Abstract This paper collects and presents unpublished notes of Kurt Gödel concerning the field many-valued logic. In order to get a picture as complete possible, both formal philosophical notes, transcribed from Gabelsberger shorthand system, are included.

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is prooftheoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...