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

Arrow Symbols: Theory for Interpretation

People often sketch diagrams when they communicate successfully among each other. Such an intuitive collaboration would also be possible with computers if the machines understood the meanings of the sketches. Arrow symbols are a frequent ingredient of such sketched diagrams. Due to the arrows’ versatility, however, it remains a challenging problem to make computers distinguish the various semantic roles of arrow symbols. The solution to this problem is highly desirable for more effective and user-friendly pen-based systems. This thesis, therefore, develops an algorithm for deducing the semantic roles of arrow symbols, called the arrow semantic interpreter (ASI). The ASI emphasizes the structural patterns of arrow-containing diagrams, which have a strong influence on their semantics. Since the semantic roles of arrow symbols are assigned to individual arrow symbols and sometimes to the groups of arrow symbols, two types of the corresponding structures are introduced: the individual structure models the spatial arrangement of components around each arrow symbol and the inter-arrow structure captures the spatial arrangement of multiple arrow symbols. The semantic roles assigned to individual arrow symbols are classified into orientation, behavioral description, annotation, and association, and the formats of individual structures that correspond to these four classes are identified. The result enables the derivation of the possible semantic roles of individual arrow symbols from their individual structures. In addition, for the diagrams with multiple arrow symbols, the patterns of their inter-arrow structures are exploited to detect the groups of arrow symbols that jointly have certain semantic roles, as well as the nesting relations between the arrow symbols. The assessment shows that for 79% of sample arrow symbols the ASI successfully detects their correct semantic roles, even though the average number of the ASI’s interpretations is only 1.31 per arrow symbol. This result indicates that the structural information is highly useful for deriving the reliable interpretations of arrow symbols

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Qualitative Spatial Reasoning with Holed Regions

The intricacies of real-world and constructed spatial entities call for versatile spatial data types to model complex spatial objects, often characterized by the presence of holes. To date, however, relations of simple, hole-free regions have been the prevailing approaches for spatial qualitative reasoning. Even though such relations may be applied to holed regions, they do not take into consideration the consequences of the existence of the holes, limiting the ability to query and compare more complex spatial configurations. To overcome such limitations, this thesis develops a formal framework for spatial reasoning with topological relations over two-dimensional holed regions, called the Holed Regions Model (HRM), and a similarity evaluation method for comparing relations featuring a multi-holed region, called the Frequency Distribution Method (FDM). The HRM comprises a set of 23 relations between a hole-free and a single-holed region, a set of 152 relations between two single-holed regions, as well as the composition inferences enabled from both sets of relations. The inference results reveal that the fine-grained topological relations over holed regions provide more refined composition results in over 50% of the cases when compared with the results of hole-free regions relations. The HRM also accommodates the relations between a hole-free region and a multi-holed region. Each such relation is called a multi-element relation, as it can be deconstructed into a number of elements—relations between a hole-free and a singleholed region—that is equal to the number of holes, regarding each hole as if it were the only one. FDM facilitates the similarity assessment among multi-element relations. The similarity is evaluated by comparing the frequency summaries of the single-holed region relations. The multi-holed regions of the relations under comparison may differ in the number of holes. In order to assess the similarity of such relations, one multi-holed region is considered as the result of dropping from or adding holes to the other region. Therefore, the effect that two concurrent changes have on the similarity of the relations is evaluated. The first is the change in the topological relation between the regions, and the second is the change in a region’s topology brought upon by elimination or addition of holes. The results from the similarity evaluations examined in this thesis show that the topological placement of the holes in relation to the hole-free region influences relation similarity as much as the relation between the hole-free region and the host of the holes. When the relations under comparison have fewer characteristics in common, the placement of the holes is the determining factor for the similarity rankings among relations. The distilled and more correct composition and similarity evaluation results enabled by the relations over holed regions indicate that spatial reasoning over such regions differs from the prevailing reasoning over hole-free regions. Insights from such results are expected to contribute to the design of future geographic information systems that more adequately process complex spatial phenomena, and are better equipped for advanced database query answering

Graph Theory and Universal Grammar

Tese arquivada ao abrigo da Portaria nº 227/2017 de 25 de Julho-Registo de Grau EstrangeiroIn the last few years, Noam Chomsky (1994; 1995; 2000; 2001) has gone quite far in the direction of simplifying syntax, including eliminating X-bar theory and the levels of D-structure and S-structure entirely, as well as reducing movement rules to a combination of the more primitive operations of Copy and Merge. What remain in the Minimalist Program are the operations Merge and Agree and the levels of LF (Logical Form) and PF (Phonological form). My doctoral thesis attempts to offer an economical theory of syntactic structure from a graph-theoretic point of view (cf. Diestel, 2005), with special emphases on the elimination of category and projection labels and the Inclusiveness Condition (Chomsky 1994). The major influences for the development of such a theory have been Chris Collins’ (2002) seminal paper “Eliminating labels”, John Bowers (2001) unpublished manuscript “Syntactic Relations” and the Cartographic Paradigm (see Belletti, Cinque and Rizzi’s volumes on OUP for a starting point regarding this paradigm). A syntactic structure will be regarded here as a graph consisting of the set of lexical items, the set of relations among them and nothing more

Concepts, Frames and Cascades in Semantics, Cognition and Ontology

This open access book presents novel theoretical, empirical and experimental work exploring the nature of mental representations that support natural language production and understanding, and other manifestations of cognition. One fundamental question raised in the text is whether requisite knowledge structures can be adequately modeled by means of a uniform representational format, and if so, what exactly is its nature. Frames are a key topic covered which have had a strong impact on the exploration of knowledge representations in artificial intelligence, psychology and linguistics; cascades are a novel development in frame theory. Other key subject areas explored are: concepts and categorization, the experimental investigation of mental representation, as well as cognitive analysis in semantics. This book is of interest to students, researchers, and professionals working on cognition in the fields of linguistics, philosophy, and psychology