Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term
Studia Logica 48 (4):479 - 494 (1989)
The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Citations of this work BETA
No citations found.
Similar books and articles
The Deduction Rule and Linear and Near-Linear Proof Simulations.Maria Luisa Bonet & Samuel R. Buss - 1993 - Journal of Symbolic Logic 58 (2):688-709.
A Complete Minimal Logic of the Propositional Contents of Thought.Marek Nowak & Daniel Vanderveken - 1995 - Studia Logica 54 (3):391 - 410.
Note About Ł Ukasiewicz's Theorem Concerning the System of Axioms of the Implicational Propositional Calculus.Bolesław Sobociński - 1978 - Notre Dame Journal of Formal Logic 19 (3):457-460.
A Note on the Completeness of Kozen's Axiomatisation of the Propositional Μ-Calculus.Igor Walukiewicz - 1996 - Bulletin of Symbolic Logic 2 (3):349-366.
A Note on the System of Propositional Calculus with Primitive Rule of Extensionality.K. Hałkowska - 1967 - Studia Logica 20 (1):150-150.
Independence of Two Nice Sets of Axioms for the Propositional Calculus.T. Thacher Robinson - 1968 - Journal of Symbolic Logic 33 (2):265-270.
Defining Relevant Implication in a Propositionally Quantified S.Philip Kremer - 1997 - Journal of Symbolic Logic 62 (4):1057-1069.
Added to index2009-01-28
Total downloads20 ( #242,783 of 2,153,830 )
Recent downloads (6 months)1 ( #398,274 of 2,153,830 )
How can I increase my downloads?