FINITE MODELS CONSTRUCTED FROM CANONICAL FORMULAS

This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229–237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113–118, 1981). The point is to develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection.

[1]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[2]  Lawrence S. Moss,et al.  Vicious circles - on the mathematics of non-wellfounded phenomena , 1996, CSLI lecture notes series.

[3]  K. Segerberg.  Decidability of S4.1 , 2008 .

[4]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[5]  De Jongh,et al.  Investigations on the intuitionistic propositional calculus , 1968 .

[6]  Lawrence S. Moss,et al.  Coalgebraic Logic , 1999, Ann. Pure Appl. Log..

[7]  Kit Fine,et al.  Normal forms in modal logic , 1975, Notre Dame J. Formal Log..

[8]  Lawrence S. Moss,et al.  Modal Correspondence for Models , 1998, J. Philos. Log..

[9]  Silvio Ghilardi,et al.  An Algebraic Theory of Normal Forms , 1995, Ann. Pure Appl. Log..