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Phenomenological and Ontological Models for Predicting Emergence
Published in Larry B. Rainey, Mo Jamshidi, Engineering Emergence, 2018
Objects exist within metric spaces. A metric space is a set of objects where each object is identifiable by the notion of “distance” between objects. Mereotopology represents objects as extended parts in its space, akin to locale theory (Johnstone 2001). Although Leśniewski did not incorporate the notion of individual points within his mereotopology, the means to add points (and therefore the concept of distance) would be to define points as objects with no proper parts. Then, distance could be construed to indicate the degree of separation. That distance might be measurable with reference to a standard (e.g., meter), by ratio (e.g., the quantitative relation between two amounts showing the number of times one value contains or is contained with the other), or by a generalized distance that results from the correlation of variables (e.g., “... a single measure of the degree of divergence in the mean values of different characteristics of a population ...” Mahalanobis 1936; Taguchi and Jugulum 2002). The boundedness of an object and the distance between objects can be measured objectively (relative to a standard) and subjectively (relative to self). Multidimensional scaling is a technique of exposing the essential dimensions and distances between objects that are inspired by subjective judgments. In this manner, objective or subjective measures can determine the distances. This emphasis on dimensionality is facilitated by interpreting the similarities, dissimilarities, or proximities of objects as patterns (which have scalability in terms of distance). Distance is a measure of difference(s) between objects as scaled by the relative juxtaposition of objects (e.g., patterns) and the absolute limits of distance imposed by the separation(s) of the objects. With objects and distances incorporated into mereological formulations, the Leśniewski formal theory for whole part relations is well suited for modeling, designing, building, and sustaining systems and system of systems. The interpretive integrative framework provides the object frame from which to organize physical objects, interactions of those objects, and behaviors that result from interactions or lack of interactions.
Logics for extended distributive contact lattices
Published in Journal of Applied Non-Classical Logics, 2018
In the classical Euclidean geometry the notion of point is taken as one of the basic primitive notions. In contrast the region-based theory of space (RBTS) has as primitives the more realistic notion of region as an abstraction of physical body, together with some basic relations and operations on regions. Some of these relations are mereological – part-of (), overlap (xOy), its dual underlap . Other relations are topological – contact (xCy), nontangential part-of , dual contact and some others definable by means of the contact and part-of relations. This is one of the reasons that the extension of mereology with these new relations is commonly called mereotopology. There is no clear difference in the literature between RBTS and mereotopology, and by some authors RBTS is related rather to the so-called mereogeometry, while mereotopology is considered only as a kind of point-free topology, considering mainly topological properties of things. The origin of RBTS goes back to Whitehead (Whitehead, 1929) and de Laguna (de Laguna, 1922). According to Whitehead points, as well as the other primitive notions in Euclidean geometry like lines and planes, do not have separate existence in reality and because of this are not appropriate for primitive notions; but points have to be definable by the other primitive notions.
A mosaic of Chu spaces and Channel Theory II: applications to object identification and mereological complexity
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019
Chris Fields, James F. Glazebrook
The key idea of mereotopology is that the parts of an object must be inside the object, that is contained within its boundary (Casati & Varzi, 1999; Smith, 1996). This constraint is, clearly, more easily satisfied for boundaries that are (at least approximately) smooth and convex. As simplicity and hence resource efficiency appear to be general principles of perceptual system organisation (Wagemans et al., 2012b), one can expect perceivers to ‘see’ smooth, convex boundaries—for example convex hulls of geometrically more complex objects—more easily. Imposing smoothness and convexity—for example by constructing the convex hull of a geometrically more complex object (Lyubova et al., 2016)—is a form of coarse-graining. We can, therefore, suggest that constructing an ‘exterior’ boundary around a collection of parts that then serves as a boundary for the whole is a coarse-graining operation. Humans are, as noted in ‘Feature-category binding and object tokens’ above, highly accomplished at such boundary construction, especially for moving objects, with the ability to rapidly and accurately identify point-light walkers and similar disconnected displays as a compelling example. Static features are minimised by design in moving light displays such as point-light walkers in order to specifically probe dorsal visual stream processing. As the dorsal stream does not ‘see’ shape (Flombaum et al., 2008), the ‘human-shaped’ boundary in this case is imposed from above, that is by the categorisation process. Imposing this boundary coarse-grains the individually erratic, but highly correlated, motion of the individual point lights into bounded object motion from left to right or vice-versa. Inverting the display inhibits categorisation and hence boundary imposition, and is standardly used as a negative control (Johnson & Hannon, 2015). If boundary construction is treated as coarse-graining, then the simplicial methods introduced in Fields and Glazebrook (2018, ‘Introducing simplicial methods on Chu spaces’) are immediately applicable, and indeed provide a general method of constructing object boundaries from the bottom up in any mereological hierarchy representable in the CCCD form as in Figure 7.
Dynamic manufacturing network – from flat semantic graphs to composite models
Published in International Journal of Production Research, 2019
David Tchoffa, Nicolas Figay, Parisa Ghodous, Ernesto Exposito, Kouami Seli Apedome, Abderrahaman El Mhamedi
Studies and experience feedback led us to consider mereotopology. Mereotopology is a first order theory, which merges mereological and topological concepts of relations among wholes, parts, parts of parts, and the boundaries between them. It allows to provide a classification of the different kinds of concepts capturing whole-part relationships and associated boundaries. The performed SoA pointed out that it has been used and studied with PLM and System Engineering area. (Demoly, Aristeideis, and Dimitris 2012) proposed meretopological descriptions of product relationship, part-to-part relationship and assembly sequence that aims at being reusable all along the phases of the product life cycle. But the approach is based on OWL-DL, which is a language based on semantic graphs. The International Defense Enterprise Architecture Specification for exchange (IDEAS) group produced a data format for military enterprise architectures, and a formal, higher-order and 4D ontology, derived from (West and Jhon 2004) which introduced a four-dimensions mereotopology. However, the whole-part defined concepts aimed at describing spatiotemporal composite systems, and are formalised in a subset of DOLCE which is formalised in OWL. The way composite model artefacts are described is not within the scope of IDEAS. Orbst (2010) is also considering mereotopology, but relies on descriptive logic and OWL as illustrated by (Orbst 2011). Based on the realised state of the art on mereotopology, preserving semantic and ensuring interoperability for multi-scale hypermodels is not addressed. The SoA also considered literature related to multi-granular modelling (Ni et al. 2016; Wang et al. 2016). Interoperability is also not addressed. If literature related to mereotopology and multiple granularity provides valuable inputs in terms of concepts and mathematical tools, it was not possible finding any approach addressing the need for federating different standards as part of a multi-scale system of system model, relying on legacy UML2 and SysML modelling solutions. It is the reasons why we propose a new approach. It consists in using UML capabilities for describing composite objects an innovative way, as described in the next section. This approach can be generalised to any modelling language proposing similar constructs for describing whole and parts, being for the model or for what is modelled.