Abstract This paper collects and presents unpublished notes of Kurt Gödel concerning the field many-valued logic.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 1986, I. Mikenberg, N. da Costa and R. Chuaqui introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather compl...

We show that a multiple-valued symmetric function has a planar ROMDD (reduced ordered multiple-valued decisio n diagram) if and only if it is a pseudo-voting function. We show that the number of such functions is where r is the number of logic values and n is the number of variables. I t follows from this that the fraction of symmetric multiple-valued functions that have planar ROMDD's approach...

This paper introduces a new design of penternary inverter gate based on graphene nanoribbon field effect transistor (GNRFET). The penternary logic is one of Multiple-valued logic (MVL) circuits which are the best substitute for binary logic because of its low power-delay product (PDP) resulting from reduced complexity of interconnects and chip area. GNRFET is preferred over Si-MOSFET for circui...

Attributional calculus ( ) is a typed logic system that combines elements of propositional logic, predicate calculus, and multiple-valued logic for the purpose of natural induction. By natural induction is meant a form of inductive learning that generates hypotheses in human-oriented forms, that is, forms that appear natural to people, and are easy to understand and relate to human knowledge. T...