Spatial–temporal reasoning: Difference between revisions

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{{Short description|Area of artificial intelligence}}

'''Spatial-temporal reasoning''' is the ability to visualize [[pattern|spatial patterns]] and mentally manipulate images over space and time. This ability, often referred to as "thinking in pictures", is important for generating and conceptualizing solutions to multi-step problems that arise in areas such as [[engineering]], [[science]], [[mathematics]], [[art]], games (e.g. [[chess]]), and everyday life.

{{about|spatial–temporal reasoning in information technology|spatial–temporal reasoning in psychology|Spatial visualization ability}}

{{technical|date=October 2012}}

'''Spatial–temporal reasoning''' is an area of [[Artificial Intelligence|artificial intelligence]] that draws from the fields of [[computer science]], [[cognitive science]], and [[cognitive psychology]]. 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 [[robotic navigation|navigating]] and understanding time and space.

== Influence from cognitive psychology ==

[[Category:Cognitive science]]

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:

# the connection relation is primitive;

{{Psych-stub}}

# 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;

# 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.

== Fragmentary representations of temporal calculi ==

Without addressing internal relations among spatial relations, AI researchers contributed many fragmentary representations. Examples of temporal calculi include [[Allen's interval algebra]], and Vilain's & Kautz's [[point algebra]]. The most prominent spatial calculi are [[Mereotopology|mereotopological calculi]], [[Andrew U. Frank|Frank]]'s [[cardinal direction calculus]], Freksa's double cross calculus, Egenhofer and Franzosa's [[9-intersection calculus|4- and 9-intersection calculi]], Ligozat's [[flip-flop calculus]], various [[region connection calculus|region connection calculi]] (RCC), and the Oriented Point Relation Algebra.

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.

== Quantitative abstraction ==

An emphasis in the literature has been on [[Qualitative reasoning|qualitative]] 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 [[Constraint satisfaction|constraint]] 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 [[Decidability (logic)|decidable]] fragments with simple qualitative (non-[[Metric (mathematics)|metric]]) languages.

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 [[Geographic information system|GIS]] queries efficiently and some may be used for navigating, and communicating with, a mobile [[robot]].

== Relation algebra ==

Most of these calculi can be formalized as abstract [[relation algebra]]s, such that reasoning can be carried out at a [[Symbolic artificial intelligence|symbolic]] level. For computing solutions of a [[constraint network]], the [[Local consistency#Path consistency (k-consistency)|path-consistency algorithm]] is an important tool.

== Software ==

* [https://github.com/m-westphal/gqr GQR], constraint network solver for calculi like RCC-5, RCC-8, Allen's interval algebra, point algebra, cardinal direction calculus, etc.

* [https://github.com/alreich/qualreas qualreas] is a [[Python (programming language)|Python]] 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.

== See also ==

*[[Cerebral cortex]]

*[[Commonsense reasoning]]

*[[Diagrammatic reasoning]]

*[[Spatial ability]]

*[[Temporal logic]]

*[[Visual thinking]]

==References==

*{{cite book | first1=J. | last1=Renz | first2=B. | last2=Nebel | chapter-url=http://users.rsise.anu.edu.au/~jrenz/papers/renz-nebel-los.pdf | chapter=Qualitative Spatial Reasoning using Constraint Calculi | editor-first1=M. | editor-last1=Aiello | editor-first2=I. | editor-last2=Pratt-Hartmann | editor-first3=J. | editor-last3=van Benthem | title=Handbook of Spatial Logics | publisher=Springer | date=2007 | isbn=9781402055867 | access-date=2007-03-01 | archive-date=2007-06-27 | archive-url=https://web.archive.org/web/20070627130346/http://users.rsise.anu.edu.au/~jrenz/papers/renz-nebel-los.pdf | url-status=dead }}

*{{cite journal | first=T. | last=Dong | title=A Comment on RCC: From RCC to RCC⁺⁺ | jstor=41217909 | journal=Journal of Philosophical Logic | year=2008 | volume=34 | issue=2 | pages=319–352| doi=10.1007/s10992-007-9074-y | s2cid=6243376 }}

*{{cite book | first1=M. | last1=Vilain | first2=H. | last2=Kautz | first3=P. | last3=van Beek | chapter-url=https://archive.org/details/readingsinqualit0000unse | chapter=Constraint propagation algorithms for temporal reasoning: A Revised Report | date=1987 | isbn=1-55860-095-7 | publisher=Morgan Kaufmann Publishers | title=Readings in qualitative reasoning about physical systems | chapter-url-access=registration }}

*{{cite book | first=T. | last=Dong | url=https://www.springer.com/en/book/9783642240577 | title=Recognizing Variable Environment -- The Theory of Cognitive Prism | series=Studies in Computational Intelligence | volume=388 | publisher=Springer-Verlag, Berlin Heidelberg | date=2012 | isbn=9783642240577}}

==External links==

*{{Commonscatinline|Spatial–temporal reasoning}}

{{DEFAULTSORT:Spatial-temporal reasoning}}

[[Category:Cognitive science]]

[[Category:Knowledge representation]]

[[Category:Educational psychology]]

[[Category:Logical calculi]]

[[Category:Reasoning]]

[[Category:Time in life]]

[[Category:Spatial cognition]]

[[Category:Space and time]]