Tonk- A Full Mathematical Solution

Arnon Avron
Tel Aviv University
There is a long tradition (See e.g. [9, 10]) starting from [12], according to which the meaning of a connective is determined by the introduction and elimination rules which are associated with it. The supporters of this thesis usually have in mind natural deduction systems of a certain ideal type (explained in Section 3 below). Unfortunately, already the handling of classical negation requires rules which are not of that type. This problem can be solved in the framework of multiple-conclusion Gentzen-type systems (also first introduced in [12]), where instead of introduction and elimination rules there are left introduction rules and right introduction rules.
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Sentence Connectives in Formal Logic.Lloyd Humberstone - forthcoming - Stanford Encyclopedia of Philosophy.
Necessity of Thought.Cesare Cozzo - 2015 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Springer. pp. 101-20.
The Explosion Calculus.Michael Arndt - 2020 - Studia Logica 108 (3):509-547.
Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.

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