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The method of axiomatic rejection for the intuitionistic propositional logic

✍ Scribed by Rafal Dutkiewicz

Publisher
Springer Netherlands
Year
1989
Tongue
English
Weight
580 KB
Volume
48
Category
Article
ISSN
0039-3215

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✦ Synopsis

We prove that the intuitionistic sentential calculus is L-decidable (decidable in the sense of Lukasiewicz), i.e. the sets of theses of Int and of rejected formulas are disjoint and their union is equal to all formulas. A formula is rejected iff it is a sentential variable or is obtained from other formulas by means of three rejection rules. One of the rules is original, the remaining two are Lukasiewicz's rejection rules: by detachement and by substitution. We extensively use the method of Beth's semantic tableaux.

📜 SIMILAR VOLUMES

A Finite Hilbert-Style Axiomatization of
A Finite Hilbert-Style Axiomatization of the Implication-Less Fragment of the Intuitionistic Propositional Calculus
✍ Jordi Rebagliato; Ventura Verdú 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 374 KB 👁 1 views

## Abstract In this paper we obtain a finite Hilbert‐style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}‐formulas containing this fragment. Mat