An algebraic analysis of implication in non-distributive logics

Ivan Chajda; Kadir Emir; Davide Fazio; Helmut Länger; Antonio Ledda; Jan Paseka

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arXiv · 2105.08528

An algebraic analysis of implication in non-distributive logics

Ivan Chajda·Kadir Emir·Davide Fazio·Helmut Länger·Antonio Ledda·Jan Paseka

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Abstract

In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g. (generalized) orthomodular lattices, and MV-algebras, which admit a natural notion of implication. In fact, it turns out that skew Hilbert algebras play a similar role for (strongly) sectionally pseudocomplemented posets as Hilbert algebras do for relatively pseudocomplemented ones. We will discuss basic properties of closed, dense, and weakly dense elements of skew Hilbert algebras, their applications, and we will provide some basic results on their structure theory.

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BibTeX RIS

Ivan Chajda, Kadir Emir, Davide Fazio, Helmut Länger, Antonio Ledda, Jan Paseka. 2021-05-18. An algebraic analysis of implication in non-distributive logics. https://arxiv.org/abs/2105.08528

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