The workshop “Exploring Baltag’s Universe” was organized by Johan van Benthem and Soroush Rafiee Rad on the 15th of January for our colleague and friend Alexandru Baltag on the occasion of his birthday.
The workshop featured short talks by Alexandru’s long-standing colleagues and collaborators including Samson Abramsky, Sonja Smets, Fenrong Liu, Alexander Kurz, Luís Soares Barbosa, Nick Bezhanishvili, Kevin Kelly, Larry Moss and Johan van Benthem.
The recording can be found below. Alternatively, click here.
(see below for titles and abstracts)
- 13:45 — 14:00 Welcome
- 14:00 — 14:30 Samson Abramsky
- 14:30 — 15:00 Sonja Smets
- 15:00 — 15:30 Fenrong Liu
- 15:30 — 15:40 Break
- 15:40 — 16:10 Nick Bezhanishvili
- 16:10 — 16:40 Luis Soares Barbosa
- 16:40 — 16:50 Break
- 16:50 — 17:20 Alexander Kurz
- 17:20 — 17:50 Kevin Kelly
- 17:50 — 18:00 Break
- 18:00 — 18:30 Larry Moss
- 18:30 — 18:50 Johan van Benthem
- 18:50 — 19:00 Alexandru Baltag
Titles & Abstracts
Samson Abramsky: Nothing will come of everything
Abstract: Some remarks on reductionism, holism, and compositionality. Two towers figure in the landscape.
Sonja Smets: Dynamic Quantum Logic: Extensions and Variations
Abstract: I will present a short overview, highlighting the key insights and main results, that were obtained in my joint work with Alexandru Baltag on Dynamic Quantum Logic. I will first highlight our view about the dynamic nature of the main ingredients such as superposition and orthocomplementation in the logical foundations of quantum mechanics. This view led in 2004 to the first design of a dynamic quantum logic that comes together with an important Representation Theorem showing that our dynamic axiomatic system is complete with respect to the natural Hilbert-space semantics for modelling single quantum systems. Second, I show how we extended our dynamic logical system in 2004-2006 to reason about compound quantum systems, which opened the door to use this logic for the specification and verification of important quantum communication protocols. Third, I highlight how in 2010-2011 we made use of the techniques coming from multi-agent classical epistemic logic to enrich our understanding of the properties that encode non-local quantum behavior. In particular, we provided a new information-logical characterization of the properties of ‘separability’ and ‘quantum entanglement’. Fourth, on the philosophical side we used dynamic quantum logic to address the old question on whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Our answer to that question is a clear ‘no’. Indeed, we have shown that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Fifth, I highlight how between 2012 and 2014, together with our collaborators, we extended our setting with probabilistic features. Using this more expressive probabilistic system allowed our team to substantially enrich the class of quantum protocols and algorithms, as studied in Quantum Information Theory, that can be verified via our logical setting. I will conclude this lecture by showing how we have now come to a point where we can formally capture, in a united setting, both the flow of classical information and the flow of quantum information in interaction. The latter development requires the design of a full-fledged quantum dynamic epistemic logic.
Fenrong Liu: A Simple Logic of the Hide and Seek Game
Abstract: We interact with each other through many games, online or offline. Different game activities elicit different types of social interaction. In this talk, I will present a simple logic to describe one of our favorite games from childhood, hide and seek, and show how a simple addition of an equality constant to describe the winning condition of the seeker makes our logic undecidable. I will also discuss the expressive power of the new logic, and its computational properties. This is joint work with Dazhu Li, Sujata Ghosh and Yaxin Tu.
Nick Bezhanishvili: The topological mu-calculus
Abstract: Among many research interests that Alexandru and I share, topological semantics of modal logic has a central place. In this talk, I will overview my recent joint work with Alexandru and David Fernandez Duque on topological semantics of the modal mu-calculus based on the Cantor derivative
Luís Soares Barbosa: Paraconsistent transition systems and their logics
Abstract: Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. This talk, reporting on recent joint work with Ana Cruz and Alexandre Madeira, introduces a variant of transition systems endowed with positive and negative accessibility relations, and a metric space over the lattice of truth values. Such paraconsistent transition systems provide a basis to generalise Belnap-Dunn four-valued logic, with possible applications in different domains, namely to reason about decoherence in current quantum computing devices.
Kevin Kelly: Characterization of Inductive Learnability when Question has Overlapping Answers
Abstract: Formal learning theory aims to characterize the computational/topological complexity of inductive learnability across a broad range of contexts of inquiry. While quite a few variations in contexts have been considered, one stubborn limitation persists: that the question under discussion has mutually exclusive potential answers. That makes sense for problems like theory test and theory choice. However, there are other important scientific problems like the estimation of causal impact on continuous variables and the accumulation of results from multiple studies in disparate domains that call for an extended analysis of contexts in which the answers to the question may overlap. In a humble bid to emulate Alexandru’s celebrated presentation style, I will heavily overload my 15 minutes of fame by sketching a learning theoretic framework that allows for overlapping answers, and by presenting a general characterization theorem for problem contexts that allow for such questions. That much is easy enough when one gets the underlying concepts right. But furthermore, I will show that global consistency and avoidance of retracting the truth are also achievable when inductive learnability is possible at all. That is not entirely trivial, since global consistency and avoidance of retracting the truth are competing aims in inductive inquiry. These results are the culmination of conversations I have been having for years with Konstantin Genin.
Johan van Benthem: Information and Dependence: Travels with Alexandru
Abstract: I will review some major interests that I have long shared with Alexandru, with our recent joint papers on dependence as a culmination. Keywords: logic, information, correlation, topology, and dynamics.At the same time, my minitalk also looks at some intellectual debts that we share, in particular to Jaakko Hintikka and Jon Barwise.