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2006•Mathematical logic quarterlyRequires access

n‐linear weakly Heyting algebras

Sergio A. Celani

Open publisher page 10 citations

Abstract

Abstract The present paper introduces and studies the variety 𝒲ℋ︁n 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 𝒲ℋ︁2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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What this paper is about

Abstract The present paper introduces and studies the variety 𝒲ℋ︁n 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 𝒲ℋ︁2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Available abstract

Abstract The present paper introduces and studies the variety 𝒲ℋ︁n 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 𝒲ℋ︁2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced in [2]. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Key concepts: Heyting algebra, Mathematics, Intuitionistic logic, Intermediate logic, Variety (cybernetics), Generalization, Axiom, Pure mathematics

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