Journal of Symbolic Logic 61 (3):1006 - 1044 (1996)

Authors
Abstract
We show how sequent calculi for some generalized quantifiers can be obtained by generalizing the Herbrand approach to ordinary first order proof theory. Typical of the Herbrand approach, as compared to plain sequent calculus, is increased control over relations of dependence between variables. In the case of generalized quantifiers, explicit attention to relations of dependence becomes indispensible for setting up proof systems. It is shown that this can be done by turning variables into structured objects, governed by various types of structural rules. These structured variables are interpreted semantically by means of a dependence relation. This relation is an analogue of the accessibility relation in modal logic. We then isolate a class of axioms for generalized quantifiers which correspond to first-order conditions on the dependence relation
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275797
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,316
External links

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

On Branching Quantifiers in English.Jon Barwise - 1979 - Journal of Philosophical Logic 8 (1):47 - 80.
Finite Partially‐Ordered Quantifiers.Herbert B. Enderton - 1970 - Mathematical Logic Quarterly 16 (8):393-397.
Stationary Logic.Jon Barwise - 1978 - Annals of Mathematical Logic 13 (2):171.
Natural Deduction and Arbitrary Objects.Kit Fine - 1985 - Journal of Philosophical Logic 14 (1):57 - 107.

View all 17 references / Add more references

Citations of this work BETA

In Conjunction with Qualitative Probability.Tim Fernando - 1998 - Annals of Pure and Applied Logic 92 (3):217-234.

Add more citations

Similar books and articles

Generalized Quantifiers in Dependence Logic.Fredrik Engström - 2012 - Journal of Logic, Language and Information 21 (3):299-324.
The Hierarchy Theorem for Second Order Generalized Quantifiers.Juha Kontinen - 2006 - Journal of Symbolic Logic 71 (1):188 - 202.
Modal Ontology and Generalized Quantifiers.Peter Fritz - 2013 - Journal of Philosophical Logic 42 (4):643-678.
Generalized Quantifiers and Modal Logic.Wiebe Van Der Hoek & Maarten De Rijke - 1993 - Journal of Logic, Language and Information 2 (1):19-58.

Analytics

Added to PP index
2013-09-30

Total views
17 ( #639,019 of 2,519,512 )

Recent downloads (6 months)
1 ( #407,153 of 2,519,512 )

How can I increase my downloads?

Downloads

My notes