David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
Theodora Achourioti & Michiel van Lambalgen (2011). A Formalization of Kant's Transcendental Logic. Review of Symbolic Logic 4 (2):254-289.
A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
G. Aldo Antonelli & Richmond H. Thomason (2002). Representability in Second-Order Propositional Poly-Modal Logic. Journal of Symbolic Logic 67 (3):1039-1054.
Nino Cocchiarella (2001). A Conceptualist Interpretation of Lesniewski's Ontology. History and Philosophy of Logic 22 (1):29-43.
Savas Konur (2011). An Event-Based Fragment of First-Order Logic Over Intervals. Journal of Logic, Language and Information 20 (1):49-68.
Matti Eklund & Daniel Kolak (2002). Is Hintikka's Logic First-Order? Synthese 131 (3):371 - 388.
Juha Kontinen (2006). The Hierarchy Theorem for Second Order Generalized Quantifiers. Journal of Symbolic Logic 71 (1):188 - 202.
Added to index2010-08-19
Total downloads61 ( #69,406 of 1,796,251 )
Recent downloads (6 months)3 ( #284,614 of 1,796,251 )
How can I increase my downloads?