David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Annals of Pure and Applied Logic 163 (3):291 - 313 (2012)
Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Preﬁxed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and preﬁxed modal tableaus are notational variants of each other, roughly in the same way that tableaus and Gentzen sequent calculi are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justiﬁcation logics that include standard modal operators.
|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
Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
Kai Brünnler (2009). Deep Sequent Systems for Modal Logic. Archive for Mathematical Logic 48 (6):551-577.
Melvin Fitting (2004). First-Order Intensional Logic. Annals of Pure and Applied Logic 127 (1-3):171-193.
Melvin Fitting (2005). The Logic of Proofs, Semantically. Annals of Pure and Applied Logic 132 (1):1-25.
Melvin Fitting (1972). Tableau Methods of Proof for Modal Logics. Notre Dame Journal of Formal Logic 13 (2):237-247.
Citations of this work BETA
No citations found.
Similar books and articles
Francesca Poggiolesi (2010). Display Calculi and Other Modal Calculi: A Comparison. Synthese 173 (3):259 - 279.
Bruce M. Kapron (1987). Modal Sequents and Definability. Journal of Symbolic Logic 52 (3):756-762.
Melvin Fitting (1995). Tableaus for Many-Valued Modal Logic. Studia Logica 55 (1):63 - 87.
Rajeev Gore, Linda Postniece & Alwen Tiu, Cut-Elimination and Proof-Search for Bi-Intuitionistic Logic Using Nested Sequents.
Kosta Došen (1985). Sequent-Systems for Modal Logic. Journal of Symbolic Logic 50 (1):149-168.
Valentin Goranko (1994). Refutation Systems in Modal Logic. Studia Logica 53 (2):299 - 324.
Grigori Mints (1997). Indexed Systems of Sequents and Cut-Elimination. Journal of Philosophical Logic 26 (6):671-696.
Reina Hayaki (2003). Actualism and Higher-Order Worlds. Philosophical Studies 115 (2):149 - 178.
Melvin Fitting, Lars Thalmann & Andrei Voronkov (2001). Term-Modal Logics. Studia Logica 69 (1):133-169.
Maria Luisa Bonet & Samuel R. Buss (1993). The Deduction Rule and Linear and Near-Linear Proof Simulations. Journal of Symbolic Logic 58 (2):688-709.
Andrew A. Fingelkurts & Alexander A. Fingelkurts (2012). Mind as a Nested Operational Architectonics of the Brain. Physics of Life Reviews 9 (1):49-50.
Added to index2011-02-09
Total downloads23 ( #79,922 of 1,101,944 )
Recent downloads (6 months)5 ( #68,246 of 1,101,944 )
How can I increase my downloads?