Chania – Crete, Greece

April 7, 2022

Opening: Belief Revision in a nutshell

Rafael Testa (Unicamp and UFRJ, Brazil)

Belief revision is the process of changing beliefs to take into account a new piece of information. The properties of these models are investigated in order to improve our understanding of how beliefs can be changed, with a particular emphasis on what it means to change one’s beliefs in a rational way. Thus, the logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.

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Keynote Talk:

Belief Revision and Argumentation Approaches to Support Commonsense Reasoning

Giorgos Flouris (FORTH-ICS, Greece)

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 In this talk, I will present recent (and partly unpublished) research that has been performed in the Symbolic AI group of FORTH-ICS, which connects the fields of commonsense reasoning with the fields of belief revision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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Belief and Credence: Bridging Doxastic Logic and Probability Theory

Matheus Rui (UFSC – Brazil).

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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Public Announcement and Intuitionistic Epistemic Logic

Alexandra Pavlova (Technische Universität Wien, Vienna – Austria and Saint Petersburg State University, Saint Petersburg – Russia)

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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Since the first edition in 2005 in Montreux, Switzerland, UNILOG has gathered many renowned researchers.

This series of world events promotes logic in all its aspects: mathematical, philosophical, computational, semiological, historical, and the relation between logic and other fields: physics, biology, economics, law, politics, religion, music, literature, pedagogy, color theory, medicine, psychology, psychoanalysis, cognitive science, architecture, artificial intelligence, sociology, linguistics, and anthropology (just to name a few). The event itself is a combination of a congress and a school. There is also a secret speaker and the world logic prizes contest.

UNILOG 2022

The event took place at the Orthodox Academy of Crete, in Chania – Crete, Greece, in April 1-11, 2022.

The 7th School on Universal Logic had 13 tutorials on all aspects of logic, while the Congress had 6 days of duration with:

• Plenary talks by Keynote Speakers either in the General Session or in a Workshop;
• Talks by Selected Contributing Speakers, presented at the General Session;
• A series of Workshops on different themes encompassing all aspects of logic;
• The World Logic Prizes Contest;

• A talk by a Secret Speaker, whose identity is revealed only at the time of their talk or after.

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Workshops

Like in other editions, the Conference had several workshops organized by specialists in distinct areas, namely: Lewis Carroll’s Logic; Logic(s) in Defective Science; Hybrid Logic; Logics of Oneness; Belief Revision; Reasoning in Text; Argumentation Logic; 100 Years of Refutation; Rough Sets; Logic and Love; Analogy; Logic and Politics; The Logic of Social Practice; Reasoning across times and cultures; Logic and Structures; Axiomatic Method.

More about UNILOG 2022

Organizers

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.