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I've found in Wikipedia an interesting formal definition of what a propositional logic (propositional calculus) "exactly" is. Unfortunately it does not cite its source. I wonder which is the original source for this definition, does someone recall it?

I have checked some typical literature (Monk1976, Barwise1993, Matiyasevich1994, Ebbinghaus1994, Rautenberg2010, Manin2010, Girard2011, Pudlak2013), however I could not find a comparable definition. Ebbinghaus comes somewhat close, but it is still far from being this one.

InfinitelyInquisitive
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    That definition seems to define propositional logic as a universal algebra. A universal algebra is a set $A$ together with a collection of operations on $A$. In this case, $A$ is the propositional variables and the operations are the logical operators. – mrp Oct 26 '15 at 12:20
  • The definition used there doesn't work quite so well for propositional calculi with functional variables (where there exist functions which are variables instead of constants). It also doesn't have anything about definitions. – Doug Spoonwood Oct 27 '15 at 04:00
  • The definition also doesn't work for propositional calculi with quantifiers. – Doug Spoonwood Oct 27 '15 at 12:24
  • Why don't you click the Talk tab on the wikipedia page and ask your question there? – Rob Arthan Oct 27 '15 at 18:12

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