Paulo Santos

Joao Kogler Jr. & Paulo Santos discuss, in chapter eleven, the geometrical and logical aspects of a cognitive agent, which distinguishes it from merely reactive and perceptive agents. What singles out the cognitive agent is the use of context- invariant information that breeds knowledge. In their approach, the perceptual system is formed by a chain of processes dealing with contextual information, beginning at the sensorial system and ending at the motor system. The perceptual chain is constrained not only at both extremities, but its transformations are geometrically connected with “holonomic” constraint propagation. On the other hand, the cognitive system comprises self-constrained processes that operate with learned transformations, so that the geometry of cognition is “non- holonomic”. Shifting to the logical approach to the problem, “qualitative spatial reasoning” is unveiled in terms of “regional connection calculus”, which describes how spatial regions are connected. The approach, as pointed by the authors, has not fared well with experimental data from cognitive psychology, which is expected since the formal approach is an abstraction from perception. Building on suggestions from advantaged properties of representations, a formalism is proposed which represents qualitative location by partitioning the visual scene around an agent into sectors, and providing relations among them, so that they form a language capable of expressing the spatial organization of the scene.

In this paper, we present a formalism for handling polysemy in spatial expressions based on supervaluation semantics called standpoint semantics for polysemy (SSP). The goal of this formalism is, given a prepositional phrase, to define its possible spatial interpretations. For this, we propose to characterize spatial prepositions by means of a triplet ⟨ image schema, semantic feature, spatial axis⟩⁠. The core of SSP is predicate grounding theories, which are formulas of a first-order language that define a spatial preposition through the semantic features of its trajector and landmark. Precisifications are also established, which are a set of formulae of a qualitative spatial reasoning formalism that aims to provide the spatial characterization of the trajector with respect to the landmark. In addition to the theoretical model, we also present results of a computational implementation of SSP for the preposition ‘in’.