Logical composition of qualitative shapes applied to solve spatial reasoning tests

Towards a model of creative understanding: deconstructing and recreating conceptual blends using image schemas and qualitative spatial descriptors

“…Spatio-temporal reasoning models deal with imprecise and incomplete knowledge on a symbolic level. Qualitative spatial descriptors that represent properties of space are the following: (i) topology: 4IM [11], 9IM [10], RCC-8 [7]; (ii) shape: QSD [14], LogC-QSD [40]; (iii) location: [22,28]; (iv) orientation: [19,36]; (v) orientation and distance: [1], etc.…”

“…Path-source-goal orientation [19,36], direction [19] Scale shape [14,40], relative length [17] Container topology [7,10,11];…”

“…11, that is: how many lines or curves are connected, what kind of angles they define, its lengths, etc. (for definitions and a more detailed description see [14,40]).…”

Spatial reasoning about qualitative shape compositions

“…Using these operators, the geometric counterparts of the composition of qualitative angles and lengths are shown. Moreover, the composition relations of angles and lengths needed to solve shape composition challenges (see Section 3) in LogC-QSD (Pich and Falomir, 2018) are provided and their correctness is proved.…”

Special issue on logics and artificial intelligence

“…In the literature, research works that use many-valued logics in AI include the following: Aksoy and Ercanoglu [1] used many-valued logics in landslide identification and classification; manyvalued logic for fuzzy control was reviewed and discussed by Moraga et al [30]; Falomir et al [22] used description logics to interpret digital images by describing each object by its colour and qualitative shape and by its main spatial features (location, relative orientation and topology) which allows to infer new object categories (e.g. doors) by reasoning; connections between weighted argumentation frames and t-norm-based logics have been explored by Corsi and Fermüller [14]; a fuzzy logic-based colour histogram analysis for discriminating benign skin lesions from malignant melanomas in dermoscopic images has been proposed by Almubarak et al [2]; logic properties of relevant notions in fuzzy logic programming and computer science have been studied by Badia et al [4] and Costa and Dellunde [16,15]; Eklund and Löfstrand [19] applied many-valued logics with the aim of enriching the language used in the manufacturing industry regarding information structure and its representation for products and production processes; Falomir and Pich [32] presented a logical approach to compose qualitative shapes and applied it to solve spatial reasoning tests; the relation between many-valued logic and decision theory under uncertainty has been analyzed by Flaminio et al [23]; Falomir et al [21] defined logics for combining a fuzzy-colour model with a Probabilistic Reference And GRounding mechanism (PRAGR) in order to obtain the most discriminative colour descriptor for an object depending on the context. And recently, a special issue on many-valued logics for reasoning has been presented by Dubois et al [18].…”