 Author
 Title
 Correspondence and canonicity in nonclassical logic
 Supervisors
 Cosupervisors
 Award date
 9 September 2015
 Number of pages
 238
 ISBN
 9789064648922
 Document type
 PhD thesis
 Faculty
 Interfacultary Research Institutes
 Institute
 Institute for Logic, Language and Computation (ILLC)
 Abstract

In this thesis we study correspondence and canonicity for nonclassical logic using algebraic and ordertopological methods. Correspondence theory is aimed at answering the question of how precisely modal, firstorder, secondorder languages interact and overlap in their shared semantic environment. The line of research in correspondence theory which concerns the present thesis is Sahlqvist correspondence theory  which was originally developed for classical modal logic, and provides a systematic translation between classical modal logic and firstorder logic. Canonicity is closely related to correspondence, and ensures that logics axiomatized by these formulas are complete with respect to relational semantics. Thus, correspondence and canonicity together establish that Sahlqvist logics are semantically complete with respect to firstorder definable classes of relational structures.
The first part of the thesis focuses on algebraic methods. In chapter 3, we prove the classical Sahlqvist correspondence theorem for basic modal logic in the algebraic setting of complex algebras of frames. We extend the algorithm ALBA to regular modal logic (modal logic with nonnormal modalities) and intuitionistic modal mucalculus in Chapters 4 and 5, respectively. In Chapter 6, we develop ALBA for distributive lattice expansions, using which we prove relativised canonicity for the metainductive inequalities. The second part of the thesis focuses on ordertopological methods. In Chapter 7, we prove a modallike duality for de Vries algebras. In Chapter 8, we prove a Sahlqvist correspondence and canonicity theorem for topological fixedpoint logic on compact Hausdorff spaces.  Note
 Research conducted at: Universiteit van Amsterdam
Series: ILLC dissertation series DS201504  Permalink
 http://hdl.handle.net/11245/1.485173
 Downloads
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.