Beschreibung:
<jats:p>
The region-based spatial logics, where variables are set to range over certain subsets of geometric space, are the focal point of the qualitative spatial reasoning, a subfield of the KR&R research area. A lot of attention has been devoted to developing the topological spatial logics, leaving other systems relatively underexplored. We are concerned with a specific example of a region-based affine spatial logic. Building on the previous results on spatial logics with convexity, we axiomatise the theory of
<jats:italic>M</jats:italic>
= 〈
<jats:italic>ROQ</jats:italic>
(R
<jats:sup>2</jats:sup>
),
<jats:italic>conv</jats:italic>
<jats:sup>M</jats:sup>
, ≤
<jats:sup>M</jats:sup>
〉, where
<jats:italic>ROQ</jats:italic>
(R
<jats:sup>2</jats:sup>
) is the set of regular open rational polygons of the real plane;
<jats:italic>conv</jats:italic>
<jats:sup>M</jats:sup>
is the convexity property and ≤
<jats:sup>M</jats:sup>
is the inclusion relation. The axiomatisation uses two infinitary rules of inference and a number of axiom schemas.
</jats:p>