David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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.
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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.
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