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Generalized tableau systems for intermediate propositional logics

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1227))

Abstract

Given an intermediate propositional logic L (obtained by adding to intuitionistic logic INT a single axiom-scheme), a pseudo tableau system for L can be given starting from any intuitionistic tableau system and adding a rule which allows to insert in any line of a proof table suitable T-signed instances of the axiom-scheme. In this paper we study some sufficient conditions from which, given a well formed formula H, the search for these instances can be restricted to a suitable finite set of formulae related to H. We illustrate our techniques by means of some known logics, namely, the logic D of Dummett, the logics PR k (k≥1) of Nagata, the logics FIN m (m≥1), the logics G n (n≥1) of Gabbay and de Jongh, and the logic KP of Kreisel and Putnam

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Authors and Affiliations

  1. Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico, 39/41, 20135, Milano, Italy

    Alessandro Avellone, Ugo Moscato, Pierangelo Miglioli & Mario Ornaghi

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  1. Alessandro Avellone
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  2. Ugo Moscato
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  3. Pierangelo Miglioli
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  4. Mario Ornaghi
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Didier Galmiche

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© 1997 Springer-Verlag Berlin Heidelberg

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Avellone, A., Moscato, U., Miglioli, P., Ornaghi, M. (1997). Generalized tableau systems for intermediate propositional logics. In: Galmiche, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1997. Lecture Notes in Computer Science, vol 1227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027404

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  • DOI: https://doi.org/10.1007/BFb0027404

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62920-7

  • Online ISBN: 978-3-540-69046-7

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