Data di Pubblicazione:
2014
Citazione:
Free Modal Algebras Revisited: the Step by Step Method / N. Bezhanishvili, S. Ghilardi, M. Jibladze - In: Leo Esakia on Duality in Modal and Intuitionistic Logics / [a cura di] G. Bezhanishvili. - [s.l] : Springer, 2014. - ISBN 978-94-017-8859-5. - pp. 43-62 [10.1007/978-94-017-8860-1_3]
Abstract:
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 [11] which undertakes a very similar approach.
Tipologia IRIS:
03 - Contributo in volume
Keywords:
free modal algebras ; step frames
Elenco autori:
N. Bezhanishvili, S. Ghilardi, M. Jibladze
Link alla scheda completa:
Titolo del libro:
Leo Esakia on Duality in Modal and Intuitionistic Logics