What is Classical Propositional Logic? J-Y. B`eziau, R.P. de Freitas, J.P. Viana

J-Y. Bèziau, R.P. de Freitas, J.P. Viana
What is Classical Propositional Logic? (A Study in Universal Logic)
The aim of this paper is to try to characterize classical propositional logic (CPL) with the notion of mathematical structure.
We start by justifying this approach. We recall the importance and significance of the notion of structure in mathematics and in logic. We explain the idea of a general theory of logics based on structures, Universal Logic.
CPL is not one structure but a class of equivalent structures, CPL-structures. The main problem is to find a notion of equivalence which permits to gather into a whole this multiplicity.
We show in particular that the modern concept of equivalence of structures, based on the notion of expansion by definition and isomorphism, is not adequate to define a satisfactory notion of equivalence that will define the class of CPL-structures. An alternative definition, postmodern equivalence, is introduced.
It appears that this tentative of characterization of the class of CPL-structures is not only relevant for Universal Logic, but also for the general theory of mathematical structures, since the case of CPL-structures shows the insufficiency of the modern concept of equivalence between structures.

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