited inferential abilities. This feature is emphasized by Depth Bounded Boolean Logics, an informational logic that models epistemic agents with inferential abilities bounded by the amount of information they can use. However, such logics do not model the ability of agents to make use of information shared by other sources. The present paper provides a first account of a Multi-Agent Depth Bounded Boolean Logic, defining agents whose limited inferential abilities can be increased through a dynamic operation of becoming informed by other data sources.

KEYWORDS: Logic of information, Resource bounded reasoning, Information transmission

Cignarale, G., Primiero, G. A Multi-Agent Depth Bounded Boolean Logic. SEFM 2020. Lecture Notes in Computer Science, vol 12524. https://doi.org/10.1007/978-3-030-67220-1_14

New group member!

We are delighted to welcome a new postdoctoral researcher, Esther Anna Corsi, who joined our group on the 1st of December! Esther got a BSc and MSc in Mathematics from the University of Siena. She will soon defend her Ph.D. thesis at TU Wien, where she has worked under the supervision of Prof. Chris Fermüller, mainly in the field of Argumentation Theory. Her research interests primarily lie in the area of Uncertain Reasoning, Logical Argumentation, Non-standard Logics and Game Theory. For more information, check out her website and our members page.

Last talk of the Online Seminar Series 2020 — V. M. Abrusci: Syllogism and linear logic

The last talk for the year within the cycle of online seminars organized by the Milan Logic Group will be given by Vito Michele Abrusci on December 3rd, 2020, at 10:30 via Zoom. Please contact us for details for joining and stay tuned to this website for upcoming news on events for 2021.


Discoveries on syllogisms, induced by linear logic, will be presented:

a)     Categorical Propositions and Syllogisms are closed under duality. The system of Aristotelian syllogisms (1st, 2nd and 3rdfigures) is complete under duality. 

b)    Categorical Propositions and Syllogisms may be represented inside multiplicative fragment of Linear Logic (no need of contraction and weakening rules, no need of first order quantifiers). Better understanding of the Aristotelian notion of “contradictory propositions”. 

c)     Syllogisms as proof-nets, and thus as geometrical objects and as programs. 

d)    Why 1st figure syllogisms are simple syllogisms, and the other syllogisms are not simple? A geometrical answer: 1st figure syllogisms are planar proof-nets, whereas other syllogisms are not planar proof-nets. 

e)    Reductions of syllogisms to 1st figure syllogisms are geometrical ways to transform non-planar graphs into planar graphs. 

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.

Effects of misinformation diffusion during a pandemic

Applied Network Science Cover Image

The role of misinformation diffusion during a pandemic is crucial. An aspect that requires particular attention in the analysis of misinfodemics is the rationale of the source of false information, in particular how the behavior of agents spreading misinformation through traditional communication outlets and social networks can influence the diffusion of the disease. We studied the process of false information transmission by malicious agents, in the context of a disease pandemic based on data for the COVID-19 emergency in Italy. We model communication of misinformation based on a negative trust relation, supported by findings in the literature that relate the endorsement of conspiracy theories with low trust level towards institutions. We provide an agent-based simulation and consider the effects of a misinfodemic on policies related to lockdown strategies, isolation, protection and distancing measures, and overall negative impact on society during a pandemic. Our analysis shows that there is a clear impact by misinfodemics in aggravating the results of a current pandemic.

KEYWORDS  Misinformation, Misinfodemics, Multi-Agent Systems

Prandi, L., Primiero, G. Effects of misinformation diffusion during a pandemic. Appl Netw Sci 5, 82 (2020). https://doi.org/10.1007/s41109-020-00327-6 (Open Access)

Boolean algebras of conditionals, probability and logic

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish the properties of conditional events which depend on probability and those which are intrinsic to the logico-algebraic structure of conditionals. Our main result provides a way to regard standard two-place conditional probabilities as one-place probability functions on conditional events. We also consider a logical counterpart of our Boolean algebras of conditionals with links to preferential consequence relations for non-monotonic reasoning. The overall framework of this paper provides a novel perspective on the rich interplay between logic and probability in the representation of conditional knowledge.

KEYWORDS Conditional probability; conditional events; Boolean algebras; preferential consequence relations

T. Flaminio, L. Godo and  H. Hosni. (2020). “Boolean algebras of conditionals, probability and logic” Artificial Intelligence.  doi.org/10.1016/j.artint.2020.103347 (Open Access)

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,

A Logic of Negative Trust

We present a logic to model the behaviour of an agent trusting or not trusting messages sent by another agent. The logic formalizes trust as a consistency checking function with respect to currently available information. Negative trust is modeled in two forms: distrust as the rejection of incoming inconsistent information; mistrust, as revision of previously held information becoming undesirable in view of new incoming inconsistent information, which the agent wishes to accept. We provide a natural deduction calculus, a relational semantics and prove soundness and completeness results. We overview a number of applications which have been investigated for the proof-theoretical formulation of the logic.

G.Primiero, A Logic of Negative Trust, Journal of Applied Non-Classical Logic,

A Fully Rational Account of Structured Argumentation Under Resource Bounds

ASPIC+ is an established general framework for argumentation and non-monotonic reasoning. However ASPIC+ does not satisfy the non-contamination rationality postulates, and moreover, tacitly assumes unbounded resources when demonstrating satisfaction of the consistency postulates. In this paper we present a new version of ASPIC+ – Dialectical ASPIC+ – that is fully rational under resource bounds.

M. D’Agostino and S. Modgil. A Fully Rational Account of Structured Argumentation Under Resource Bounds. Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence (IJCAI-20)

IJCAI, the International Joint Conference on Artificial Intelligence, is the premier conference for the international AI community to communicate the advances and achievements of AI research. 
IJCAI-PRICAI20 received  4717 valid submissions, of which only 592 have been accepted, for a record-low overall acceptance rate of 12.6%.