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@article{2250993, author = {Chajda, Ivan and Emir, Kadir and Fazio, Davide and Langer, Helmut and Ledda, Antonio and Paseka, Jan}, article_location = {Oxford}, article_number = {1}, doi = {http://dx.doi.org/10.1093/logcom/exac041}, keywords = {Hilbert algebras; skew Hilbert algebras; pseudocomplemented lattices; sectionally pseudocomplemented lattices; orthomodular lattices; implication algebras}, language = {eng}, issn = {0955-792X}, journal = {Journal of logic and computation}, title = {An algebraic analysis of implication in non-distributive logics}, url = {https://doi.org/10.1093/logcom/exac041}, volume = {33}, year = {2023} }
TY - JOUR ID - 2250993 AU - Chajda, Ivan - Emir, Kadir - Fazio, Davide - Langer, Helmut - Ledda, Antonio - Paseka, Jan PY - 2023 TI - An algebraic analysis of implication in non-distributive logics JF - Journal of logic and computation VL - 33 IS - 1 SP - 47-89 EP - 47-89 PB - Oxford University Press SN - 0955792X KW - Hilbert algebras KW - skew Hilbert algebras KW - pseudocomplemented lattices KW - sectionally pseudocomplemented lattices KW - orthomodular lattices KW - implication algebras UR - https://doi.org/10.1093/logcom/exac041 N2 - 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. ER -
CHAJDA, Ivan, Kadir EMIR, Davide FAZIO, Helmut LANGER, Antonio LEDDA and Jan PASEKA. An algebraic analysis of implication in non-distributive logics. \textit{Journal of logic and computation}. Oxford: Oxford University Press, 2023, vol.~33, No~1, p.~47-89. ISSN~0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exac041.
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