6 Algebras and coalgebras [chapter]

Yde Venema
2007 Studies in Logic and Practical Reasoning  
This chapter 1 sketches some of the mathematical surroundings of modal logic. First, we discuss the algebraic perspective on the field, showing how the theory of universal algebra, and more specifically, that of Boolean algebras with operators, can be used to prove significant results in modal logic. In the second and last part of the chapter we describe how modal logic, and its model theory, provides many natural manifestations of the more general theory of universal coalgebra. 1 This text has
more » ... been written as a chapter for the Handbook of Modal Logic (to appear), edited by Johan van Benthem, Patrick Blackburn and Frank Wolter. Accordingly, the introductory section on the basics of modal logis is written rather scantily; it does provide definitions but depends for explanation and context on other chapters. Also, at some specific points, the final version of this text will contain references to (specific parts of) other chapters of the book; for the time being, these references are represented by the letters 'HBML'.
doi:10.1016/s1570-2464(07)80009-7 fatcat:e77uebqxdferlcg2nlfe5hobpq