The enduring scandal of deduction

@article{DAgostino2008TheES,
  title={The enduring scandal of deduction},
  author={Marcello D'Agostino and L. Floridi},
  journal={Synthese},
  year={2008},
  volume={167},
  pages={271-315}
}
Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable… 
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