Tom Sterkenburg: Solomonoff Induction
This talk discusses the Solomonoff approach to universal prediction. The crucial ingredient in the approach is the notion of computability, and I present the main idea as an attempt to meet two plausible computability desiderata for a universal predictor. This attempt is unsuccessful, which is shown by a generalization of a diagonalization argument due to Putnam. I then critically discuss purported gains of the approach, in particular it providing a foundation for the methodological principle of Occam’s razor, and it serving as a theoretical ideal for the development of machine learning methods.
Baptiste Mélès: Implicit linguistic aspects of programming languages
It may sound strange to use linguistics to examine formal languages such as programming languages. As a matter of fact, all their components seem to be explicit: alphabet, syntax, semantics. However, I will show that a linguistic approach may reveal some hidden aspects in the practice of such languages: concerning the alphabet, one should distinguish between a graphetics and a graphematics; the lexicon has a differential structure; a morphology is hidden under the syntax; a pragmatics comes on top of the semantics. All such features in the practice of programming languages makes their practice close to that of human languages.
Brice Halimi: Functorial Context-Dependence
Context-dependence covers all the cases in natural language where the semantic content of an expression depends on the context of its utterance. It is a massive and complex phenomenon, of which the case of indexicals (such as “I” or “here”) is a basic illustration. Context-dependence is supposed to elude any formal representation (this diagnosis defines “contextualism”), unless it is modeled on indexical context-dependence (“indexicalism”), or reduced to it (“minimalism”). In my talk, I will argue that these logico-philosophical stances are based on too narrow a picture of what a formal representation can be; that context-dependence, once it is approached as a radically dynamic process based on context-shift, is amenable to a formal representation; but that new mathematical concepts have to be called upon to that end. I will show that this perspective leads to understanding context-dependence as the transposition of semantic content from one context to another, and to analyzing the latter in the form of a functorial computation. Accordingly, two parallel aspects of the relationship between semantic content and linguistic meaning will be sharply distinguished.
Daniel Leube: Synergies in logic - in the light of partial information decomposition
Partial information decomposition (PID) is an extension of Shannon's classical information theory that aims to decompose multivariate mutual information into parts that are unique, redundant and synergistic with respect to some sources. Based on the concept of mereological PID I would like to argue that in a qualitative manner PID may also purposefully be applied to logical formulae. In this way, parthood lattices of mereological PID become interpretable as frames of possible worlds in Kripke semantics. This leads to new perspectives on classical vs. intuitionistic and modal logic in terms of how they deal with synergistic effects between atomic formulae.
