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The decidability of dependency in intuitionistic propositional logic

  • Dick de Jongh (a1) and L. A. Chagrova (a2)

Abstract

A definition is given for formulae A1, …, An in some theory T which is formalized in a propositional calculus S to be (in)dependent with respect to S. It is shown that, for intuitionistic propositional logic IPC, dependency (with respect to IPC itself) is decidable. This is an almost immediate consequence of Pitts’ uniform interpolation theorem for IPC. A reasonably simple infinite sequence of IPC-formulae Fn (p, q) is given such that IPC-formulae A and B are dependent if and only if at least on of the Fn (A, B) is provable.

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[1970] de Jongh, D. H. J., A characterization of the intuitionistic propositional calculus, in Kino, Myhill, and Vesley [1970] pp. 211217.
[1982] de Jongh, D. H. J., Formulas of one propositional variable in intuitionistic arithmetic, in Troelstra and van Dalen [1982] pp. 5164.
[1993] de Jongh, D. H. J. and Visser, A., Embeddings of Hey ting algebras, ILLC Prepublications ML-93-14, ILLC, University of Amsterdam, Amsterdam.
[1970] Kino, A., Myhill, J., and Vesley, R. E. (editors), Intunionism and proof theory, North-Holland, Amsterdam.
[1982] Maksimova, L. L., Interpolation properties of superintuitionistic, positive and modal logics, Intensional logic: Theory and Applications, Acta Philosophica Fennica, vol. 35, pp. 7078; Societas Philosophica Fennica, Helsinki.
[1992] Pitts, A., On an interpretation of second order quantification in first order intuitionistic propositional logic, this Journal, vol. 57, pp. 3352.
[1992] Rybakov, V. V., Rules of inference with parameters for intuitionistic logic, this Journal, vol. 57, pp. 912923.
[1993] Shavrukov, V., Subalgebras of diagonalizable algebras of theories containing arithmetic, Dissertationes Mathematicae/Rozprawy Matematyczne, vol. 323.
[1978] Shehtman, V. B., Rieger-Nishimura lattices, Soviet Mathematics Doklady, vol. 19, pp. 10141018.
[1973] Smoryński, C., Applications of Kripke models, in Troelstra [1973] pp. 324391.
[1973] Troelstra, A. S. (editor), Metamathematical investigations of intuitionistic arithmetic and analysis, Lecture Notes in Mathematics, vol. 344, Springer, Berlin.
[1982] Troelstra, A. S. and van Dalen, D. (editors), The L. E. J. Brouwer centenary symposium, North-Holland, Amsterdam.

The decidability of dependency in intuitionistic propositional logic

  • Dick de Jongh (a1) and L. A. Chagrova (a2)

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