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On the Skeleton of Stonian p-Ortholattices [chapter]

Michael Winter, Torsten Hahmann, Michael Gruninger
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We show that the skeleton of every Stonian p-ortholattice is a BCA, and, conversely, that every BCA is isomorphic to the skeleton of a Stonian p-ortholattice.  ...  Furthermore, we prove the equivalence between algebraic conditions on Stonian p-ortholattices and the axioms C5, C6, and C7 for BCAs.  ...  the Boolean algebra of a BCA as the skeleton of the Stonian p-ortholattice.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04639-1_24">doi:10.1007/978-3-642-04639-1_24</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4ghr4e7d7ndpfjmadmuxpyr2c4">fatcat:4ghr4e7d7ndpfjmadmuxpyr2c4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303161410/http://pdfs.semanticscholar.org/cc70/2518e36dbf136e7ba6ef88175abda9fbc49d.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/70/cc702518e36dbf136e7ba6ef88175abda9fbc49d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-04639-1_24"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Stonian p-ortholattices: A new approach to the mereotopology RT0

Torsten Hahmann, Michael Winter, Michael Gruninger
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/weoplee4x5anpi62cco5v4higa" style="color: black;">Artificial Intelligence</a> </i> &nbsp;
the natural class of Stonian p-ortholattices can be defined.  ...  Moreover, it is shown that the class of models of RT − EC is isomorphic to the non-distributive Stonian p-ortholattices and a characterization of RT is given by a set of four algebras of which one need  ...  Acknowledgements The authors are grateful to Alasdair Urquhart and Ivo Düntsch for their remarks and insightful comments during a discussion of an earlier version of the work presented here.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.artint.2009.07.001">doi:10.1016/j.artint.2009.07.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/epmzswitvbcszdcnqisq5lw6oa">fatcat:epmzswitvbcszdcnqisq5lw6oa</a> </span>
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On the algebra of regular sets

Michael Winter, Torsten Hahmann, Michael Grüninger
<span title="">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j2td7x4trvgx7pjoienrccryxq" style="color: black;">Annals of Mathematics and Artificial Intelligence</a> </i> &nbsp;
The mereotopology RT − has in Stonian p-ortholattices its algebraic counterpart.  ...  We study representability of these lattices and show that not all Stonian p-ortholattices can be represented by the set of regular sets of a topological space.  ...  Subsequent work [15] demonstrated that the skeleton, i.e. the set of all closed sets, of a Stonian p-ortholattice is a model of RCC and every model of RCC can be extended to a Stonian p-ortholattice  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10472-012-9301-2">doi:10.1007/s10472-012-9301-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nmo5nlsninhy3m5bm7mdqa46g4">fatcat:nmo5nlsninhy3m5bm7mdqa46g4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170813094604/http://www.cs.toronto.edu/~torsten/publications/MWinter_AIMA-12.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ff/8d/ff8d0cc69e2257b903ea7c393a24bd4973381aca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10472-012-9301-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>