### Seminar Series 2020

**Despite the COVID-19 pandemic, the Seminar Series 2020 successfully took place via Microsoft Teams.**

The sessions were as follows:

**19/03 ** Pere Prado (University of Milan).

*Towards a Tractable Epistemic Logic.*

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

*Sequent-based deductive argumentation.*

Sequent-based argumentation is a general approach to reasoning with deductive (logical) argumentation, motivated by proof-theoretic considerations. In this talk we review some of the principles of this approach and describe several results concerning its characteristics. In particular, we present completeness results in terms of dynamic proofs, show their relations to reasoning with maximal consistency, and study the satisfiability of common rationality postulates in several sequent-based settings. (This is a joint work with Christian Strasser and in some parts also with Anne Marie Borg.)

**07/05 **Jonathan Lawry (University of Bristol).

*Vagueness and Probability: Borderline Cases and Blurred Boundaries.*

This talk will consider the relationship between various aspects of vagueness and probability. Along the way we will consider what are potentially the best ways of modelling borderline cases of vague propositions and what type of measures naturally arise if you define probabilities over such models. Adopting this approach, we will outline a probabilistic semantics for fuzzy logic and explore relationships with Dempster-Shafer theory. Finally, we discuss the role of vagueness in consensus formation and show some results from multi-agent systems and swarm robotics.

**14/05** Marcelo Finger (University of Sao Paulo).

*Logic and Numbers — Combining logical reasoning with probabilities and counting.*

We present a research program which investigates the intersection of deductive reasoning with explicit quantitative capabilities. These capabilities encompass probabilistic reasoning, counting and counting quantifiers, and similar systems. The need to have a combined reasoning system that enables a unified way of reasoning with quantities has always been recognized in modern logic, as proposals of probabilistic logic reasoning are present since the work of Boole [1854]. Equally ubiquitous is the need to deal with cardinality restrictions on finite sets. More recently, a well-founded probabilistic theory has been developed for non-classical settings as well, such as probabilistic reasoning over Lukasiewicz infinitely-valued logic.

We show that there is a common way to deal with these several deductive quantitative capabilities, involving a framework based on Linear Algebra and Linear Programming. The distinction between classical and non-classical reasoning on the one hand, and probabilistic and cardinality reasoning on the other hand, comes from the different family of algebras employed. The quantitative logic systems also allow for the introduction of inconsistency measurements, which quantify the degree of inconsistency of a given quantitative logic theory, following some basic principles of inconsistency measurements.

On the computational level, we aim at exploring quantitative logic systems in which the complexity of reasoning is “only NP-complete”. We provide open-source implementations for solvers operating over those systems and study some notable empirical properties, such as the presence of a phase transition. After a general introduction of the research program, we will detail the classical probabilistic reasoning engine.

**21/05** Nina Gierasimczuk (Danish Technical University).

*From grammar inference to learning action models. A case for Explainable AI.*

The endeavour of finding patterns in data spans over many different fields, from computational linguistics to self-driving cars. Machine learning is undeniably a great source of progress across the board. In my talk I will resurrect the old way of thinking about learning, long the lines of symbolic artificial intelligence. I will report on a recent work about inferring action models from descriptions of action executions. Such a framework constitutes an informed, reliable and verifiable way of learning, in which the learner can not only classify objects correctly, but can also report on the symbolic representation she bases her conjectures on. It is nice that the ability for AI to “explain itself” in such a way is nowadays a growing demand in the community. My action models are those of Dynamic Epistemic Logic, and the methodology is automata-theoretic in spirit.

**27/05** Anthia Solaki (University of Amsterdam).

*Bridging Epistemic Logic and Resource-Bounded Human Reasoning.*

Standard epistemic logic suffers from the problem of logical omniscience: its agents are perfect reasoners with unlimited inferential power. We argue that, even from a normative point of view, this modelling is inadequate for it sets requirements that cannot be actually attained, according to solid empirical evidence on performance of humans in reasoning tasks. We therefore design a non-standard framework in line with experimental findings about the cognitive effort involved in deductive reasoning. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles and at the same time account for (limited) reasoning steps. We further show that our models can be reduced to awareness-like structures; this allows for useful technical results like a sound and complete axiomatization. We finally discuss how this approach can be combined with actions of external information, and result in a more cognitively plausible modelling of group reasoning as well.

**PROGRAMME & ABSTRACTS**

14:00 — 15:00 Carlos Caleiro (Universidade de Lisboa).

*Semantics for joint calculi. *

* *In this talk we show how to endow the general mechanism for combining logics known as fibring with a meaningful and useful semantics given by partial non-deterministic logical matrices (PNmatrices). We present and study the properties of two semantical operations: a unary operation of omega-power of a given PNmatrix, and a binary operation of strict product of PNmatrices with possibly distinct similarity types (signatures). We show that, together, these operations can be used to characterize the fibring of propositional logics, thus providing a meaningful semantics for joint Hilbert calculi. We illustrate the constructions with a few meaningful examples, hinting also at multiple-conclusion logics and calculi and the precise role played by omega-powers.

Joint work with Sérgio Marcelino.

* *

15:00 — 16:00 Sérgio Marcelino (Universidade de Lisboa).

Adding axioms: semantics and analytic calculi*.*

In this talk we consider the general problem of strengthening the logic of a given PNmatrix with a set of axioms, and then providing an analytic calculus for the resulting logic.

Our first result has three key ingredients: (1) the very general but not very effective method stemming from the theory of combined logics, (2) the technique of rexpansions developed by Avron and coauthors, and most prominently (3) the idea of lookahead values previously used by Ciabattoni, Lahav, Spendier, and Zamansky. Namely, under certain restrictions on the given semantics and the shape of the axioms we provide an effective method for obtaining a neat PNmatrix characterization of the resulting logic, and show that it covers a myriad of examples in the literature.

Our second result shows, independently, how to obtain analytic multiple-conclusion calculi for the logic associated to any given monadic PNmatrix, with emphasis on the way we deal with partiality. We illustrate our constructions with several meaningful examples. Joint work with Carlos Caleiro.

16:00 — 16:30 Coffee break

16:30 — 17:30 João Marcos ( Universidad Federal do Rio Grande do Norde ).

*Consequence Beyond Truth and Proof*

In this talk I shall experiment with a provocative analysis of logical

consequence done neither in terms of preservation of truth nor in

terms of preservation of warrant to assert. The analysis will be done

instead from an abstract viewpoint, taking the perspective of

judgmental agents that entertain certain cognitive attitudes towards

the informational content of given sentences. In this approach,

neither truth-values nor inference rules need to be taken as

primitive, for they can be fruitfully explicated in terms of a

conceptually prior notion of compatibility between possibly

overlapping cognitive attitudes of a given agent. I will discuss some

effects of such an approach on the provision of a satisfactory theory

of meaning that goes beyond truth and proof, but will also show how

the announced analysis maps naturally into a four-valued

non-deterministic semantics, and into an analytic bi-dimensional proof

system. If time permits, I will also discuss how logical consequence

so understood may pave the way towards a novel approach concerning the

understanding of gappy and glutty reasoning.

**2nd** **Workshop on Logic and Information**

November 28 2019

09:00-13:15

**PROGRAMME**

09:00 — 09:45 Costanza Larese (SNS Pisa). *Towards Depth-Bounded First-Order Logics.*

09:45 — 10:30 Paolo Baldi (Università degli Studi di Milano).*Depth-Bounded Belief functions.*

10:30 — 10:45 Coffee break

10:45 — 11:30 Marco Zaffalon (IDSIA Lugano). * On the beauty and unifying character and power of coherence.*

11:30 — 12:15 Alessandro Facchini (IDSIA Lugano).

*The logic of desirability, bounded rationality and entanglement.*

12:15 — 12:30 Coffee break

12:30 — 13:15 Tommaso Flaminio (IIIA – CSIC Barcellona). *The probability, the geometry and the logic of (strict) coherence on Łukasiewicz events*

**VENUE** Sala Enzo Paci, Dipartimento di Filosofia

Università degli Studi di Milano, Via Festa del Perdono 7, 20122 Milano.

November 5th, 2019, 16.00

Venue: Sala Enzo Paci, Via Festa del Perdono 7, Milan

**Speaker**: Jacopo Tagliabue (COVEO)**Title**: “A Rose by any other Name”. Exploiting Knowledge Graphs for Lexical Learning in Information Retrieval**Abstract: **Information retrieval (IR) systems need to constantly update their knowledge as objects and language change over time. Due to linguistic data sparsity in the long tail of search queries, learning lexical concepts resists standard embedding-based approaches. We propose a learning framework that leverages symbolic information as encoded in knowledge graphs, both as a source of prior knowledge over lexical meanings and as a means of generating experiments to update this prior. The proposed framework is a novel combination of two ideas from cognitive science, lexical learning as inference and optimal experiment design, for the purpose of efficient IR. In this talk, we introduce the key components of this system, discuss preliminary results in idealized settings and share our roadmap for future improvements.**BIO: **Jacopo Tagliabue, Lead AI Scientist, Coveo, New York

Jacopo Tagliabue was co-founder, CTO and nerd in chief at Tooso – a Gartner “Cool Vendor” company acquired by Coveo in 2019. Before Tooso, he has been a Best & Brightest fellow at the Santa Fe Institute and led the Data Science team of AxonVibe in New York. In previous lives, he managed to get a Ph.D. (UNISR/MIT), do scienc-y things for a professional basketball team, simulate a pre-Columbian civilization and give an academic talk on video games (among others improbable “achievements”). His research and industry work has been featured several times in international conferences and the general press.

June 12 2019, 16:30h

Luis Estrada-González (National Autonomous University of Mexico)

The Bochum Plan & the foundations of contra-classical logics

**Logic Seminar**

May 15 2019, 16:30h

Anna Zamansky (University of Haifa)

Paraconsistent reasoning: between theory and practice

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

May 15 2019, 16:30h

Paolo Baldi (Università degli studi di Milano)

Modal logics for reasoning about uncertainty

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

May 8 2019, 16:30h

Gabriella Pigozzi (Université Paris-Dauphine)

Group argument evaluation

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

April 3 2019, 16:30h

Davide Ciucci (Università degli Studi di Milano Bicocca)

A unifying framework for several logics of uncertain and conflicting information

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

March 20 2019, 16:30h

Daniele Porello (CNR)

Social Mechanisms for Aggregating Ontologies

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

March 6 2019, 16:30h

Giuseppe Primiero (UniMi)

A Logic of Negative Trust.**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

February 20 2019, 16:30h

Nikos Gorogiannis (Facebook)

Challenges and research opportunities for formal methods in the “real world”.

**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Logic Seminar**

February 7 2019, 14:30h

Vincenzo Crupi & Andrea Iacona (Università di Torino)

Three Ways of Being Non-Material.**Venue**

Sala Enzo Paci, Dipartimento di Filosofia.

**Workshop on Formal Argumentation**29 January — 1st February 2019

**PROGRAMME**

29 January 2019

10:30– 12:30 Marcello D’Agostino (Università degli Studi di Milano)

30 January 2019

10:00– 11:30 Sanjay Modgil (King’s College London)

11:30– 13:00 Jesse Heyninck (Ruhr Universität Bochum)

31 January 2019

10:00– 11:30 Chris Fermüller (Technische Universität Wien)

11:30– 13:00 Marcello D’Agostino (Università degli Studi di Milano)

1 February 2019

10:30– 12:30 Hykel Hosni (Università degli Studi di Milano)

**VENUE**

Sala Enzo Paci, Dipartimento di Filosofia

Universitá degli Studi di Milano, Via Festa del Perdono 7, 20122 Milano.

**Workshop on Logic and Information**

January 16 2019

14:00-17:00

**PROGRAMME** 14:00– 15:00 Patrick Allo (Vrije Universiteit Brussel)

*The Epistemology of Nondistributive Profiles*

15:00– 16:00 Marcello D’Agostino and Hykel Hosni (Universitá degli Studi di Milano)

*Depth-bounded logic and probability*

16:00– 17:00 Giuseppe Primiero (Universitá degli Studi di Milano)

*A Logic of Efficient and Optimal Designs*

**VENUE** Sala Enzo Paci, Dipartimento di Filosofia

Universitá degli Studi di Milano, Via Festa del Perdono 7, 20122 Milano.