Sahlqvist Correspondence for Modal mu-calculus

We define analogues of modal Sahlqvist formulas for the modal mu-calculus, and prove a correspondence theorem for them.

[1]  J.F.A.K. van Benthem,et al.  Modal logic and classical logic , 1983 .

[2]  Jörg Flum,et al.  Finite model theory , 1995, Perspectives in Mathematical Logic.

[3]  Yde Venema,et al.  The preservation of Sahlqvist equations in completions of Boolean algebras with operators , 1999 .

[4]  Johan van Benthem A Note on Modal Formulae and Relational Properties , 1975, J. Symb. Log..

[5]  Johan van Benthem,et al.  Minimal predicates, fixed-points, and definability , 2005, Journal of Symbolic Logic.

[6]  A. Tarski A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[7]  G. Fontaine,et al.  Modal fixpoint logic: some model theoretic questions , 2010 .

[8]  E. Grädel The decidability of guarded fixed point logic , 1999 .

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

[10]  Ian M. Hodkinson,et al.  Sahlqvist theorem for modal fixed point logic , 2012, Theor. Comput. Sci..

[11]  Patrick Doherty,et al.  Computing Circumscription Revisited: A Reduction Algorithm , 1997, Journal of Automated Reasoning.

[12]  Dov M. Gabbay,et al.  Quantifier Elimination in Second-Order Predicate Logic , 1992, KR.

[13]  Kit Fine,et al.  An incomplete logic containing S4 , 1974 .

[14]  Valentin Goranko,et al.  Algorithmic correspondence and completeness in modal logic. V. Recursive extensions of SQEMA , 2010, J. Appl. Log..

[15]  Maarten Marx,et al.  Hybrid logics with Sahlqvist axioms , 2005, Log. J. IGPL.

[16]  Valentin Goranko,et al.  Elementary canonical formulae: extending Sahlqvist's theorem , 2006, Ann. Pure Appl. Log..

[17]  M. K. Luhandjula Studies in Fuzziness and Soft Computing , 2013 .

[18]  Johan van Benthem,et al.  Modal Frame Correspondences and Fixed-Points , 2006, Stud Logica.

[19]  Giovanni Sambin,et al.  A new proof of Sahlqvist's theorem on modal definability and completeness , 1989, Journal of Symbolic Logic.

[20]  Marcus Kracht,et al.  How Completeness and Correspondence Theory Got Married , 1993 .

[21]  Robert Goldblatt,et al.  The McKinsey–Lemmon logic is barely canonical , 2007 .

[22]  A. Dawar FINITE MODEL THEORY (Perspectives in Mathematical Logic) , 1997 .

[23]  Henrik Sahlqvist Completeness and Correspondence in the First and Second Order Semantics for Modal Logic , 1975 .

[24]  Valentin Goranko,et al.  Model theory of modal logic , 2007, Handbook of Modal Logic.

[25]  A. Szałas,et al.  A Fixpoint Approach to Second-Order Quantifier Elimination with Applications to Correspondence Theory , 1999 .

[26]  Max J. Cresswell,et al.  An incomplete decidable modal logic , 1984, Journal of Symbolic Logic.

[27]  Philippe Balbiani,et al.  Every world can see a Sahlqvist world , 2006, Advances in Modal Logic.