David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantiﬁers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantiﬁers are not present, this is not really a ﬁrst-order logic, but it is not exactly propositional either. For propositional logics such as K, T and D, adding such machinery produces a decidable logic, but adding it to S5 produces an undecidable one. Further, if an equality symbol is in the language, and interpreted by the equality relation, logics from K4 to S5 yield undecidable versions. (Thus transitivity is the villain here.) The proof of undecidability consists in showing that classical ﬁrst-order logic can be embedded.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Melvin Fitting (2004). First-Order Intensional Logic. Annals of Pure and Applied Logic 127 (1-3):171-193.
Melvin Fitting (2006). FOIL Axiomatized. Studia Logica 84 (1):1 - 22.
Similar books and articles
G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
Melvin Fitting (2002). Interpolation for First Order S5. Journal of Symbolic Logic 67 (2):621-634.
Roman Kontchakov, Agi Kurucz & Michael Zakharyaschev (2005). Undecidability of First-Order Intuitionistic and Modal Logics with Two Variables. Bulletin of Symbolic Logic 11 (3):428-438.
Minghui Ma (2010). Toward Model-Theoretic Modal Logics. Frontiers of Philosophy in China 5 (2):294-311.
Richard Zach (2004). Decidability of Quantified Propositional Intuitionistic Logic and S4 on Trees of Height and Arity ≤Ω. Journal of Philosophical Logic 33 (2):155-164.
Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209 - 223.
Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209-223.
Torben Braüner (2005). Proof-Theoretic Functional Completeness for the Hybrid Logics of Everywhere and Elsewhere. Studia Logica 81 (2):191 - 226.
Marta Bílková (2007). Uniform Interpolation and Propositional Quantifiers in Modal Logics. Studia Logica 85 (1):1 - 31.
Rohan French (2012). Denumerably Many Post-Complete Normal Modal Logics with Propositional Constants. Notre Dame Journal of Formal Logic 53 (4):549-556.
Patrick Blackburn & Maarten Marx (2003). Constructive Interpolation in Hybrid Logic. Journal of Symbolic Logic 68 (2):463-480.
Nobu-Yuki Suzuki (1990). Kripke Bundles for Intermediate Predicate Logics and Kripke Frames for Intuitionistic Modal Logics. Studia Logica 49 (3):289 - 306.
Added to index2010-12-22
Total downloads10 ( #235,035 of 1,726,249 )
Recent downloads (6 months)6 ( #118,705 of 1,726,249 )
How can I increase my downloads?