Pure Second-Order Logic with Second-Order Identity
Notre Dame Journal of Formal Logic 51 (3):351-360 (2010)
| Abstract | 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 | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,631 |
| External links |
  Try with proxy. |
| Through your library | Configure |
Similar books and articlesJuha 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 (forthcoming). An Event-Based Fragment of First-Order Logic Over Intervals. Journal of Logic, Language and Information.
Nino B. 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.
T. Achourioti & M. van Lambalgen (forthcoming). A Formalisation of Kant's Transcendental Logic. Review of Symbolic Logic.
Analytics
Monthly downloads |
Added to index2010-08-19Total downloads35 ( #34,066 of 548,969 )Recent downloads (6 months)3 ( #25,799 of 548,969 )How can I increase my downloads? |
My notes
Discussion
