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Shape composition is a challenge in spatial reasoning. Qualitative Shape Descriptors (QSD) have proven to be rotation and location invariant, which make them useful in spatial reasoning tests. QSD uses qualitative representations for angles and lengths, but their composition operations have not been defined before. In this paper, the Qualitative Model for Angles (QMAngles) and the Qualitative Model for Lengths (QMLengths) are presented in detail by describing their arity, reference systems and operators. Their operators are defined taking the well-known temporal model by Allen (Commun. ACM 26(11), 832–843 (1983). 10.1145/182.358434) as a reference. Moreover, composition tables are built, and the composition relations of qualitative angles and lengths are proved using their geometric counterparts. The correctness of these composition tables is also proved computationally using a logic program implemented using Swi-Prolog. [ABSTRACT FROM AUTHOR]

Computational models of novel concept understanding and creativity are addressed in this paper from the viewpoint of conceptual blending theory (CBT). In our approach, a novel, unknown concept is addressed in a communication setting, where this novel concept, created as a blend by an emitter agent, sends a communicative object (words, or in this paper, a visual representation of that concept) to another agent. When received by a computational agent, a novel concept for that communicative object can only be understood by blending concepts already known by that agent. In this paper, we first posit that understanding new concepts via blending is also a creative process. Albeit different from generating conceptual blends, understanding a novel concept via blending involves the disintegration and decompression of that novel concept, in such a way that the receiver of that concept is able to re-create the conceptual network supposedly intended by the emitter of the novel concept. Secondly, we also propose image schemas as a tool that agents can use to interpret the spatial information obtained when disintegrating/unpacking novel concepts and then re-create the new blend. This process is studied in a communication setting where semiotics and meaning are conveyed by visual and spatial signs (instead of the usual setting of natural language or text). In this case study, qualitative spatial descriptors are applied for obtaining a formal description of an icon or pictogram, which is later assigned a meaning by a process of conceptual blending using image schemas. [ABSTRACT FROM AUTHOR]