Belief Revision Workshop at

7th World Congress and School on Universal Logic

Orthodox Academy of Crete, Greece
April 1 – 11, 2022

Organizer of the Workshop

Rafael Testa (CLE-Unicamp and IFCS-UFRJ, Brazil)

Belief Revision (Belief Change) is the research field that makes use of tools and methods of formal logic to produce models of how human and artificial agents change their beliefs in response to new information. These models serve as a basis for understanding how beliefs can be changed, and how these changes can be regarded as rational. This is a multidisciplinary task, with applications to several areas including Formal Epistemology, Artificial Intelligence, Ontology, Databases, and many more.

The aim of this workshop is twofold: on the one hand, we intend to provide an introduction to the subject, tackling distinct models presented in the literature. On the other hand, we intend to gather contributions related to distinct applications and studies on the ramifications of the area.

Schedule (April 7)

Rafael Testa	Belief Revision in a Nutshell (Workshop opening)	14h00 – 14h30
Matheus de Lima Rui	Belief and Credence: Bridging Doxastic Logic and Probability Theory	14h30 – 15h00
Alexandra Pavlova	Public Announcement and Intuitionistic Epistemic Logic	15h00 – 15h30
Maria Martinez-Ordaz	Preserving scientific understanding after belief revision	15h30 – 16h00
	Coffee Break	16h00 – 16h30
Giorgos Flouris (keynote speaker)	Belief Revision and Argumentation Approaches to Support Commonsense Reasoning	16h30 – 17h15+ε

Abstracts

Giorgos Flouris

http://users.ics.forth.gr/~fgeo/

fgeo@ics.forth.gr

FORTH-ICS

Greece

Belief Revision and Argumentation Approaches to Support Commonsense Reasoning

Allowing artificial agents to model and reason about commonsense phenomena is one of the major problems of AI research since its conception. In this talk, I will present recent (and partly unpublished) research that has been performed in the Symbolic AI group of FORTH-ICS, which connects the fields of commonsense reasoning with the fields of belief revision and computational argumentation. The talk will be split in two parts.

In the first part, I will consider how belief revision can support agents in their reasoning about events, their effects, and their preconditions, which is one of the main desiderata of commonsense reasoning. Event Calculus is a powerful non-monotonic language for allowing this kind of reasoning, enabling the modelling of commonsense phenomena in causal domains, but no belief revision methods for Knowledge Bases modelled using Event Calculus exist. As a result, agents cannot handle unexpected observations, i.e., observations that are inconsistent with the agent’s perceived world view, as dictated by the events that the agent has witnessed (and their expected effects). To address this problem, I will describe work that adapts well-known ideas from belief revision to apply on Event Calculus theories, proposing a belief revision algorithm for Event Calculus that satisfies the main principles of belief change.

In the second part of this talk, I will present recently-proposed extensions of the standard frameworks for Computational Argumentation, which are more suitable for reasoning about the scope of arguments, their exceptions, and their relevance for specific contexts, an important concept of commonsense and non-monotonic reasoning. In the proposed extensions, arguments are equipped with a domain of application, referring to the objects in the universe that each argument applies to. Appropriate semantics for these frameworks are presented, through which attacks among arguments limit their domain of application, rather than invalidating them altogether (as in classical Computational Argumentation settings). Thus, the proposed models inherently support the notions of exception and scope of arguments.

The presented work has been published in Commonsense-17, AMAI and IJCAI-21.

This research was supported by the Hellenic Foundation for Research and Innovation (H.F.R.I.) under the “1st Call for H.F.R.I. Research Projects to support Faculty Members and Researchers and the procurement of high-cost research equipment” grant (Project Number: 4195).

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Alexandra Pavlova

https://www.univ-paris1.academia.edu/AlexandraPavlova/CurriculumVitae

Université Paris 1 – Panthéon-Sorbonne – France

Public Announcement and Intuitionistic Epistemic Logic

We introduce a system for public announcement in a variant of intuitionistic epistemic logic, namely IEL proposed in [1] and prove its soundness and completeness with respect to the corresponding Kriple models. We consider only the system IEL modeling knowledge as opposed to the system IEL⁻ dealing with belief. IEL extends intuitionistic logic by a new modal operator K interpreted as knowledge. It is based on the intuition behind the BHK semantics, where truth of a formula 𝜑 is interpreted as having a proof 𝜑. Knowledge K𝜑 is then interpreted as “it is verified that 𝜑 holds intuitionisticly”, i.e., that 𝜑 has a proof which is not necessarily specified in the process of verification (cf. [1]). The idea that knowledge corresponds to the existence of a verification for some formula in question yields specific conditions on K operator different from the standard classical account. Formula [!𝜑]𝜓 operator of public announcement is read as “after every public announcement of 𝜑, it holds that 𝜓”. We introduce a Hilbert-style proof system for IPAL[].

The work was supported by a grant of Russian Science Foundation (project No. 20-18-00158 “Formal philosophy of argumentation and a comprehensive methodology for finding and selecting solutions to a dispute”).

[1] Artemov, S., Protopopescu, T.: “Intuitionistic epistemic logic’, in The Review of Symbolic Logic, vol. 9, n. 2: 2016, pp. 266-298.

[2] Balbiani, Ph., Galmiche, D.: “About intuitionistic public announcement logic”,

in 11th Conference on Advances in Modal logic (AiML 2016), Budapest, Hungary: 2019, pp. 97 116.

[3] van Ditmarsch, H., Halpern, J. Y., van der Hoek, W., Kooi, B. P.: Handbook of Epistemic Logic, College Publications: 2015, p. 655.

[4] Protopopescu, T.: Three Essays in Intuitionistic Epistemology, PhD thesis: 2016.

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María del Rosario Martínez-Ordaz

https://www.mariamartinezordaz.com/

Federal University of Rio de Janeiro – Brazil

Preserving Scientific Understanding after Belief Revision

Scientific understanding has been considered to “consist of knowledge about relations of dependence. When one understands something, one can make all kinds of correct inferences about it” (Ylikoski: 100). Understanding is a fundamental component of any successful scientific enterprise and it consists of building networks that successfully connect our scientific knowledge about the world. It has been traditionally assumed to be factive, meaning that its content can only include true propositions – propositions to which, in a probabilistic model, agents would assign the probability 1. This is, scientists legitimately understand only propositions that they know to be true and to adequately refer to facts of the world (cf. Grimm 2006, 2014; Lawler 2016, 2018). The factivity requirement entails that the content of understanding cannot include any defective (vague, incomplete, conflicting, inconsistent) beliefs and that understanding cannot be preserved if any of the beliefs that are in its content is revised -and weakened or abandoned. Nonetheless, in large part of scientific practice, the achievement and preservation of understanding is a dynamic phenomenon which includes both systematic processes of belief revision and defeasible reasoning, as well as the reliable use of defective data. The combination

of this leaves philosophers of science with the need of explaining whether it is possible to achieve understanding from defective data as well as under which circumstances could scientists, rationally, weaken (or even give up) a full belief that is located in the content of their understanding without losing what has been understood.

Here I aim at exploring under which circumstances can scientific understanding be preserved even when removing full beliefs from the network of understanding. In order to do so, I proceed in three steps.

• First, I characterize the achievement of scientific understanding as building networks that successfully connect our scientific beliefs about the world. The networks of scientific understanding are sets of sets of worlds, contents are propositions, which are sets of worlds; and in a world, agents can relate the propositions that when combined reinforce the structure of their network in that world. An agent understand A if she can identify the role that A plays for the reinforcement of the network of understanding in the relevant worlds.

• Second, I sketch a way according to which scientific understanding’s can be preserved even if the data which is understood is not fully true or has been recently revised. I ilustrate this with a case study from the empirical sciences.

• Finally, I suggest in which way the adoption of probabilistic belief dynamics such as the ones of the Multistate Model of Probabilistic Revision (Cf. Hansson 2020) can be of use when explaining the preservation of understanding after belief revision.

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Matheus Rui

https://ufsc.academia.edu/MatheusDeLimaRui

Federal University of Santa Catarina – Brazil

Belief and Credence: Bridging Doxastic Logic and Probability Theory

Formal epistemology literature has been fighting for a better oriented, and personally preferred, representation of a doxastic state. In one hand, we have a traditionally recognized notion denominated as “binary belief”, or just belief (simpliciter). On the other hand, we have a more idiosyncratic quantitative notion of “credence”, also known as “subjective probability”. Traditional epistemology has treated belief as an indispensable constituent for knowledge, while credence is the building block of Bayesian Epistemology. Some formal epistemologists are devoting themselves to provide an explanation of how these two concepts are related. My aim here is to draw attention to some endeavors to bridge these two notions by means of a “bridge principle”. I shall focus on two approaches: Leitgeb’s “Stability Theory of Belief” and Lin & Kelly’s “Tracking Theory”. In its synchronic aspect, both of them have a nearly similar approach for a consistent (and deductively closed) bridge principle. The mainly breaking point between them concerns the diachronic portion of the bridge principle, more specifically, on the theory of belief revision for binary belief. While Leitgeb’s version is based on AGM theory, Lin & Kelly’s claims that only their approach, based on a non-monotonic theory for belief revision, is able to properly track bayesian conditional reasoning and, therefore, be a well constructed bridge.

References:

[1] Alchourrón, C., Gärdenfors, P., Makinson, D.: On the Logic of Theory Change: Partial meet contraction and revision functions. Journal of Symbolic Logic, JSTOR 50(2), 510–530 (1985).

[2] Leitgeb, H.: The Stability of Belief: How Rational Belief Coheres with Probability. Oxford University Press, New York (2017).

[3] Lin, H., Kelly, K.: A Geo-Logical Solution to the Lottery Paradox, with Applications to Conditional Logic. Synthese, Springer 186(2), 531–575, (2012a).

[4] Lin, H., Kelly, K.: Propositional Reasoning that Tracks Probabilistic Reasoning. J Philos Logic, 41(0), 957–981 (2012b).

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Outputs: Youtube Playlist

Venue

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Workshops at UNILOG 2022

• Lewis Carroll’s Logic
• Logic(s) in Defective Science
• Hybrid Logic
• Logics of Oneness
• Argumentation Logic
• Reasoning across times and cultures
• Logic and Politics
• 100 Years of Refutation
• The Logic of Social Practice
• Belief Revision
• Logic and Love
• Rough Sets
• Liar Paradox
• Logic and Structures
• Analogy
• Axiomatic Method
• Logic and Ethical Reasoning
• Reasoning in Text

About UNILOG 2022

Organizers

Jean-Yves Beziau is the founder of UNILOG and the president of the Logica Universalis Association. Originally from Switzerland, he is Professor and Researcher in Rio de Janeiro, Brazil, since 2010.

Ioannis Vandoulakis is the vice-president of the Logica Universalis Association. Originally from Crete, he is now living in Athens, working at the Hellenic Open University.

Antonis Kalogerakis is the head of the Institute of Theology and Ecology of the Orthodox Academy of Crete. Responsible for conferences organization at OAC.

Organizing Committee

– Evgenios Avgerinos, Dept of Education, Mathematics, Didactic and Media Lab, University of the Aegean, Greece

– Maria Dimarogkona, Dept of Mathematics, National Technical University of Athens, Greece

– Kostas Dimitrakopoulos, Department of History and Philosophy of Science, University of Athens, Greece

– Katarzyna Gan-Krzywoszyńska, Faculty of Philosophy, Adam Mickiewicz University, Poznan, Poland

– Christafis Hertonas, Dept of Computer Science & Engineering, University of Thessaly, Greece

– Giorgos Koletsos, Division of Computer Science, National Technical University of Athens, Greece

– Ioannis Kriouvrekis, Dept of Mathematics, National Technical University of Athens, Greece

– Eftychios Papadopetrakis, University of Patras & Greek Mathematical Society, Branch of Chania, Greece

– Przemsylaw Krzywoszyński, Dept of Law and Administration, Adam Mickiewicz University, Poznan, Poland

– Nikos Spanoudakis, Applied Mathematics and Computers Laboratory, Technical University of Crete, Greece

– Petros Stefaneas , Dept of Mathematics, National Technical University of Athens, Greece

– Stathis Zachos, Division of Computer Science, National Technical University of Athens, Greece

Scientific Committee

– Arnon Avron, University of Tel-Aviv, Israel

– Johan van Benthem, University of Amsterdam, The Netherlands

and Stanford University, USA

– Patrick Blackburn, Roskilde University, Denmark

– Ross Brady, La Trobe University, Melbourne, Australia

– Carlos Caleiro, IST, Lisbon, Portugal

– Mihir Chakraborty, Calcutta Logic Circle and IIIT Delhi, India

– Newton da Costa, UFSC, Florianópolis, Brazil

– Michael Dunn, School of Informatics, Indiana University, USA

– Dov Gabbay, King’s College, London, UK

– Val Goranko, University of Stockholm, Sweden

– Andrzej Indrzejczak, University of Lodz, Poland

– Gerhard Jaeger, University of Bern, Switzerland

– Arnold Koslow, City University of New York, USA

– Srecko Kovac, Philosophy Institute, Zagreb, Croatia

– Elena Lisanyuk, University of St Petersurg, Russia

– Maria Manzano, University of Salamanca, Spain

– Raja Natarajan, Tata Institute of Fundamental Research, Mumbai, India

– Istvan Nemeti, Hungarian Academy of Sciences, Budapest

– Mykola Nikitchenko, Taras Shevchenko National University of Kyiv, Ukraine

– Francesco Paoli, University of Cagliari, Italy

– Ahti-Veikko Pietarinen, Nazabayev University, Astana, Republic of Kazakhstan

– Göran Sundholm, Leiden University, The Netherlands

– Vladimir Vasyukov, Academy of Sciences, Moscow, Russia

– Heinrich Wansing, Bochum University, Germany