Speaker
Grigory Olkhovikov
RuhrUniversitaet Bochum
Talks at this conference:
Tuesday, 17:45, J222 
Conditionals in constructive logics 
We consider the problems arising in figuring out the right counterparts to the basic conditional logic \(\mathsf{CK}\) when the propositional basis of the logic is no longer assumed to be classical. We argue that, as long as the new underlying logic is constructive, this problem shows essential resemblance to the problem of figuring out the right intuitionistic counterparts to the wellknown classical modal logics as addressed, e.g. in [3], where the famous set of six requirements was put forward. Among these requirements, the last and the most important one demands an explanation of the semantics of conditionals/modalities in terms of the firstorder version of the underlying nonclassical logic, and we fundamentally agree with A. Simpsonâ€™s intepretation of this explanation as the faithfulness of the embedding into the firstorder version of the underlying logic provided for the candidate conditional/modal logic by the standard translation borrowed from the classical case. However, both the choice of the underlying nonclassical logic and the peculiar features of the conditional logic may pose additional challenges. We illustrate these challenges by the examples \(\mathsf{IntCK}\) and \(\mathsf{N4CK}\), the two recently proposed analogues of \(\mathsf{CK}\) (see [1] and [2]) based on the intuitionistic propositional logic and on the paraconsistent variant of Nelsonâ€™s logic of strong negation, respectively. Bibliography
