20 Year Anniversary: Proof Theory of Finite Valued Logics

Twenty years ago this month I submitted my Diplomarbeit (MA thesis) on the proof theory of finite valued logics.  Still kinda proud of it.

The main results of this report are: the use of signed formula expressions and partial normal forms to provide a unifying framework in which clause translation calculi, sequent calculi, natural deduction, and also tableaux can be represented; bounds for partial normal forms for general and induced quantifiers; and negative resolution. The cut-elimination theorems extend previous results, and the midsequent theorem, natural deduction systems for many-valued logics as well as results on approximation of axiomatizable propositional logics by many-valued logics are all new.

Here’s an old blog post on the whole idea.

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