Workshop Report: Logic of Denial

Here is a short report from the 2nd FLC workshop on the Logic of Denial.

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Workshop Report

The Logic of Denial, October 24th - 25th

2nd Foundations of Logical Consequence Workshop

FLC, The Foundations of Logical Consequence, is an AHRC-funded project run by the Arché Research Centre in the University of St Andrews. The four year project is currently in its second phase, The Structure of Logical Consequence. As part of the regular activity, FLC has just hosted its second workshop, entitled The Logic of Denial. 

Since Frege, the analysis of denial as assertion of a negation has been the received view in formal logic. However, recent literature has seen a number of attempts at introducing denial into formal systems as a primitive alongside assertion. The workshop invited its speakers to discuss how one best treats denial in a formal framework. In particular, how does denial correspond to different negations, and what is the relationship between logical consequence and rational demands imposed by the norms of assertion and denial?

The workshop's first day started with Dave Ripley (Institut Jean-Nicod, Paris) on  'Embedding Denial'. He discussed the strategy of introducing a primitive denial operator to address problems with expressive power in paracomplete and paraconsistent approaches to semantic paradoxes. Arguing from broader considerations about the nature of denial, he concludes that these theories ought to include a "complete" and "consistent" denial operator. Heinrich Wansing (Dresden) developed a proof-theoretic semantics for bi-intuitionistic logics with a denial-like negation. BHK (Brouwer-Heyting-Kolmogorov) semantics is extended by applying proofs, disproofs and their duals. In a similar vein, Luca Tranchini (Tübingen) offered a dualisation of proof-theoretic semantics in terms of refutation. For this purpose he developed a natural deduction (single-premise, multiple-conclusion) for dual-intuitionistic logic. Finally, Ian Rumfitt (Birkbeck, London) rounded off the first day by revisiting his bilateralist theory (where content is specified by both assertion- and denial-conditions), and offering arguments for another theory of content-determination: Evidentialism.

Peter Schroeder-Heister (Tübingen) started us off on the second day with an extension of his proof-theoretic semantics, using a denial operator in programming clauses, and developing corresponding harmony principles between assertion and denial rules. Next up was Michael De (Arché, St Andrews), with an investigation into how the norms of denial are affected by falsity-preservation consequence. Colin Caret (Arché, St Andrews) returned to the topic of semantic paradoxes discussed by Ripley the day before. He explored how we can get a denial operator that blocks revenge paradoxes while preserving as many intuitions about denial as possible. Greg Restall (Melbourne) had the honour of closing the workshop. He developed his theory that multiple-conclusion derivations can be interpreted as rational constraints on assertion and denial, extending it to discussing issues such as logicality and tonk.

The workshop had about 30 participants. We hope they all share our opinion that the event created significant impetus to future work with the logic of denial, highlighting common ground for researchers from a number of different fields. If there was one single conclusion from the workshop as a whole it was that formal approaches to denial offer interesting enrichments of expressive power both in theories about semantic paradoxes and in proof-theoretic semantics.

More information about Arché and FLC events can be found at:

http://www.st-andrews.ac.uk/~arche/index.php

The Organisers,

Stephen Read

Colin Caret

Ole Thomassen Hjortland