Axiomatization of the infinite-valued predicate calculus
- 12 March 1963
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 28 (1) , 77-86
- https://doi.org/10.2307/2271339
Abstract
The infinite-valued statement calculus to which this paper refers is that of Łukasiewicz [10], whose axiomatization was proved complete in [5]. In [9], Rutledge extended this system to include predicates and quantifiers2 and presented a deductively complete set of axioms for the monadic predicate calculus. This paper represents an attempt to axiomatize the full predicate calculus; for the proposed axiomatization, a property akin to but weaker than completeness is proved. An attempt to prove full completeness along similar lines failed; it has since been shown [11] that the set of valid formulas of the infinite-valued predicate calculus is not recursively enumerable. The method of this paper was suggested by Professor J. Barkley Rosser.Keywords
This publication has 4 references indexed in Scilit:
- Algebraic analysis of many valued logicsTransactions of the American Mathematical Society, 1958
- Fragments of many-valued statement calculiTransactions of the American Mathematical Society, 1958
- Many-valued Logics. By J.B. Rosser and A.R. Turquette. Pp. 124. F1. 12. 1952. Studies in logic and the foundations of mathematics. (North-Holland Publishing Co., Amsterdam)The Mathematical Gazette, 1953
- The Degree of Completeness of the ℵ0 -Valued Łukasiewicz Propositional CalculusJournal of the London Mathematical Society, 1953