An algebraic analysis of implication in non-distributive logics
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Periodical |
| Magazine / Source | Journal of logic and computation |
| MU Faculty or unit | |
| Citation | |
| Web | https://doi.org/10.1093/logcom/exac041 |
| Doi | http://dx.doi.org/10.1093/logcom/exac041 |
| Keywords | Hilbert algebras; skew Hilbert algebras; pseudocomplemented lattices; sectionally pseudocomplemented lattices; orthomodular lattices; implication algebras |
| Description | 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 and their applications, and we will provide some basic results on their structure theory. |
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