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Hyper-digital logic

Abstract

The title "hyper-digital logic" or "hyper-propositional" [1] denotes a generalization of traditional propositional logic by introducing formulas of arbitrary degree and thus both a whole syntactical and semantical hierarchy. It simultaneously stands for a project, which aims to explore the properties and possibilities of these kind of logical systems.

The intention is to publicly manage this major project by dividing it into several minor projects. Some of them already resulted in a more or less self-containing text. Others only reached the state of a vague idea or sketchy draft so far. The following is a list of these minor projects.

Links to the minor projects

1. Hyper-digital logic: Summarized overview of its syntax and semantics

2. Introduction to hyper-digital logic

3. Set field logic and its embedding into hyper-propositional logic

4. Algebraic properties of hyper-digital logic

5. Mixed hyper-digital logic

6. Hyper-digital and modal logic

7. Hyper-propositional normalizations and canonizations

Footnotes

[1] To find an appropriate title for this (assumedly new) logical system is still an open problem. The prefix "hyper" is chosen because somehow it is a generalization of propositional logic on "higher (and lower) levels". "Propositional" is chosen due to the genealogy, but actually the association is too restrictive and replacing it by the more abstract and neutral word "digital" or "bit" seems more appropriate. On the other hand, it can also be useful to use both titles: "hyper-propositional logic" for the logic of hyper-propositional formulas in the narrower sense, and "hyper-digital logic" for the broader view, which also includes the bit table algebras.

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