Graduate studies at Western
Journal of Symbolic Logic 61 (3):1006-1044 (1996)
|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)|
|Through your library||Configure|
Similar books and articles
Peter Fritz (2013). Modal Ontology and Generalized Quantifiers. Journal of Philosophical Logic 42 (4):643-678.
Wiebe Van Der Hoek & Maarten De Rijke (1993). Generalized Quantifiers and Modal Logic. Journal of Logic, Language and Information 2 (1):19-58.
Lauri Hella, Kerkko Luosto & Jouko Väänänen (1996). The Hierarchy Theorem for Generalized Quantifiers. Journal of Symbolic Logic 61 (3):802-817.
Johan van Benthem & Dag Westerståhl (1995). Directions in Generalized Quantifier Theory. Studia Logica 55 (3):389-419.
Michiel Lambalgen Natasha Alechinvana (1996). Generalized Quantification as Substructural Logic. Journal of Symbolic Logic 61 (3).
Juha Kontinen (2006). The Hierarchy Theorem for Second Order Generalized Quantifiers. Journal of Symbolic Logic 71 (1):188 - 202.
Juha Kontinen & Jakub Szymanik (2011). Characterizing Definability of Second-Order Generalized Quantifiers. In L. Beklemishev & R. de Queiroz (eds.), Proceedings of the 18th Workshop on Logic, Language, Information and Computation, Lecture Notes in Artificial Intelligence 6642. Springer.
Natasha Alechina (1995). On a Decidable Generalized Quantifier Logic Corresponding to a Decidable Fragment of First-Order Logic. Journal of Logic, Language and Information 4 (3):177-189.
Fredrik Engström (2012). Generalized Quantifiers in Dependence Logic. Journal of Logic, Language and Information 21 (3):299-324.
Added to index2009-01-28
Total downloads5 ( #170,394 of 740,065 )
Recent downloads (6 months)1 ( #61,960 of 740,065 )
How can I increase my downloads?