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      AUTHOR = {Blackburn, Patrick and de Rijke, Maarten and Vennema, Ide},
      TITLE = {The Algebra of Modal Logic},
      YEAR = {1994},
      MONTH = {November},
      NUMBER = {47},
      ADDRESS = {Saarbrücken},
      TYPE = {CLAUS-Report},
      INSTITUTION = {Universität des Saarlandes},
      URL = {},
      ABSTRACT = {Our main aim is to review the frame semantics and axiomatics of modal logic from the perspective of the duality between (Kripke) frames and boolean algebras with operators as defined by Jónsson and Tarski. To this end, we introduce modal languages and their interpretation in models and frames in Part II. We define and discuss the notion of a modal formula characterizing a class of frames or models, and give the Sahlqvist algorithm which yields, given a suitable modal formula as input, the corresponding first-order condition on the class of frames characterized by the formula. We define the concept of a normal modal logic and explain the canonical frame method for proving completeness of a logic with respect to classes of frames. In Part III we develop the algebraic perspective on modal logic. We introduce boolean algebras with operators and show how they arise naturally in both the semantic and the axiomatic approach towards algebraizing modal logic. We discuss in detail how the category of boolean algebras with operators and homomorphisms links up with the category of frames with so-called bounded morphisms. Finally, we apply this duality to give easy proofs for some important and well-known results from modal logic.},
      ANNOTE = {COLIURL : Blackburn:1994:AML.dvi}
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