**Date:** 5-6 November 2019

**Venue:** TU Vienna

This meeting is devoted to exchanging recent work and ideas (mainly) in the intersection of logic and argumentation. We also want to discuss prospects for further joint activities. The event is intended as a follow-up to a similar meeting in Milano, end of January 2019.

We will kick-off the meeting by a **joint dinner** on the evening of Monday,
November 4 to which all participants are invited by our department.

*Place:* Wieden-Bräu, Waaggasse 5, 1040 Wien

*Time:* 7pm at the Restaurant
or 6.50pm at Chris' office

Location:

**Meeting room:** "Menger" 3rd floor, Favoritenstraße 11, Stiege 3, entrance
to Dept. "Logic & Computation (192)" opposite the elevator that you'll
find passing the porter's lodge, if entering from Favoritenstr. 11

**Office of Chris:** Favoritenstr. 9, Stiege 2 (Elevator), 3rd floor, call
18543 at the door to get access

List of participants:

- Ofer Arieli
- Paolo Baldi
- Esther Corsi
- Marcello D'Agostino
- Chris Fermüller
- Davide Grossi
- Jesse Heyninck
- Pere Pardo
- Anna Rapberger
- Kees van Berkel

**Preliminary Schedule:**

Tuesday, November 5

10.00-10.45 Jesse Heyninck
*An Argumentative Characterization of Disjunctive Logic Programming* [Abstract]

10.45-11.30 Esther Corsi
*Attack Principles in Logical Argumentation Theory* [Abstract]

11.30-11.45 Coffee break

11.45-12.45 Ofer Arieli
*Sequent-Based Argumentation Frameworks: Some Recent Results * [Abstract]

12.45-14.00 Lunch break

14.00-15.00 Pere Pardo
*Deontic argumentation for practical reasoning* [Abstract]

15.00-15.45 Paolo Baldi
*Depth-Bounded Belief functions* [Abstract]

15.45-16.00 Coffee break

16.00-17.30 Discussions

Wednesday, November 6

10.00-11.00 Marcello D'Agostino
*Logical Arguments and Dialectic* [Abstract]

11.00-11.15 Coffee break

11.15-12.00 Kees van Berkel
*Evaluating Networks of Structured Arguments with Support:
A Case Study in Mimamsa Dialectics* [Abstract]

12.00-12.30 Anna Rapberger
*Collective Attacks in Claim-centered Abstract Argumentation* [Abstract]

12.30-14.00 Lunch break

14.00-16.30 discussions and (long) coffee break

16.30-17.30 Davide Grossi
*Credulous Acceptability, Poison Games and Modal Logic* [Abstract]

Sequent-based argumentation is a general approach to reasoning with logical argumentation, motivated by proof-theoretic considerations. In this talk we recall some of the principles of this approach and describe recent results concerning its characteristics. In particular, we consider relations between sequent-based argumentation and reasoning with maximal consistency, and study the satisfaction of common rationality postulates in several sequent-based settings.

We present results which extend those of Caminada and Schulz [1] by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs. For this, we incorporate the setting of Heyninck and Arieli (see [2]), in which reasoning with assumption-based argumentation frameworks is based on certain core logics and that the strict/defeasible assumptions may be arbitrary formulas in those logics. In our case, the core logic respects some inference rules for disjunction, which allows disjunctions in the heads of the programs rules to be handled properly.

References:

- Martin Caminada and Claudia Schulz. On the equivalence between assumption-based argumentation and logic programming. Journal of Artificial Intelligence Research, 60:779825, 2017. 7.
- Jesse Heyninck and Ofer Arieli. On the semantics of simple contrapositive assumption-based argumentation frameworks. In Proc. COMMA18, volume 305 of Frontiers in Artificial Intelligence and Applications, pages 920. IOS Press, 2018. 20.

We explore the connection between logical attack principles and sequent-based argumentation frames. By interpreting the logical attack principles first introduced in semi-abstract argumentation frameworks in logical argumentation theory, the role of two key properties such as minimality and consistency of the support parts emerge. The logical attack principles justified by most attack functions are the same justified by the modal interpretation of the attack relation introduced in (Corsi and Fermüller, 2017). Therefore a new argumentative semantic for LM, a sub-logic of LK, can be defined. Finally we show how it is possible to use the interpreted attack principles to define additional elimination rules that can be used as shortcuts in the dynamic derivations.

This talk will present a system for norm-based practical deliberation in plans and games. The system models how a deliberative agent can accomplish two tasks: goal selection (with argumentation semantics) and action selection (with planning or game-theoretic tools).

Goals originate from conditional obligations, desires, laws or any other normative code, together with a preference among these sources of normativity. This preference captures different agent types: more or less altruistic, hedonistic or lawful. Once the agent goals are established, available actions must be selected towards their fulfilment.

The two selection tasks are interconnected: selected goals motivate actions, but the execution of these actions can generate new goals. As a consequence, the usual planning algorithms and game-theoretic solutions must be adapted to normative reasoning. We discuss different ways to do so and compare them in different examples.

This combined approach brings advantages to different areas: deliberative planning can solve certain puzzles from deontic logic, practical syllogisms can be used in automated planning, and utility functions in games can be induced from the existing norms. The main theoretical results are about the formal properties of deontic consequence relations and the search algorithms built upon them.

This talk is based on joint work with Christian Strasser.

This talk will be about formal argumentation. In particular, we will focus on structured argumentation, that is, formal argumentation networks in which one does not abstract away from the content of the arguments involved. We formalize networks of arguments which include attacks, preference attacks and support relations. We then show how such networks are mapped to theories in ASPIC+, a state-of-the-art framework for structured argumentation. Finally, we show how such ASPIC+ theories can instantiate familiar (extended) Abstract Argumentation Frameworks, which allows for the semantic evaluation of sets of `winning arguments' in the source network. The methodology is illustrated through a collaboration between scholars of South Asian philosophy, logicians and formal argumentation theorists, analyzing excerpts of Sanskrit texts concerning a controversial normative debate within (ancient) South Asian Jurisprudence.

In this talk I will draw some novel interfaces between abstract argumentation, the theory of games played on graphs, and modal logic. A key decision problem in abstract argumentation is to determine whether a given framework contains a non-empty admissible set (that is, whether it contains credulously acceptable arguments). This decision problem has an elegant operationalisation in the form of a game known in the graph theory literature as poison game. The game, in turn, defines in a natural way a novel modal logic, which I call poison modal logic. The logic is expressive enough to capture the notion of credulous acceptability. I will report on results concerning the model theory of such logic, its satisfiability problem, and its links with hybrid logics and related systems.

This is joint work with Simon Rey (Institute for Logic, Language and Computation, Amsterdam).

We discuss the limitations of standard approaches to structured argumentation for a practical, resource-bounded account of dialectical reasoning. Next, we propose a new account of classical logic argumentation that accommodates real-world modes of dialectical reasoning and is rational under resource bounds.

Abstract argumentation offers widely used and well understood methods for conflict resolution in argumentation scenarios. However, since the evaluation of AFs yields sets of jointly acceptable arguments, there is a certain discrepancy regarding argumentation systems where the evaluation of coherent claims is required: While arguments are unique, claims can appear as conclusions of several arguments. The research question we tackle is as follows: Is it possbile to combine different arguments sharing the same claim to a single abstract argument without affecting the overall results (and which abstract formalisms can serve such a purpose)? As a main result we show that the class of well-formed frameworks, where arguments with the same claim have the same outgoing attacks, can be equivalently (for all standard semantics) represented as argumentation frameworks with collective attacks where each claim occurs in exactly one argument.

We introduce and investigate Depth-bounded Belief functions, a logic-based representation of quantified uncertainty. Depth-bounded Belief functions are based on the framework of Depth-bounded Logics, which provide a hierarchy of approximations to classical logic. Similarly, Depth-bounded Belief functions give rise to a hierarchy of increasingly tighter lower and upper bounds over classical measures of uncertainty. This has the rather welcome consequence that ``higher logical abilities'' lead to sharper uncertainty quantification. In particular, our main results identify the conditions under which Dempster-Shafer Belief functions and probability functions can be represented as a limit of a suitable sequence of Depth-bounded Belief functions.