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The logic is the sentential logic defined in the language with just implication → by the axiom of reflexivity or identity “” and the rule of Modus Ponens “from φ and to infer ψ”. The theorems of this logic are exactly all formulas of the form . We argue that this is the simplest protoalgebraic logic, and that in it every set of assumptions encodes in itself not only all its consequences...
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