Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

A Fuzzy Spatio-Temporal-based Approach for Activity Recognition

International audienceOver the last decade, there has been a significant deployment of systems dedicated to surveillance. These systems make use of real-time sensors that generate continuous streams of data. Despite their success in many cases, the increased number of sensors leads to a cognitive overload for the operator in charge of their analysis. However, the context and the application requires an ability to react in real-time. The research presented in this paper introduces a spatio-temporal-based approach the objective of which is to provide a qualitative interpretation of the behavior of an entity (e.g., a human or vehicle). The process is formally supported by a fuzzy logic-based approach, and designed in order to be as generic as possible

An adverbial approach for the formal specification of topological constraints involving regions with broad boundaries

Topological integrity constraints control the topological properties of spatial objects and the validity of their topological relationships in spatial databases. These constraints can be specified by using formal languages such as the spatial extension of the Object Constraint Language (OCL). Spatial OCL allows the expression of topological constraints involving crisp spatial objects. However, topological constraints involving spatial objects with vague shapes (e.g., regions with broad boundaries) are not supported by this language. Shape vagueness requires using appropriate topological operators (e.g., strongly Disjoint, fairly Meet) to specify valid relations between these objects; otherwise, the constraints cannot be respected. This paper addresses the problem of the lack of terminology to express topological constraints involving regions with broad boundaries. We propose an extension of Spatial OCL based on a geometric model for objects with vague shapes and an adverbial approach for topological relations between regions with broad boundaries. This extension of Spatial OCL is then tested on an agricultural database

A MODEL OF FUZZY TOPOLOGICAL RELATIONS FOR SIMPLE SPATIAL OBJECTS IN GIS

The goal of this paper is to present a new model of fuzzy topological relations for simple spatial objects in Geographic Information Sciences (GIS). The concept of computational fuzzy topological space is applied to simple fuzzy objects to efficiently and more accurately solve fuzzy topological relations, extending and improving upon previous research in this area. Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on computational fuzzy topology. And then, we also propose a new model to compute fuzzy topological relations between simple spatial objects, an analysis of the new model exposes:(1) the topological relations of two simple crisp objects; (2) the topological relations between one simple crisp object and one simple fuzzy object; (3) the topological relations between two simple fuzzy objects. In the end, we have discussed some examples to demonstrate the validity of the new model, through an experiment and comparisons of existing models, we showed that the proposed method can make finer distinctions, as it is more expressive than the existing fuzzy models

Topological relationships between a circular spatially extended point and a line : spatial relations and their conceptual neighborhoods

This paper presents the topological spatial relations that can exist in the geographical space between a Circular Spatially Extended Point and a Line and describes the use of those spatial relations in the identification of the conceptual neighbourhood graphs that state the transitions occurring among relations. The conceptual neighbourhood graphs were identified using the snapshot model and the smooth-transition model. In the snapshot model, the identification of neighbourhood relations is achieved looking at the topological distance existing between pairs of spatial relations. In the smooth-transition model, conceptual neighbours are identified analysing the topological deformations that may change a topological spatial relation. The graphs obtained were analysed as an alternative to map matching techniques in the prediction of the future positions of a mobile user in a road network.(undefined

Stability and statistical inferences in the space of topological spatial relationships

Modelling topological properties of the spatial relationship between objects, known as the extit{topological relationship}, represents a fundamental research problem in many domains including Artificial Intelligence (AI) and Geographical Information Science (GIS). Real world data is generally finite and exhibits uncertainty. Therefore, when attempting to model topological relationships from such data it is useful to do so in a manner which is both extit{stable} and facilitates extit{statistical inferences}. Current models of the topological relationships do not exhibit either of these properties. We propose a novel model of topological relationships between objects in the Euclidean plane which encodes topological information regarding connected components and holes. Specifically, a representation of the persistent homology, known as a persistence scale space, is used. This representation forms a Banach space that is stable and, as a consequence of the fact that it obeys the strong law of large numbers and the central limit theorem, facilitates statistical inferences. The utility of this model is demonstrated through a number of experiments

Modeling fuzzy topological predicates for fuzzy regions

Spatial database systems and Geographical Information Systems (GIS) are currently only able to handle crisp spatial objects, i.e., objects whose extent, shape, and boundary are precisely determined. However, GIS applications are also interested in managing vague or fuzzy spatial objects. Spatial fuzziness captures the inherent property of many spatial objects in reality that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. While topological relationships have been broadly explored for crisp spatial objects, this is not the case for fuzzy spatial objects. In this paper, we propose a novel model to formally define fuzzy topological predicates for simple and complex fuzzy regions. The model encompasses six fuzzy predicates (overlap, disjoint, inside, contains, equal and meet), wherein here we focus on the fuzzy overlap and the fuzzy disjoint predicates only. For their computation we consider two low-level measures, the degree of membership and the degree of coverage, and map them to high-level fuzzy modifiers and linguistic values respectively that are\ud deployed in spatial queries by end-users.FAPESP (grant numbers 2012/12299-8 and 2013/19633-3)CAPESCNPqNational Science Foundation (grant number NSF-IIS-0915914

A survey of qualitative spatial representations

Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work

Qualitative spatial logics for buffered geometries

This paper describes a series of new qualitative spatial logics for checking consistency of sameAs and partOf matches between spatial objects from different geospatial datasets, especially from crowd-sourced datasets. Since geometries in crowd-sourced data are usually not very accurate or precise, we buffer geometries by a margin of error or a level of tolerance a E R≥0, and define spatial relations for buffered geometries. The spatial logics formalize the notions of 'buffered equal' (intuitively corresponding to `possibly sameAs'), 'buffered part of' ('possibly partOf'), 'near' (`possibly connected') and 'far' ('definitely disconnected'). A sound and complete axiomatisation of each logic is provided with respect to models based on metric spaces. For each of the logics, the satisfiability problem is shown to be NP-complete. Finally, we briefly describe how the logics are used in a system for generating and debugging matches between spatial objects, and report positive experimental evaluation results for the system