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      AUTHOR = {Blackburn, Patrick and Tzakova, Miroslava},
      TITLE = {Hybrid Completeness},
      YEAR = {1998},
      MONTH = {June},
      NUMBER = {95},
      PAGES = {27},
      ADDRESS = {Saarbrücken},
      TYPE = {CLAUS Report},
      INSTITUTION = {Universität des Saarlandes},
      URL = {},
      ABSTRACT = {In this paper we discuss two hybrid languages, and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to 'label' states by using binders to bind special state variables. This paper explores the consequences of hybridization for completeness. As we shall show, the challenge is to blend the modal idea of canonical models with the classical idea of witnessed maximal consistent sets. The languages discussed provide us with two extreme examples of the issues involved. In the one case we can combine these ideas relatively straightforwardly with the aid of analogs of the Barcan axioms coupled with a modal theory of labeling. In the other case, although we can still formulate a theory of labeling, the Barcan analogs are not valid. We show how to overcome this difficulty by using COV, an infinite collection of additional rules of proof which has been used in a number of investigations of extended modal logic.},
      ANNOTE = {COLIURL : Blackburn:1998:HC.pdf Blackburn:1998:HC.dvi}
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