The Bounds of Finitude: S3 and S4

John Slaney

18. 11. Meyer long ago posed the question of the number of non-equivalent formulas in restricted fragments of various non-classical logics. In the case of the one-variable pure implication fragments of Anderson-Belnap relevant logics T and E, this problem has been open for over 40 years. In this talk, I shall explain why the problem is interesting despite having no direct practical application, and present solutions for the closely related modal logics S3 and S4.

This talk is mainly for those interested in non-classical logic, but does not presuppose a great deal of technical familiarity with the field.