Studia Logica 84 (2):277 - 322 (2006)
In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full first-order expressivity).We show that hybrid logic offers a genuinely first-order perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of non-orthodox rules. We discuss these rules in detail and prove non-eliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to first-order hybrid logic.
|Keywords||Philosophy Computational Linguistics Mathematical Logic and Foundations Logic|
|Categories||categorize this paper)|
References found in this work BETA
Semantical Considerations on Modal Logic.Saul A. Kripke - 1963 - Acta Philosophica Fennica 16 (1963):83-94.
Semantical Analysis of Modal Logic I. Normal Propositional Calculi.Saul A. Kripke - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (5‐6):67-96.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Citations of this work BETA
No citations found.
Similar books and articles
Constructive Interpolation in Hybrid Logic.Patrick Blackburn & Maarten Marx - 2003 - Journal of Symbolic Logic 68 (2):463-480.
Model Checking for Hybrid Logic.Martin Lange - 2009 - Journal of Logic, Language and Information 18 (4):465-491.
Hybrid Logics with Infinitary Proof Systems.Rineke Verbrugge, Gerard Renardel de Lavalette & Barteld Kooi - unknown
A Proof–Theoretic Study of the Correspondence of Hybrid Logic and Classical Logic.H. Kushida & M. Okada - 2006 - Journal of Logic, Language and Information 16 (1):35-61.
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
Added to index2009-01-28
Total downloads23 ( #210,658 of 2,146,969 )
Recent downloads (6 months)1 ( #385,507 of 2,146,969 )
How can I increase my downloads?
There are no threads in this forum
Nothing in this forum yet.