n‐linear weakly Heyting algebras

Mathematical Logic Quarterly 52 (4):404-416 (2006)
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Abstract

The present paper introduces and studies the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋn of n-linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋ2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]

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Citations of this work

On the variety of strong subresiduated lattices.Sergio Celani & Hernán J. San Martín - 2023 - Mathematical Logic Quarterly 69 (2):207-220.

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References found in this work

A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Logic with truth values in a linearly ordered Heyting algebra.Alfred Horn - 1969 - Journal of Symbolic Logic 34 (3):395-408.
Bounded distributive lattices with strict implication.Sergio Celani & Ramon Jansana - 2005 - Mathematical Logic Quarterly 51 (3):219-246.
Speaking about transitive frames in propositional languages.Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev - 1998 - Journal of Logic, Language and Information 7 (3):317-339.

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