A Note on Gödel, Priest and Naïve Proof

A Note on the Gödel-Gentzen Translation

Proof theory of witnessed Gödel logic: A negative result

We introduce a first sequent-style calculus for witnessed Gödel logic. Our calculus makes use of the cut rule. We show that this is inescapable by establishing a general result on the non-existence of suitable analytic calculi for a large class of first-order logics. These include witnessed Gödel logic, (fragments of) Łukasiewicz logic, and intuitionistic logic extended with the quantifiers of ...

Towards a Proof Theory of Gödel Modal Logics

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the manyvalued semantics of Gödel logic. The calculi are used to establish completeness and complexity results for these fragments.

The Easy Way to Gödel ’ s Proof and Related Matters

This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders the proof of the so–called fixed point theorem transparent. We also point out various historical details and make some observations on circularity and some comparisons with natural language. The sketch does not include the messy details of the arithmetization o...

A note on SAT algorithms and proof complexity

We apply classical proof complexity ideas to transfer lengths-of-proofs lower bounds for a propositional proof system P into examples of hard unsatisfiable formulas for a class Alg(P ) of SAT algorithms determined by P . The class Alg(P ) contains those algorithms M for which P proves in polynomial size tautologies expressing the soundness of M . For example, the class Alg(Fd) determined by a d...