Repetition ranks: "why don't you just keep Felscher's rules?"
Nicolas Clerbout
Salle D. Corbin
Résumé :
Apart from S. Rahman and his collaborators, most of the people knowing and/or working on dialogues keep Felscher's account in mind. This is mostly because his presentation is technically precise and because he provided one of the first accurate and complete proofs of an equivalence theorem in [3]. Even in the last decade, almost every work about dialogues which was not done by a direct collaborator of S. Rahman was done with Felscher's rules: for example [4, 5, 6, 7]. Thus, it is no suprise that we often face the question "Why don't you just keep Felscher's rules?", especially in reaction to the device of repetition ranks as I introduced it [1, 2].
The main purpose of this talk is to give an answer to this disguised reproach. To do this I will recall and comment quite extensively Felscher's rules. Although it is an excuse to insist once more on the benefits of repetition ranks, there is another good reason for this flashback. As dialogicians we must be able to discuss with people knowing only Felscher's rules, if only to explain and convince that our account should be preferred. So we must know the answers to questions such as:
- What is the E-rule and what is the big deal with it?
- Does Felscher have something like ranks?
- etc
The comparison is also helpful to get a good grip on important issues related but not limited to proving results: finite vs. infinite plays, separation of rules and strategies, redundancy of rules, etc.
[1] Clerbout, N.: 2013a, ``First-Order Dialogical Games and Tableaux''. To appear in Journal of Philosophical Logic.
[2] Clerbout, N.: 2013b, Etude sur quelques sémantiques dialogiques. Concepts fondamentaux et éléments de metathéorie. PhD dissertation, Lille/Leiden.
[3] Felscher, W.: 1985, ``Dialogues, Strategies, and Intuitionistic Provability''. Annals of Pure and Applied Logic 28, pp. 217-254.
[4] Sorensen, M. and Urzyczyn, P.: 2006, Lectures on the Curry-Howard Isomorphism, Elsevier.
[5] Sorensen, M. and Urzyczyn, P.: 2007, ``Sequent Calculus, Dialogues, and Cut Elimination''. In Barendsen et al. (eds.), Reflections on Type Theory, Lambda Calculus, and the Mind, pp. 253-261.
[6] Uckelman, S.: ``Some remarks on the E-rule in dialogical logic''. Submitted manuscript, available on the author's website.
[7] Uckelman, S., Alama, J. and Knocks, A.: ``A curious dialogical logic and its composition problem''. Submitted manuscript.
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