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CEFISES Seminar: Sara Ayhan, “How to secure uniqueness of logical connectives in bilateralism”
Series: Explanatory Inference
Abstract: In the literature on uniqueness it has been clearly shown that the question whether a connective is uniquely characterized by its set of rules is strongly related to the logic, its specific representation, and in particular to the underlying consequence relation. I will show the problems that are encountered when dealing with uniqueness of connectives in a bilateralist setting within the larger framework of proof-theoretic semantics and suggest a solution. Therefore, I will present and argue for a specific – and so far underrated – form of bilateralism: one that is bilateral not only on the level of rules, but also on a meta-level, namely concerning inferential relations. This is realized in the logic 2Int, for which I introduce a sequent calculus system, displaying – just like the corresponding natural deduction system – a consequence relation for provability as well as one dual to provability. I will propose a modified characterization of uniqueness incorporating such a duality of consequence relations, with which we can maintain uniqueness in a bilateralist setting. Finally, I want to discuss some implications of these considerations with regard to what may be considered more or less suitable representations of logics as well as possible extensions to forms of multilateralism.