Tonk- A Full Mathematical Solution

Authors
Arnon Avron
Tel Aviv University
Abstract
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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