Workshop on Substructural Logics and Metainferences
August 27, 2020
SADAF – Online Conference
The Buenos Aires Logic Group (BA LOGIC) invites researchers and scholars in philosophy, mathematics, computer science, linguistics, and related topics to attend to the workshop to be held in Buenos Aires this August 27th, 2020.
This Workshop aims to bring together researchers to discuss different topics on Logic and Philosophical Logic, related with Substructural Logics and Metainferences.
The conferences will be held on-line. If you’re interested in joining us, please request the zoom link with an e-mail to the following address:
bruno.horacio.da.re [at] gmail.com
21:00 to 22:00 (GMT-03) – Dave Ripley: A toolkit for metainferential logics (Abstract)
22:15 to 23:15 (GMT-03) – Bruno Da Ré, Damián Szmuc and Paula Teijeiro: “Derivability and Metainferential Validity” (Abstract)
Dave Ripley: “A toolkit for metainferential logics”
Recent work in the study of metainferential logics and metainferential hierarchies has shed new light on a range of logical systems. This work has mostly begun from specific languages and models (typically strong Kleene models for a propositional language) and used the resources present there to build a range of notions of counterexample (or equivalently of satisfaction), applying at different metainferential levels.
Much of this structure, however, already exists in a very general setting, where we assume nothing at all about our language or our models. The structure provided by metainferences of various levels, and by relating notions of counterexample at different levels, is a structure rich enough to support investigation in its own right, without requiring extra assumptions about connectives, truth values, or the like. This talk aims to develop a toolkit at this level of generality. Such a toolkit sheds light on existing results, by letting us see what does and doesn’t depend on the specifics of strong Kleene models. I hope it can also help with future investigations into metainferential logics based on very different languages or models.
Bruno Da Ré, Damián Szmuc and Paula Teijeiro: “Derivability and Metainferential Validity”
The aim of this article is to study the notion of Derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics ST and TS. In this respect, we show that this notion does not coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the so-called notion of Local validity. Following this, and building on some previous work by Humberstone, we prove that in these systems Derivability can be characterized in terms of a notion we call Absolute Global validity. However, arriving at these results does not lead us to disregard Local validity. First, because we discuss the conditions under which Local, and also Global validity, can be expected to coincide with Derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe Derivability for different calculi used to present ST and TS.
We are thankful for the support provided by CONICET