In this chapter, we present the method of Socratic proofs for a number of propositional modal logics called basic. In [11], the author presented erotetic calculi for the class of basic modal propositional logics. By basic modal logics, we mean \(\textsf {K}\) and all of its proper extensions, characterized by any combination of the following properties of the accessibility relation: seriality (also called ‘extendability’), reflexivity, transitivity, symmetry, and Euclideanness. These five semantic properties can be combined in \(2^5=32\) ways, including the empty one, but some combinations of properties entail others.

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Erotetic Calculi for Propositional Modal Logics

  • Dorota Leszczyńska-Jasion

摘要

In this chapter, we present the method of Socratic proofs for a number of propositional modal logics called basic. In [11], the author presented erotetic calculi for the class of basic modal propositional logics. By basic modal logics, we mean \(\textsf {K}\) and all of its proper extensions, characterized by any combination of the following properties of the accessibility relation: seriality (also called ‘extendability’), reflexivity, transitivity, symmetry, and Euclideanness. These five semantic properties can be combined in \(2^5=32\) ways, including the empty one, but some combinations of properties entail others.