What is propositional classical logic? (a study in universal logic).

Аннотация

The aim o f this paper is to try to characterize classical propositional logic (CPL) with the notion o f mathematical structure.

We start by justifying this approach. We recall the importance and significance o f the notion o f structure in mathematics and in logic. We explain the idea o f a general theory> o f logics based on structures, Universal Logic.

CPL is not one structure but a class o f equivalent structures, CPLstructures. We survey a series o f structures that can be considered as CPL-structures. The main problem is to find a notion o f equivalence which permits to gather into a whole this multiplicity.

We show in particular that the modern concept o f equivalence o f structures, based on the notion o f expansion by definition and isomorphism, is not adequate to define a satisfactory notion o f equivalence that will define the class o f CPL-structures. An alternative definition, postmodern equivalence, is introduced.

It appears that this tentative o f characterization o f the class o f CPL-structures is not only relevant fo r Universal Logic, but also fo r the general theory; o f mathematical structures, since the case o f CPLstructures shows the insufficiency o f the modern concept o f equivalence between structures.