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    <p>Premise - remember that a SQL-based<sup>1</sup> DBMS is a (quite capable) inference engine, as can be seen from these comparisons between SQL and Prolog:</p> <ul> <li><a href="https://stackoverflow.com/questions/724377/prolog-to-sql-converter/1682486#1682486">prolog to SQL converter</a></li> <li><a href="https://stackoverflow.com/questions/2117651/difference-between-sql-and-prolog/2124585#2124585">difference between SQL and Prolog</a></li> </ul> <p>To address specifically your spatio-temporal applications, this book will help:</p> <ul> <li><a href="http://books.google.com/books?id=grTubz0fjSEC" rel="nofollow noreferrer">TEMPORAL DATA AND THE RELATIONAL MODEL</a> - A Detailed Investigation into the Application of <strong>Interval and Relation Theory</strong> to the Problem of Temporal Database Management.</li> </ul> <p>That is, combining Interval and Relation Theory is possible to reasoning about spatio-temporal problems effectively (see <a href="http://books.google.com/books?id=grTubz0fjSEC&amp;lpg=PP1&amp;pg=PA81#v=onepage&amp;q=a%20rectangular%20plot%20of%20ground" rel="nofollow noreferrer">5.2 Applications of Intervals</a>).</p> <p>Of course, if your SQL-based DBMS is not (yet) equipped with interval (and other) operators you will need to extend it appropriately (<em>via</em> store-procedures and/or User-Defined Functions - UDFs).</p> <p><strong>Update:</strong> skimming the paper pointed out <a href="https://stackoverflow.com/questions/2469567/rules-engine-for-spatial-and-temporal-reasoning/2481625#2481625">in comments by timemirror</a> (<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.9354" rel="nofollow noreferrer">Towards a 3D Spatial Query Language for Building Information Models</a>) they do essentially what I touched on above:</p> <blockquote> <p><em>(last page)</em></p> <p>IMPLEMENTATION CONCEPTS</p> <p>The implementation of the abstract type system into a query language will be performed on the basis of the query language SQL, which is a widely established standard in the field of object-relational databases. The international standard SQL:1999 extends the relational model to include object-oriented aspects, such as the possibility to define complex abstract data types with integrated methods.</p> </blockquote> <p>I do not concur with the "object-relational database" terminology (for reason off-topic here) but I think the rest is pertinent.</p> <p><br /> <strong>Update:</strong> a quote regardind 3D and interval theory from the book cited above:</p> <blockquote> <p>NOTE: All of the intervals discussed so far can be thought of as one-dimensional. However, we might want to combine two one-dimensional intervals to form a twodimensional interval. For example, a rectangular plot of ground might be thought of as a two-dimensional interval, because it is, by definition, an object with length and width, each of which is basically a one-dimensional interval measured along some axis. And, of course, <strong>we can extend this idea to any number of dimensions</strong>. For example, a (rather simple!) building might be regarded as a three-dimensional interval: It is an object with length, width, and height, or in other words a cuboid. (More realistically, a building might be regarded as a set of several such cuboids that overlap in various ways.) And so on. In what follows, however, we will restrict our attention to one-dimensional intervals specifically, barring explicit statements to the contrary, and we will omit the "one-dimensional" qualifier for simplicity.</p> </blockquote> <p><strong>Note</strong></p> <ol> <li>I wrote <em>SQL-based</em> and not <em>relational</em> because there are ways to use such DBMSes that completely deviate from relational theory.</li> </ol>
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