Time: 2024/05/10 (Friday) 14:00-18:00

Location: Room B112, Lee Shau Kee Humanities Buildings No.2 (李兆基人文学苑2号楼), Peking University

There are two talks in this section.

Speaker 1：Sonja Smets (Professor at Institute for Logic, Language and Computation, University of Amsterdam, and Zheng Gang Fellow at Joint Research Centre for Logic, Tsinghua University)

Title：Reasoning about Epistemic Superiority and Data Exchange

Abstract：

In this talk I present a framework based on a variation of dynamic epistemic logic that deals with data-exchange scenarios, in which agents can 'read' (or otherwise gain access to), communicate or exchange all the information originating in specific sources ('locations', websites, folders, databases, etc). This includes *information of a nonpropositional nature* (such as numerical or graphical data, passwords, keys, secret identities etc). We can think of the sources of information as 'agents' who 'own' these data (or are somehow already in possession of them). The 'reading' agents may attempt to gain access to the data of the "owning" agents, thus gaining **epistemic superiority** over them.

I will present different examples of epistemic superiority and I will draw a connection to the logic of functional dependence by A. Baltag and J. van Benthem [2]. I give an axiomatization of the static logic of (distributed) knowledge and epistemic superiority, and use it to further axiomatize the logic of data-exchange events (without common knowledge), via appropriate reduction/recursion laws.

Moving on to the extension of this logic with common knowledge, I show that what is needed is a new concept of **common distributed knowledge**, which generalizes both distributed knowledge and common knowledge, and combines features of both. This notion allows us to have reduction laws for common (and common distributed) knowledge for a large class of data-exchange events (-the so-called "*semi-public* events"), and to obtain a complete axiomatization of this logic. This presentation is based on joint work with A. Baltag in [1].

REFERENCES:

[1] A. Baltag and S. Smets, Learning what others know, in L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming, AI and Reasoning, EPiC Series in Computing, 73:90-110, 2020.

[2] A. Baltag and J. van Benthem. A Simple Logic of Functional Dependence, Journal of Philosophical logic, vol. 50, pp. 939-1005, 2021.

Speaker 2：Alexandru Baltag (Professor at Institute for Logic, Language and Computation, University of Amsterdam, and Zheng Gang Fellow at Joint Research Centre for Logic, Tsinghua University)

Title：Data-exchange events with preconditions and knowledge of values

Abstract：

This talk builds upon and continues Sonja's talk. First, I extend the setting she presented by adding **preconditions** (and later post-conditions) to data-exchange events: in this way, the resulting logic embeds classical DEL inside it. This allows us to express complex scenarios involving communication, exchange and manipulation of both propositional and non-propositional data.

Second, I consider the problem of axiomatizing the resulting logic in the presence of **common knowledge**. There are two standard approaches to axiomatizing full DEL (with common knowledge), but the resulting axioms and rules are rather convoluted and opaque. By looking at recursion axioms as systems of equations, we are led to extend the static language with **polyadic conditionals** that are obtained as solutions to such systems of equations. Epistemically, these polyadic modalities capture various *complex levels of conditional group knowledge*, so they can be considered as generalizations of the common-distributed knowledge operator. As such, they can be given a transparent axiomatization and a filtration-based completeness proof, and the recursion/reduction laws (for arbitrary data-exchange events) become extremely simple and elegant. There is a price for achieving that though: we need to drop the "epistemic superiority" atoms, for which we don't have reduction laws (-I will explain why, and how this connects to an outstanding open problem concerning the conditional extension of the Logic of Functional Dependence). As a result, we lose the most straightforward way to capture the effects of data-exchange events.

To compensate for this, I add operators K_a x for **knowledge of (the value of) a variable x (by an agent a)**, notion borrowed from Yanjing's work. These do express in some sense the effect of a data-exchange event: the "reading" agent gets to know all the data that was known by the source. I show that, in the context of data-exchange events, what we need is actually an operator for **distributed knowledge K_A x of the value** (of a variable x, by a group of agents A). Moreover, to have reduction laws for this in the presence of events with preconditions, we need **conditional** or ``hypothetical" distributed knowledge K_A^P x (of the value by a group of agents) given some hypothetical condition (expressed by some proposition P). Finally, I argue that to make the standard methods of proving completeness (for distributed knowledge) work in this case, we need to have a language that can actually *denote* this **'hypothetical' value of x according to A given condition P**: so I introduce a term k_A^P x, denoting this value. I investigate the resulting logic (that puts together everything mentioned above) and present a complete axiomatization. Timepermitting, I may sketch the ideas behind the proof of completeness and decidability.

This talk is based on joint work: references [1,2,4], joint with S. Smets; reference [3,5], joint with J. van Benthem; and it relates to my older work [6].

REFERENCES:

[1] A. Baltag & S. Smets. Knowing, changing and exchanging data values. Unpublished Manuscript.

[2] A. Baltag & S. Smets. Logics for Data Exchange and Communication. Submitted to AiML 2024.

[3] A. Baltag & J. van Benthem: Updates, Generalized p-Morphisms, and (Co-)Recursive Equations. In J. van Benthem & F. Liu (eds), Graph Games and Logic Design – Recent developments and further directions, Springer 2024 to appear.

[4] A. Baltag and S. Smets: Learning what Others Know. In L. Kovacs and E. Albert (eds.), LPAR23 proceedings of the International Conference on Logic for Programming AI and Reasoning, EPiC Series in Computing, Volume 73, pp 90-110, 2020.

[5] A. Baltag and J. van Benthem. A Simple Logic of Functional Dependence, Journal of Philosophical logic, vol. 50, pp. 939-1005, 2021.

[6] A. Baltag, To Know is to Know the Value of a Variable, Adv. in Modal Logic 2016, 135– 155, 2016.