- Free modal algebras revisited: the step-by-step method
- Book title
- Leo Esakia on Duality in Modal and Intuitionistic Logics
- Pages (from-to)
- Dordrecht: Springer
- ISBN (electronic)
- Outstanding contributions to logic
- Volume (Serie)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
We review the step-by-step method of constructing finitely generated free modal algebras. First we discuss the global step-by-step method, which works well for rank one modal logics. Next we refine the global step-by-step method to obtain the local step-by-step method, which is applicable beyond rank one modal logics. In particular, we show that it works well for constructing the finitely generated free algebras for such well-known modal systems as T, K4 and S4. This yields the notions of one-step algebras and of one-step frames, as well as of universal one-step extensions of one-step algebras and of one-step frames. We show that finitely generated free algebras for T, K4 and S4 and their dual spaces can be obtained by iterating the universal one-step extensions of one-step algebras and of one-step frames. In the final part of the chapter we compare our construction with recent literature, especially with  which undertakes a very similar approach.
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