Many-valued hybrid logic

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is proof theoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.

[1]  M. Fitting Proof Methods for Modal and Intuitionistic Logics , 1983 .

[2]  Patrick Blackburn,et al.  Terminating Tableau Calculi for Hybrid Logics Extending K , 2009, M4M.

[3]  L. Godo,et al.  Logical approaches to fuzzy similarity-based reasoning: an overview , 2008 .

[4]  Torben Braüner,et al.  Tableau-based Decision Procedures for Hybrid Logic , 2006, J. Log. Comput..

[5]  Melvin Fitting How True It Is = Who Says It’s True , 2009, Stud Logica.

[6]  Patrick Blackburn,et al.  Termination for Hybrid Tableaus , 2007, J. Log. Comput..

[7]  Yakoub Salhi,et al.  A family of Gödel hybrid logics , 2010, J. Appl. Log..

[8]  W. B. Ewald,et al.  Intuitionistic tense and modal logic , 1986, Journal of Symbolic Logic.

[9]  Valeria C V de Paiva,et al.  Intuitionistic Hybrid Logic , 2006 .

[10]  R. C.,et al.  A Hybrid Intuitionistic Logic : Semantics and Decidability , 2005 .

[11]  Maarten Marx,et al.  Tableaux for Quantified Hybrid Logic , 2002, TABLEAUX.

[12]  Melvin Fitting,et al.  Many-valued modal logics II , 1992 .

[13]  Jens Ulrik Hansen A Tableau system for a first-order hybrid logic , 2007 .

[14]  Melvin Fitting,et al.  Tableaus for many-valued modal logic , 1995, Stud Logica.

[15]  Melvin Fitting,et al.  Modal proof theory , 2007, Handbook of Modal Logic.

[16]  A. Troelstra,et al.  Constructivism in Mathematics: An Introduction , 1988 .

[17]  T. Braüner Hybrid Logic and its Proof-Theory , 2010 .

[18]  Melvin Fitting,et al.  Many-valued modal logics , 1991, Fundam. Informaticae.

[19]  Patrick Blackburn,et al.  Internalizing labelled deduction , 2000, J. Log. Comput..

[20]  Torben Braüner,et al.  Why does the proof-theory of hybrid logic work so well? , 2007, J. Appl. Non Class. Logics.