Spatial Humanities 3.0: Qualitative Spatial Representation and Semantic Triples as New Means of Exploration of Complex Indigenous Spatial Representations in Sixteenth Century Early Colonial Mexican Maps

For some time now, the field of Spatial Humanities has acknowledged the need for a system capable of the spatial exploration of historical and archaeological phenomena beyond Geographic Information Systems (GIS). This idea comes from the need to analyse holistically spatial information, including that which is not geographic (i.e. vague, symbolic and imaginary space). In addition, this need becomes more apparent when dealing with traditions that do not conform to the Modern/European/Cartesian conception of space in which GIS is rooted. This article, explores the use of Qualitative Spatial Representation (QSR) and Semantic Triples as possible alternative means to model complex and diverse expressions of spatial information, including social and symbolic conceptions in 16th century Mexican maps. Using as case study the map from the region of Atengo-Misquiahuala (Hidalgo) which combine the Mesoamerican and European traditions, we explore how these approaches might open new venues of research, potentially shedding light to long discussed and problematic Mesoamerican spatial categories. Focusing on a contained and partial example, we examine from a theoretical perspective and as a starting point, the possible future implementation of these approaches for historical and archaeological research.

Towards Verified Construction for Planar Class of a Qualitative Spatial Representation

PLCA is a framework for qualitative spatial reasoning, using symbolic objects and relationships between them. To show construction of a PLCA expression, the second and the third authors introduced inductive constructions. They also proved that expressions obtained by inductive constructions are planar (planarity) and planar PLCA expressions can be obtained by inductive constructions (realizability). The former one is proven with Coq proof assistant, but the latter is proven with pen-and-paper.We are currently proving the latter with Coq. We locate some oversights in the original inductive constructions and the proof. In this paper, we report these oversights, re-formalization of inductive constructions and modified proofs. We prove planarity and a base case of realizability with Coq, and induction step of realizability with Coq and pen-and-paper proof.

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.

Reasoning about Space, Actions, and Change

Qualitative spatial conceptualizations provide a relational abstraction and interface to the metrical realities of the physical world. Humans, robots, and systems that act and interact, are embedded in space. The space itself undergoes change all the time, typically as a result of volitional actions performed by an agent, and events, both deterministic and otherwise, which occur in the environment. Both categories of occurrences are a critical link to the external world, in a predictive as well as an explanatory sense: anticipations of spatial reality conform to commonsense knowledge of the effects of actions and events on material entities. Similarly, explanations of the perceived reality too are established on the basis of such apriori established commonsense notions. The author reasons about space, actions, and change in an integrated manner, either without being able to clearly demarcate the boundaries of each type of reasoning, or because such boundaries do not exist per se. This chapter is an attempt to position such integrated reasoning as a useful paradigm for the utilization of qualitative spatial representation and reasoning techniques in relevant application domains. From a logical perspective, the author notes that formalisms already exist and that effort need only be directed at specific integration tasks at a commonsense conceptual, formal representational, and computational level.

Reasoning about Space, Actions, and Change

Qualitative spatial conceptualizations provide a relational abstraction and interface to the metrical realities of the physical world. Humans, robots, and systems that act and interact, are embedded in space. The space itself undergoes change all the time, typically as a result of volitional actions performed by an agent, and events, both deterministic and otherwise, which occur in the environment. Both categories of occurrences are a critical link to the external world, in a predictive as well as an explanatory sense: anticipations of spatial reality conform to commonsense knowledge of the effects of actions and events on material entities. Similarly, explanations of the perceived reality too are established on the basis of such apriori established commonsense notions. The author reasons about space, actions, and change in an integrated manner, either without being able to clearly demarcate the boundaries of each type of reasoning, or because such boundaries do not exist per se. This chapter is an attempt to position such integrated reasoning as a useful paradigm for the utilization of qualitative spatial representation and reasoning techniques in relevant application domains. From a logical perspective, the author notes that formalisms already exist and that effort need only be directed at specific integration tasks at a commonsense conceptual, formal representational, and computational level.