Logics for approximate and strong entailments

We consider two kinds of similarity-based reasoning and formalise them in a logical setting. In one case, we are led by the principle that conclusions can be drawn even if they are only approximately correct. This leads to a graded approximate entailment, which is weaker than classical entailment. In the other case, we follow the principle that conclusions must remain correct even if the assumptions are slightly changed. This leads to a notion of a graded strong entailment, which is stronger than classical entailment. We develop two logical calculi based on the notions of approximate and of strong entailment, respectively. © 2011 Elsevier B.V.The authors acknowledge partial support of the bilateral Austrian-Spanish project HA2008-0017 and the Eurocores-LogICCC ESF project LoMoReVI. Esteva and Godo also acknowledge partial support of the Spanish project FFI2008-03126-E/FILO and Rodrıguez acknowledges the projects CyT-UBA X484 and the research CONICET program PIP 12-200801-02543 2009-2011. Finally, Esteva, Godo and Rodrıguez also acknowledge partial support of the MaToMUVI project (PIRSES-GA-2009- 247584).Peer Reviewe