Abstract
We study some properties of directoids and their expansions by additional signature, including bounded involutive directoids and complemented directoids. Among other results, we provide a shorter proof of the direct decomposition theorem for bounded involutive directoids given in Chajda and Länger (Directoids. An algebraic approach to ordered sets. Heldermann Verlag, Lemgo 2011); we present a description of central elements of complemented directoids; we show that the variety of directoids, as well as its expansions mentioned above, all have the strong amalgamation property.
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Acknowledgments
I. Chajda gratefully acknowledges the support of Project CZ.1.07/2.3.00/20.0051 “Algebraic Methods in Quantum Logic”. M. Kolařík gratefully acknowledges the support of Project CZ.1.07/2.3.00/20.0060 “International Center for Information and Uncertainty”. A. Ledda gratefully acknowledges the support of the Italian Ministry of Scientific Research (MIUR) within the FIRB project “Structures and Dynamics of Knowledge and Cognition”, Cagliari: F21J12000140001.
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Communicated by C. Tsinakis.
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Chajda, I., Gil-Férez, J., Giuntini, R. et al. On some properties of directoids. Soft Comput 19, 955–964 (2015). https://doi.org/10.1007/s00500-014-1504-5
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DOI: https://doi.org/10.1007/s00500-014-1504-5