*7 - 9 November 2019, Institute of Philosophy, Prague*

**Thursday **

18:00 informal get together - discussion

dinner

**Friday **

9:30 - 9:45 opening

9:45 - 11:15 **Gabriella Pigozzi** An Opinion Diffusion Model With Deliberation

11:15 - 11:30 coffee

11:30 - 12:30 **Chris Fermueller** Judgement Aggregation from a Many-valued Logic Perspective

12:30 - 14:00 lunch

14:00 - 15:30 **Davide Grossi** Foundations for Liquid Democracy

15:30 - 15:45 coffee

15:45 - 16:45 **Tadeusz Litak** Infinite Populations, Choice and Determinacy

17:00 discussion

dinner

**Saturday **

9:45 - 11:15 **Allessandra Palmigiano** The Tiglath-Pileser Principle and a Model of Persuasion

11:15 - 11:30 coffee

11:30 - 12:30 **Ondrej Majer** Judgement Aggregation in the Framework of Four-Valued

12:30 - 14:00 lunch

14:00 - 15:30 **Daniele Porello** Judgment Aggregation in Substructural Logics

discussion

-------------------

An Opinion Diffusion Model With Deliberation

**Gabriella Pigozzi**

We propose an agent-based model of group decision-making, where discussions happen in dyadic inter-individual steps and moments of collective argumentative deliberation. Agents are argumentative vigilant, as they do not change opinion unless some justification is given to them. We study the evolution and convergence of opinions, the presence of extremism, and the correctness of decisions taken within the deliberating population. (Joint work with George Butler and Juliette Rouchier).

Judgement Aggregation from a Many-valued Logic Perspective

**Chris Fermueller**

We offer some comments and observations on the standard set-up for judgment aggregation from a many-valued logic point of view. Various links between topics in fuzzy logics and generalized forms of judgment aggregation have not yet been fully exploited. In particular, we will explore the following three approaches: (1) aggregation functions as generalized quantifiers; (2) valuation based abstract aggregation; (3) relaxations of individual rationality.

Foundations for Liquid Democracy

**Davide Grossi**

Liquid democracy is a proxy voting method where proxies are delegable: individual A may delegate her vote to B, who in turn may delegate it to C and so on. Ultimately, an individual's vote carries the weight given by the number of other individuals who (directly or indirectly) entrusted her as proxy. Liquid democracy has been used and popularised by a number of parties (e.g, the Piratenpartei in Germany, the Demoex Party in Sweden), associations and grassroots initiatives for democratic reforms (e.g., Interaktieve Democratie, Liquid US, Democracy Earth Foundation). Yet little scientific work exists on it. In this talk I will present recent work aiming at providing theoretical foundations for this novel voting method from the perspective of judgment aggregation, network theory, and game theory. The talk presents joint work with Zoé Christoff (Bayreuth), Daan Bloembergen (CWI Amsterdam) and Martin Lackner (TU Wien).

Infinite Populations, Choice and Determinacy

**Tadeusz Litak**

This talk criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow's theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the "Hildenbrand criterion" and argue that results based on unrestricted Axiom of Choice (AC) do not meet this criterion. The technically novel part is a proposal to use a set-theoretic principle known as the Axiom of Determinacy (AD), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of AD from the point of view of the research area in question is its game-theoretic flavor.

The Tiglath-Pileser Principle and a Model of Persuasion

**Allessandra Palmigiano**

This talk will go through several stories, and an open-ended discussion about the possibility of tying them together in a logical framework built around insights from historiography.

Judgement Aggregation intThe Framework of Four-Valued Probability

**Ondrej Majer**

Bellnap and Dunn introduced a four valued propositional logic allowing, in addition to the classical truth values True and False, the attribution of non-classical truth values Neither and Both accounting for possibly incomplete or contradictory information concerning a particular proposition. More recently there has been attempts to study also the probabilistic extensions of this logic by Dunn and Childers, Majer and Milne. The presented work picks up on the non-classical probability functions defined by Dunn but redefine the logical connectives in a way to avoid some undesirable properties of the original setting and introduce the necessary ingredients for defining conditional probabilities. Finally we propose strategies for aggregating four valued probability assignments and show the standard properties for the proposed aggregation procedures. (Joint work with Dominik Klein and Soroush Rafiee-Rad from the University of Bayreuth).

Judgment Aggregation in Substructural Logics

**Daniele Porello**

This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. We take a proof theoretical view of logical systems and we place our analysis within the realm of substructural logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, Linear Logic and Relevant Logics.

Nonclassical Logics and Judgement Aggregation

*7 - 9 November 2019, Institute of Philosophy, Prague*

**Thursday **

18:00 informal get together - discussion

dinner

**Friday **

9:30 – 9:45 opening

9:45 - 11:15 **Gabriella Pigozzi** An Opinion Diffusion Model With Deliberation

11:15 - 11:30 coffee

11:30 -12:30 **Chris Fermueller** Judgement Aggregation from a Many-valued Logic Perspective

12:30 - 14:00 lunch

14:00 - 15:30 **Davide Grossi** Foundations for Liquid Democracy

15:30 -15:45 coffee

15:45 -16:45 **Tadeusz Litak** Infinite Populations, Choice and Determinacy

17:00 discussion

dinner

**Saturday **

9:45 - 11:15 **Allessandra Palmigiano** The Tiglath-Pileser Principle and a Model of Persuasion

11:15 - 11:30 coffee

11:30 -12:30 **Ondrej Majer** Judgement Aggregation in the Framework of Four-Valued Probability

12:30 - 14:00 lunch

14:00 - 15:30 **Daniele Porello** Judgment Aggregation in Substructural Logics

discussion

-------------------

An Opinion Diffusion Model With Deliberation

**Gabriella Pigozzi**

We propose an agent-based model of group decision-making, where discussions happen in dyadic inter-individual steps and moments of collective argumentative deliberation. Agents are argumentative vigilant, as they do not change opinion unless some justification is given to them. We study the evolution and convergence of opinions, the presence of extremism, and the correctness of decisions taken within the deliberating population. (Joint work with George Butler and Juliette Rouchier).

Judgement Aggregation from a Many-valued Logic Perspective

**Chris Fermueller**

We offer some comments and observations on the standard set-up for judgment aggregation from a many-valued logic point of view. Various links between topics in fuzzy logics and generalized forms of judgment aggregation have not yet been fully exploited. In particular, we will explore the following three approaches: (1) aggregation functions as generalized quantifiers; (2) valuation based abstract aggregation; (3) relaxations of individual rationality.

Foundations for Liquid Democracy

**Davide Grossi**

Liquid democracy is a proxy voting method where proxies are delegable: individual A may delegate her vote to B, who in turn may delegate it to C and so on. Ultimately, an individual's vote carries the weight given by the number of other individuals who (directly or indirectly) entrusted her as proxy. Liquid democracy has been used and popularised by a number of parties (e.g, the Piratenpartei in Germany, the Demoex Party in Sweden), associations and grassroots initiatives for democratic reforms (e.g., Interaktieve Democratie, Liquid US, Democracy Earth Foundation). Yet little scientific work exists on it. In this talk I will present recent work aiming at providing theoretical foundations for this novel voting method from the perspective of judgment aggregation, network theory, and game theory. The talk presents joint work with Zoé Christoff (Bayreuth), Daan Bloembergen (CWI Amsterdam) and Martin Lackner (TU Wien).

Infinite Populations, Choice and Determinacy

**Tadeusz Litak**

This talk criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow's theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the "Hildenbrand criterion" and argue that results based on unrestricted Axiom of Choice (AC) do not meet this criterion. The technically novel part is a proposal to use a set-theoretic principle known as the Axiom of Determinacy (AD), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of AD from the point of view of the research area in question is its game-theoretic flavor.

The Tiglath-Pileser Principle and a Model of Persuasion

**Allessandra Palmigiano**

This talk will go through several stories, and an open-ended discussion about the possibility of tying them together in a logical framework built around insights from historiography.

Judgement Aggregation intThe Framework of Four-Valued Probability

**Ondrej Majer**

Bellnap and Dunn introduced a four valued propositional logic allowing, in addition to the classical truth values True and False, the attribution of non-classical truth values Neither and Both accounting for possibly incomplete or contradictory information concerning a particular proposition. More recently there has been attempts to study also the probabilistic extensions of this logic by Dunn and Childers, Majer and Milne. The presented work picks up on the non-classical probability functions defined by Dunn but redefine the logical connectives in a way to avoid some undesirable properties of the original setting and introduce the necessary ingredients for defining conditional probabilities. Finally we propose strategies for aggregating four valued probability assignments and show the standard properties for the proposed aggregation procedures. (Joint work with Dominik Klein and Soroush Rafiee-Rad from the University of Bayreuth).

Judgment Aggregation in Substructural Logics

**Daniele Porello**

This work contributes to the theory of judgment aggregation by discussing a number of significant non-classical logics. We take a proof theoretical view of logical systems and we place our analysis within the realm of substructural logics. After adapting the standard framework of judgment aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, Linear Logic and Relevant Logics.