Workshop on Substructural Logics

Workshop on Substructural Logics

July 29, 2019
Argentinean Society
of Philosophical Analysis (SADAF)
Buenos Aires, Argentina


14:00 to 15:10 – Paul Egré (CNRS-EHESS-ENS) “Extracting connectives from consequence relations” (with E. Chemla)

15:20 to 16:30 – Bruno Da Ré, Federico Pailos, Damián Szmuc, and Paula Teijeiro (UBA and IIF-SADAF-CONICET) “On Duality and Metainferences”

17:00 to 18:10 – Shawn Standefer (University of Melbourne) “The Limits of Relevance”

18:20 to 19:30 – Dave Ripley (Monash University) “Metainferences: an abstract valuational approach”


Paul Egré: “Extracting connectives from consequence relations” (joint work with E. Chemla)

Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but on what we call Gentzen-regular connectives (including negation, conjunction, and disjunction). For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations. In this presentation, specific emphasis will be put on the 3-valued case, on the extraction of Gentzen-regular conditionals given a consequence relation.

Bruno Da Ré, Federico Pailos, Damián Szmuc, and Paula Teijeiro: “On Duality and Metainferences”

Bruno Da Ré, Federico Pailos, Damián Szmuc, and Paula Teijeiro: “On Duality and Metainferences”

Shawn Standefer: “The Limits of Relevance”

Routley-Meyer frames are used to provide a frame semantics for relevant and substructural logics. What are the limits, if any, of the sorts of connectives that can be interpreted on these frames while maintaining the broad relevance ideas that motivated relevant logics? This talk will present the start of an answer to this question.

Dave Ripley: “Metainferences: an abstract valuational approach”

In studying consequence relations, sometimes complex models are useful: they can have possible worlds, lots of truth values, domains of individuals, and so on. But sometimes very simple models, for example just assignments of 1s and 0s, can shed light from another direction. The abstract valuational approach to consequence relations pursued for example by Scott, Shoesmith & Smiley, and Humberstone shows that a number of interesting results can be forthcoming from such very simple models. In this talk, I attempt to extend these simple valuational tools to the study of metainferences.


July 31 to August 2 @ SADAF: VIII Workshop on Philosophical Logic


We are thankful for the support provided by CONICET