{"id":190493,"date":"2024-06-02T10:24:28","date_gmt":"2024-06-02T15:24:28","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2024\/06\/dynamic-mereotopology-a-point-free-theory-of-changing-regions-i-stable-and-unstable-mereotopological-relations"},"modified":"2024-06-02T10:24:28","modified_gmt":"2024-06-02T15:24:28","slug":"dynamic-mereotopology-a-point-free-theory-of-changing-regions-i-stable-and-unstable-mereotopological-relations","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2024\/06\/dynamic-mereotopology-a-point-free-theory-of-changing-regions-i-stable-and-unstable-mereotopological-relations","title":{"rendered":"Dynamic Mereotopology: A Point-free Theory of Changing Regions. I. Stable and unstable mereotopological relations"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/dynamic-mereotopology-a-point-free-theory-of-changing-regions-i-stable-and-unstable-mereotopological-relations2.jpg\"><\/a><\/p>\n<p>It sure looks like other philosophers are using the Stone duality in ways that are a lot more sophisticated than my own way!<\/p>\n<p>Abstract In this paper we present a point-free theory of Whiteheadean style of space and time.<\/p>\n<hr>\n<p>In this paper we present a point-free theory of Whiteheadean style of space and time. Its algebraic formulation, called dynamic contact algebra (DCA), is a Boolean algebra whose elements symbolized dynamic regions changing in time, with two spatio-temporal mereotopological relations between them: stable and unstable contact. We prove several representation theorems for DCAs, representing them in structures arising from products of contact algebras or from products of topological spaces. We also present a decidable quantifier-free constraint logic for reasoning about stable and unstable mereotopological relations between dynamic regions. We consider the paper as a first step in point-free dynamic mereotopology.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It sure looks like other philosophers are using the Stone duality in ways that are a lot more sophisticated than my own way! Abstract In this paper we present a point-free theory of Whiteheadean style of space and time. In this paper we present a point-free theory of Whiteheadean style of space and time. Its [\u2026]<\/p>\n","protected":false},"author":661,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-190493","post","type-post","status-publish","format-standard","hentry","category-futurism"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/190493","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/661"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=190493"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/190493\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=190493"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=190493"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=190493"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}