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Contact Join-semilattices

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Abstract

Contact algebra is one of the main tools in region-based theory of space. In ([7, 8, 22, 23]) it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the operation meet. Thus we obtain structures, called contact join-semilattices (CJS) and structures, called distributive contact join-semilattices (DCJS). We obtain a set-theoretical representation theorem for CJS and a relational representation theorem for DCJS. As corollaries we get also topological representation theorems. We prove that the universal theory of CJS and of DCJS is the same and is decidable.

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Acknowledgements

I am grateful to Dimiter Vakarelov for his hints on Section 6 and for his valuable remarks on the paper. I thank the anonymous referees for giving me a better motivation for eliminating the meet operation and improving the motivation for removing the complement operation; also for their valuable remarks which improved the readability of the paper. This paper is supported by National program “Young scientists and Postdoctoral candidates” 2020 of Ministry of Education and Science of Bulgaria.

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  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Tatyana Ivanova

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Ivanova, T. Contact Join-semilattices. Stud Logica 110, 1219–1241 (2022). https://doi.org/10.1007/s11225-022-09994-1

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