Annals of Pure and Applied Logic 163 (12):1928-1939 (2012)
AbstractA class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained types of modal definability on the level of Kripke models, we give characterization theorems in the usual form, in terms of algebraic closure conditions. As some consequences of these, various preservation results are presented. Also, some characterizations are strengthened by replacing closure under ultraproducts with closure under ultrapowers
Similar books and articles
Modal Logic Over Finite Structures.Eric Rosen - 1997 - Journal of Logic, Language and Information 6 (4):427-439.
Uniform Short Proofs for Classical Theorems.Kees Doets - 2001 - Notre Dame Journal of Formal Logic 42 (2):121-127.
Rules in Relevant Logic - I: Semantic Classification.Ross T. Brady - 1994 - Journal of Philosophical Logic 23 (2):111 - 137.
Interpolation and Preservation In.Holger Sturm - 1998 - Notre Dame Journal of Formal Logic 39 (2):190-211.
Paranormal Modal Logic – Part II: K?, K and Classical Logic and Other Paranormal Modal Systems.R. Silvestre - 2013 - Logic and Logical Philosophy 22 (1):89-130.
Kripke Semantics for Modal Substructural Logics.Norihiro Kamide - 2002 - Journal of Logic, Language and Information 11 (4):453-470.
Paranormal Modal Logic–Part I: The System K? And the Foundations of the Logic of Skeptical and Credulous Plausibility.Ricardo S. Silvestre - 2012 - Logic and Logical Philosophy 21 (1):65-96.
Syntactical Results on the Arithmetical Completeness of Modal Logic.Paolo Gentilini - 1993 - Studia Logica 52 (4):549 - 564.
On Preservation Theorems for Two-Variable Logic.Erich Gradel & Eric Rosen - 1999 - Mathematical Logic Quarterly 45 (3):315-325.
A General Lindström Theorem for Some Normal Modal Logics.Sebastian Enqvist - 2013 - Logica Universalis 7 (2):233-264.
A Unified Completeness Theorem for Quantified Modal Logics.Giovanna Corsi - 2002 - Journal of Symbolic Logic 67 (4):1483-1510.
Expressive Logics for Coalgebras Via Terminal Sequence Induction.Dirk Pattinson - 2004 - Notre Dame Journal of Formal Logic 45 (1):19-33.
Arithmetical Interpretations and Kripke Frames of Predicate Modal Logic of Provability.Taishi Kurahashi - 2013 - Review of Symbolic Logic 6 (1):1-18.
Added to PP
Historical graph of downloads
Citations of this work
Characterising Modal Definability of Team-Based Logics Via the Universal Modality.Katsuhiko Sano & Jonni Virtema - 2019 - Annals of Pure and Applied Logic 170 (9):1100-1127.
Existential Definability of Modal Frame Classes.Tin Perkov & Luka Mikec - 2020 - Mathematical Logic Quarterly 66 (3):316-325.
References found in this work
Derivation Rules as Anti-Axioms in Modal Logic.Yde Venema - 1993 - Journal of Symbolic Logic 58 (3):1003-1034.
The Range of Modal Logic: An Essay in Memory of George Gargov.Johan van Benthem - 1999 - Journal of Applied Non-Classical Logics 9 (2):407-442.
The Range of Modal Logic: An Essay in Memory of George Gargov.Johan van Benthem - 1999 - Journal of Applied Non-Classical Logics 9 (2-3):407-442.
Characterizations of Negative Definability in Modal Logic.Marco Hollenberg - 1998 - Studia Logica 60 (3):357-386.