Floppy logic as a generalization of standard Boolean logic

Abstract

The topic of this article is a floppy logic, a new multi-valued logic. Floppy logic is related to fuzzy logic and the theory of probability, but it also has interesting links to probability logic and standard Boolean logic. It provides a consistent and simple theory that is easy to apply in practice. This article examines the isomorphism theorem, which plays an important role in floppy logic. The theorem is described and proved. The most important consequences of the isomorphism theorem are: 1) All statements which are equivalent in standard Boolean logic are also equivalent in floppy logic. 2) Floppy logic has all the properties of standard Boolean logic which can be formulated as an equivalence. These include, for example, distributivity, the contradiction law, the law of excluded middle, and others. The article mainly examines floppy implication. We show that floppy implication does not satisfy Adam’s Thesis and that floppy logic is not limited by Lewis’ triviality result. We also present a range of inference rules which are generalizations of modus ponens and modus tollens. These rules hold in floppy logic, and of course, also apply to standard Boolean logic. All these results lead us to the notion that floppy logic is a many-valued generalization of standard Boolean logic.