Importing Logics: Soundness and Completeness Preservation

Importing subsumes several asymmetric ways of combining logics, including modalization and temporalization. A calculus is provided for importing, inheriting the axioms and rules from the given logics and including additional rules for lifting derivations from the imported logic. The calculus is shown to be sound and concretely complete with respect to the semantics of importing as proposed in J. Rasga et al. (100(3):541–581, 2012) Studia Logica.

[1]  Dov M. Gabbay,et al.  Fibred Semantics and the Weaving of Logics , 2012 .

[2]  Cristina Sernadas,et al.  A Graph-theoretic Account of Logics , 2009, J. Log. Comput..

[3]  P. Mateus,et al.  Exogenous Semantics Approach to Enriching Logics , 2005 .

[4]  Robert Goldblatt,et al.  Mathematical modal logic: A view of its evolution , 2003, J. Appl. Log..

[5]  Cristina Sernadas,et al.  Fibring as Biporting Subsumes Asymmetric Combinations , 2014, Stud Logica.

[6]  Rohit Chadha,et al.  Reasoning about probabilistic sequential programs , 2007, Theor. Comput. Sci..

[7]  Marcelo Finger,et al.  Non-normal Modalisation , 2002, Advances in Modal Logic.

[8]  Dov M. Gabbay,et al.  Fibred semantics and the weaving of logics. Part 1: Modal and intuitionistic logics , 1996, Journal of Symbolic Logic.

[9]  Yuri Gureoich Intuitionistic Logic , 2008 .

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

[11]  Cristina Sernadas,et al.  Importing Logics , 2012, Stud Logica.

[12]  Amílcar Sernadas,et al.  Weakly complete axiomatization of exogenous quantum propositional logic , 2005, Inf. Comput..

[13]  Dov M. Gabbay,et al.  Adding a temporal dimension to a logic system , 1992, J. Log. Lang. Inf..

[14]  Marcelo Finger,et al.  The Unrestricted Combination of Temporal Logic Systems , 2002, Log. J. IGPL.

[15]  Burghard von Karger,et al.  Temporal algebra , 1998, Mathematical Structures in Computer Science.