David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 33 (2):265-270 (1968)
Kanger  gives a set of twelve axioms for the classical propositional Calculus which, together with modus ponens and substitution, have the following nice properties: (0.1) Each axiom contains $\supset$ , and no axiom contains more than two different connectives. (0.2) Deletions of certain of the axioms yield the intuitionistic, minimal, and classical refutability1 subsystems of propositional calculus. (0.3) Each of these four systems of axioms has the separation property: that if a theorem is provable in such a system, then it is provable using only the axioms of that system for $\supset$ , and for the other connectives, if any, actually occurring in that theorem. (0.4) All twelve axioms are independent. It is easily seen that two of Kanger's axioms can be shortened, and that two others can be replaced by a single axiom which is the same length as one of the two which it replaces, without disturbing properties (0.1)-(0.3). These alterations have advantages of simplicity and elegance, but bring property (0.4) into question, in that similarities among some of the axioms in the altered system make demonstrations of independence considerably more difficult. It is the purpose of this paper to show that independence is nonetheless provable for the simplified system, and in another system which also satisfies (0.1)-(0.3), in which f (falsehood) is taken to be primitive instead of ∼ (negation). Nonnormal truth-tables2 are used to obtain the independence of one of the axioms
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Sara Miner More & Pavel Naumov (2010). An Independence Relation for Sets of Secrets. Studia Logica 94 (1):73 - 85.
Dolph Ulrich (1996). The Shortest Possible Length of the Longest Implicational Axiom. Journal of Philosophical Logic 25 (1):101 - 108.
Brigitte Hösli & Gerhard Jäger (1994). About Some Symmetries of Negation. Journal of Symbolic Logic 59 (2):473-485.
Colin McLarty (1991). Axiomatizing a Category of Categories. Journal of Symbolic Logic 56 (4):1243-1260.
Maurice L'Abbé (1951). On the Independence of Henkin's Axioms for Fragments of the Propositional Calculus. Journal of Symbolic Logic 16 (1):43-45.
Stanisław Jaśkowski (1975). Three Contributions to the Two-Valued Propositional Calculus. Studia Logica 34 (1):121 - 132.
G. E. Hughes (1957). The Independence of Axioms in the Propositional Calculus. Australasian Journal of Philosophy 35 (1):21 – 29.
Louis Narens (1974). Measurement Without Archimedean Axioms. Philosophy of Science 41 (4):374-393.
Nadejda Georgieva (1971). Independence of the Axioms and Rules of Inference of One System of the Extended Propositional Calculus. Notre Dame Journal of Formal Logic 12 (2):214-218.
Added to index2009-01-28
Total downloads8 ( #164,408 of 1,096,632 )
Recent downloads (6 months)6 ( #38,815 of 1,096,632 )
How can I increase my downloads?