Algebraic properties of hyper-digital logic

online since July 2007


Having defined the syntax and semantics of hyper-digital logic (see [1]), this paper investigates the basic properties of the quasi-order relation on hyper-propositional formulas of a given carrier set A and degree k.

One set of properties immediately derives from the fact that these formula algebras are quasi-boolean algebras. We for example have

Another set of properties involves the "box" and "diamond" operators and many results are similar to axioms and theorems of modal logic, such as But not all phenomena fit into the perspective of traditional logical systems: From a deeper point of understanding of course, these "surprising" phenomena turn into perfectly normal behaviour.

The text

The full text is currently under construction.


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

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