David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 51 (3):351-360 (2010)
Pure second-order logic is second-order logic without functional or first-order variables. In "Pure Second-Order Logic," Denyer shows that pure second-order logic is compact and that its notion of logical truth is decidable. However, his argument does not extend to pure second-order logic with second-order identity. We give a more general argument, based on elimination of quantifiers, which shows that any formula of pure second-order logic with second-order identity is equivalent to a member of a circumscribed class of formulas. As a corollary, pure second-order logic with second-order identity is compact, its notion of logical truth is decidable, and it satisfies a pure second-order analogue of model completeness. We end by mentioning an extension to n th-order pure logics
|Keywords||second-order logic nth-order logic elimination of quantifiers compactness decidability of validity model completeness|
|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
No citations found.
Similar books and articles
Juha Kontinen (2006). The Hierarchy Theorem for Second Order Generalized Quantifiers. Journal of Symbolic Logic 71 (1):188 - 202.
Matti Eklund & Daniel Kolak (2002). Is Hintikka's Logic First-Order? Synthese 131 (3):371 - 388.
Savas Konur (2011). An Event-Based Fragment of First-Order Logic Over Intervals. Journal of Logic, Language and Information 20 (1):49-68.
Nino Cocchiarella (2001). A Conceptualist Interpretation of Lesniewski's Ontology. History and Philosophy of Logic 22 (1):29-43.
G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
Theodora Achourioti & Michiel van Lambalgen (2011). A Formalization of Kant's Transcendental Logic. Review of Symbolic Logic 4 (2):254-289.
Added to index2010-08-19
Total downloads57 ( #59,957 of 1,726,249 )
Recent downloads (6 months)2 ( #289,836 of 1,726,249 )
How can I increase my downloads?