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<title>Spatial–temporal reasoning</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Spatial–temporal reasoning</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">This article is about spatial–temporal reasoning in information technology. For spatial–temporal reasoning in psychology, see <a href="Spatial_visualization_ability" title="Spatial visualization ability">Spatial visualization ability</a>.</div>

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<p><b>Spatial–temporal reasoning</b> is an area of <a href="Artificial_Intelligence" class="mw-redirect" title="Artificial Intelligence">artificial intelligence</a> that draws from the fields of <a href="Computer_science" title="Computer science">computer science</a>, <a href="Cognitive_science" title="Cognitive science">cognitive science</a>, and <a href="Cognitive_psychology" title="Cognitive psychology">cognitive psychology</a>. The theoretic goal—on the cognitive side—involves representing and reasoning spatial-temporal knowledge in mind. The applied goal—on the computing side—involves developing high-level control systems of automata for <a href="Robotic_navigation" class="mw-redirect" title="Robotic navigation">navigating</a> and understanding time and space.

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<div class="mw-heading mw-heading2"><h2 id="Influence_from_cognitive_psychology">Influence from cognitive psychology</h2></div>

<p>A convergent result in cognitive psychology is that the connection relation is the first spatial relation that human babies acquire, followed by understanding orientation relations and distance relations. Internal relations among the three kinds of spatial relations can be computationally and systematically explained within the theory of cognitive prism as follows:

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<ol><li>the connection relation is primitive;</li>

<li>an orientation relation is a distance comparison relation: you being in front of me can be interpreted as you are nearer to my front side than my other sides;</li>

<li>a distance relation is a connection relation using a third object: you being one meter away from me can be interpreted as a one-meter-long object connected with you and me simultaneously.</li></ol>

<div class="mw-heading mw-heading2"><h2 id="Fragmentary_representations_of_temporal_calculi">Fragmentary representations of temporal calculi</h2></div>

<p>Without addressing internal relations among spatial relations, AI researchers contributed many fragmentary representations. Examples of temporal calculi include <a href="Allen's_interval_algebra" title="Allen's interval algebra">Allen's interval algebra</a>, and Vilain's & Kautz's point algebra. The most prominent spatial calculi are <a href="Mereotopology" title="Mereotopology">mereotopological calculi</a>, <a href="Andrew_U._Frank" title="Andrew U. Frank">Frank</a>'s cardinal direction calculus, Freksa's double cross calculus, Egenhofer and Franzosa's 4- and 9-intersection calculi, Ligozat's flip-flop calculus, various <a href="Region_connection_calculus" title="Region connection calculus">region connection calculi</a> (RCC), and the Oriented Point Relation Algebra.

</p><p>Recently, spatio-temporal calculi have been designed that combine spatial and temporal information. For example, the spatiotemporal constraint calculus (STCC) by Gerevini and Nebel combines Allen's interval algebra with RCC-8. Moreover, the qualitative trajectory calculus (QTC) allows for reasoning about moving objects.

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<div class="mw-heading mw-heading2"><h2 id="Quantitative_abstraction">Quantitative abstraction</h2></div>

<p>An emphasis in the literature has been on <a href="Qualitative_reasoning" title="Qualitative reasoning">qualitative</a> spatial-temporal reasoning which is based on qualitative abstractions of temporal and spatial aspects of the common-sense background knowledge on which our human perspective of physical reality is based. Methodologically, qualitative <a href="Constraint_satisfaction" title="Constraint satisfaction">constraint</a> calculi restrict the vocabulary of rich mathematical theories dealing with temporal or spatial entities such that specific aspects of these theories can be treated within <a href="Decidability_(logic)" title="Decidability (logic)">decidable</a> fragments with simple qualitative (non-<a href="Metric_(mathematics)" class="mw-redirect" title="Metric (mathematics)">metric</a>) languages.

</p><p>Contrary to mathematical or physical theories about space and time, qualitative constraint calculi allow for rather inexpensive reasoning about entities located in space and time. For this reason, the limited expressiveness of qualitative representation formalism calculi is a benefit if such reasoning tasks need to be integrated in applications. For example, some of these calculi may be implemented for handling spatial <a href="Geographic_information_system" title="Geographic information system">GIS</a> queries efficiently and some may be used for navigating, and communicating with, a mobile <a href="Robot" title="Robot">robot</a>.

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<div class="mw-heading mw-heading2"><h2 id="Relation_algebra">Relation algebra</h2></div>

<p>Most of these calculi can be formalized as abstract <a href="Relation_algebra" title="Relation algebra">relation algebras</a>, such that reasoning can be carried out at a <a href="Symbolic_artificial_intelligence" title="Symbolic artificial intelligence">symbolic</a> level. For computing solutions of a constraint network, the <a href="Local_consistency#Path_consistency_(k-consistency)" title="Local consistency">path-consistency algorithm</a> is an important tool.

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<div class="mw-heading mw-heading2"><h2 id="Software">Software</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://github.com/m-westphal/gqr">GQR</a>, constraint network solver for calculi like RCC-5, RCC-8, Allen's interval algebra, point algebra, cardinal direction calculus, etc.</li>

<li><a rel="nofollow" class="external text" href="https://github.com/alreich/qualreas">qualreas</a> is a <a href="Python_(programming_language)" title="Python (programming language)">Python</a> framework for qualitative reasoning over networks of relation algebras, such as RCC-8, Allen's interval algebra, and Allen's algebra integrated with Time Points and situated in either Left- or Right-Branching Time.</li></ul>

<ul><li><a href="Cerebral_cortex" title="Cerebral cortex">Cerebral cortex</a></li>

<li><a href="Commonsense_reasoning" title="Commonsense reasoning">Commonsense reasoning</a></li>

<li><a href="Diagrammatic_reasoning" title="Diagrammatic reasoning">Diagrammatic reasoning</a></li>

<li><a href="Spatial_ability" title="Spatial ability">Spatial ability</a></li>

<li><a href="Temporal_logic" title="Temporal logic">Temporal logic</a></li>

<li><a href="Visual_thinking" title="Visual thinking">Visual thinking</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFRenzNebel2007" class="citation book cs1">Renz, J.; Nebel, B. (2007). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070627130346/http://users.rsise.anu.edu.au/~jrenz/papers/renz-nebel-los.pdf">"Qualitative Spatial Reasoning using Constraint Calculi"</a> <span class="cs1-format">(PDF)</span>. In Aiello, M.; Pratt-Hartmann, I.; van Benthem, J. (eds.). <i>Handbook of Spatial Logics</i>. Springer. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781402055867</bdi>. Archived from <a rel="nofollow" class="external text" href="http://users.rsise.anu.edu.au/~jrenz/papers/renz-nebel-los.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2007-06-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2007-03-01</span></span>.</cite></li>

<li><cite id="CITEREFDong2008" class="citation journal cs1">Dong, T. (2008). "A Comment on RCC: From RCC to RCC⁺⁺". <i>Journal of Philosophical Logic</i>. <b>34</b> (2): <span class="nowrap">319–</span>352. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10992-007-9074-y">10.1007/s10992-007-9074-y</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41217909">41217909</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6243376">6243376</a>.</cite></li>

<li><cite id="CITEREFVilainKautzvan_Beek1987" class="citation book cs1">Vilain, M.; Kautz, H.; van Beek, P. (1987). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/readingsinqualit0000unse">"Constraint propagation algorithms for temporal reasoning: A Revised Report"</a></span>. <i>Readings in qualitative reasoning about physical systems</i>. Morgan Kaufmann Publishers. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>1-55860-095-7</bdi>.</cite></li>

<li><cite id="CITEREFDong2012" class="citation book cs1">Dong, T. (2012). <a rel="nofollow" class="external text" href="https://www.springer.com/en/book/9783642240577"><i>Recognizing Variable Environment -- The Theory of Cognitive Prism</i></a>. Studies in Computational Intelligence. Vol. 388. Springer-Verlag, Berlin Heidelberg. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9783642240577</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><span class="noviewer" typeof="mw:File"></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Spatial%E2%80%93temporal_reasoning" class="extiw external" title="commons:Category:Spatial–temporal reasoning">Spatial–temporal reasoning</a> at Wikimedia Commons</li></ul></div><div><div class="zim-footer">

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