Abstract
Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame 〈Q+, ≤,D〉, where Q+ is the set of non-negative rational numbers, ≤is the numerical relation “less or equal then” and D is the domain function such that for all v, w ∈ Q+, Dv ≠ φ and if v ≤ w, then D v . D v \( \subseteq \) D w . Moreover, simple completeness proofs of extensions of Q-LC are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Corsi A cut-free calculus for Dummett's LC quantified Zeitschrift für Mathematische Logic, 35, (1989), pp. 289–301.
G. Corsi, A logic characterized by the class of connected models with nested domains, Studia Logica XLVIII (1989), pp. 15–22.
G. Corsi and S. Ghilardi, Directed frames, Archive for Mathematical Logic 29 (1990), pp. 53–67.
M. Dummett, A propositional calculus with denumerable matrix, Journal of Symbolic Logic 24 (1959), pp. 96–107.
K. Fine, Model theory for modal logic, Part I, De Re/De Dicto Distinction, Journal of Philosophical Logic 7 (1978), pp. 125–156.
S. Kripke, Semantical analysis in intuitionistic logic, in Formal systems and recursive functions. Proc. of the 8th Logic Colloquium, Amsterdam. 1965, pp. 92–130.
H. Ono, On finite linear intermediate predicate logics, Studia Logica, 4 (1988), pp. 81–89.
M. Takano, Studia Logica, 46, 2 (1987), pp. 137–148.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Corsi, G. Completeness theorem for dummett's LC quantified and some of its extensions. Stud Logica 51, 317–335 (1992). https://doi.org/10.1007/BF00370118
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00370118