David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 30 (5):395-438 (2001)
We explore a relation we call 'anticipation' between formulas, where A anticipates B (according to some logic) just in case B is a consequence (according to that logic, presumed to support some distinguished implicational connective →) of the formula A → B. We are especially interested in the case in which the logic is intuitionistic (propositional) logic and are much concerned with an extension of that logic with a new connective, written as "a", governed by rules which guarantee that for any formula B, aB is the (logically) strongest formula anticipating B. The investigation of this new logic, which we call ILa, will confront us on several occasions with some of the finer points in the theory of rules and with issues in the philosophy of logic arising from the proposed explication of the existence of a connective (with prescribed logical behaviour) in terms of the conservative extension of a favoured logic by the addition of such a connective. Other points of interest include the provision of a Kripke semantics with respect to which ILa is demonstrably sound, deployed to establish certain unprovability results as well as to forge connections with C. Rauszer's logic of dual intuitionistic negation and dual intuitionistic implication, and the isolation of two relations (between formulas), head-implication and head-linkage, which, though trivial in the setting of classical logic, are of considerable significance in the intuitionistic context
|Keywords||New intuitionistic connectives dual intuitionistic negation rules conservative extension|
|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
Dov M. Gabbay (1986). Semantical Investigations in Heyting's Intuitionistic Logic. Journal of Symbolic Logic 51 (3):824-824.
Nuel Belnap (1962). Tonk, Plonk and Plink. Analysis 22 (6):130-134.
Arnold Koslow (1992/2005). A Structuralist Theory of Logic. Cambridge University Press.
Krister Segerberg (1968). Propositional Logics Related to Heyting's and Johansson's. Theoria 34 (1):26-61.
Citations of this work BETA
Lloyd Humberstone (2008). Béziau's Translation Paradox. Theoria 71 (2):138-181.
Lloyd Humberstone (2008). Contrariety and Subcontrariety: The Anatomy of Negation (with Special Reference to an Example of J.-Y. Béziau). Theoria 71 (3):241-262.
Similar books and articles
Giambattista Amati, Luigia Carlucci-Aiello & Fiora Pirri (1997). Intuitionistic Autoepistemic Logic. Studia Logica 59 (1):103-120.
Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393-430.
Peter W. O'Hearn & David J. Pym (1999). The Logic of Bunched Implications. Bulletin of Symbolic Logic 5 (2):215-244.
Xavier Caicedo & Roberto Cignoli (2001). An Algebraic Approach to Intuitionistic Connectives. Journal of Symbolic Logic 66 (4):1620-1636.
Stefano Berardi (1999). Intuitionistic Completeness for First Order Classical Logic. Journal of Symbolic Logic 64 (1):304-312.
Linda Postniece, Combining Derivations and Refutations for Cut-Free Completeness in Bi-Intuitionistic Logic.
Philip Kremer (1997). On the Complexity of Propositional Quantification in Intuitionistic Logic. Journal of Symbolic Logic 62 (2):529-544.
L. Humberstone & D. Makinson (2012). Intuitionistic Logic and Elementary Rules. Mind 120 (480):1035-1051.
Lloyd Humberstone (2000). Contra-Classical Logics. Australasian Journal of Philosophy 78 (4):438 – 474.
A. D. Yashin (1999). Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness. Journal of Philosophical Logic 28 (2):175-197.
Added to index2009-01-28
Total downloads19 ( #185,201 of 1,789,994 )
Recent downloads (6 months)1 ( #424,764 of 1,789,994 )
How can I increase my downloads?