Expert Algorithmic and Imagistic Problem Solving Strategies in Advanced Chemistry

Abstract

Visualization and imagistic reasoning appear central to expert practice in science; however, expert use of these strategies on authentic tasks has not been examined in detail. This study documents how science experts use both algorithms and imagistic reasoning to solve problems. Using protocol analysis, we report expert chemists' preferential use of algorithms for solving spatial problems and imagistic reasoning for deducing spatial transformations. We observed experts employ algorithms to solve the majority of spatial tasks while reserving imagistic strategies to solve a class of tasks that required translating between representations. Strategy used varied widely among experts and tasks.     

External Cue Effects on Memory for Spatial Location within a Rotated Task Field

Abstract

We propose a mathematical model of the Path Integration (PI) process. Its core assumption is that orientations of a path are summarized by circular probability distributions. We compare our model with classical, deterministic models of PI and find that, although they are indistinguishable in terms of information encoded, the probabilistic model is more parsimonious when considering navigation strategies. We show how sensory events can enrich the probability distributions memorized, resulting in a continuum of navigation strategies, from PI to stimulus-triggered response. We analyze the combination of circular probability distributions (e.g., multicue fusion), and demonstrate that, contrary to the linear case, adding orientation cues does not always increase reliability of estimates. We discuss experimental predictions entailed by our model.     

Reasoning about Depth and Motion from an Observer's Viewpoint

ABSTRACT

The goal of this paper is to present a logic-based formalism for representing knowledge about objects in space and their movements, and show how this knowledge could be built up from the viewpoint of an observer immersed in a dynamic world. In this paper space is represented using functions that extract attributes of depth, size and distance from snapshots of the world. These attributes compose a novel spatial reasoning system named Depth Profile Calculus (DPC). Transitions between qualitative relations involving these attributes are represented by an extension of this calculus called Dynamic Depth Profile Calculus (DDPC). We argue that knowledge about objects in the world could be built up via a process of abduction on DDPC relations.     

Special issue introduction: Approaching spatial uncertainty visualization to support reasoning and decision making

While research on uncertainty and decision-making has a long history across several disciplines, recent technological developments compel researchers to rethink how to best address and advance the understanding of how humans reason and make decisions under spatial uncertainty. This introduction presents a visual summary graphic to provide an overview of each article in this special issue. Upon viewing these visual summaries, the reader will find that each of these articles covers different topics in the uncertainty visualization domain, offering complementary research in this field. Extending this body of research and finding new ways to explore how these visualizations may help or hinder the analytical and reasoning process of humans continues to be a necessary step towards designing more effective uncertainty visualizations to support reasoning and decision-making.     

The Space within Fisherman's Folly: Playing with a Puzzle in Mereotopology

Abstract

In this paper we propose a spatial ontology for reasoning about holes, rigid objects and a string, taking a classical puzzle as a motivating example. In this ontology the domain is composed of spatial regions whereby a theory about holes is defined over a mereotopological basis. Within this theory we define a data structure, named chain, that facilitates a clear and efficient representation of the puzzle states and its solution.     

Mining Spatial Associations with Limited Sensory Information

Abstract

Human navigation in an unknown environment requires an understanding of the spatial relationships of the terrain. For example, a soldier who is on a reconnaissance mission in a new city needs to “know” the spatial layout of the surroundings with high confidence. Oftentimes, this understanding must be acquired within a very short amount of time and with limited sensory inputs. The soldier would benefit from a digital avatar that draws inferences about the spatial layout of the city based on an initial set of observations and guides the soldier either in further exploring the environment or in making decisions based on these inferences. In this paper, we present and evaluate an inductive approach to learning spatial associations using sensory data that is available from the simulation environment of a computer game, Unreal Tournament. We study two kinds of spatial relationships between nodes on a level of a game map: nodes that are placed near each other to satisfy some spatial requirement and nodes that are placed near each other to satisfy the design preferences of a level architect. We show that we can infer both kinds of relationships using an association rule mining algorithm. Furthermore, we show how to use an ontology to distinguish between these relationships in order to discover different types of spatial arrangements on a specific map. We discuss how the inferred associations can be used to control an avatar that makes recommendations for navigating unexplored areas on a map. We conclude with some thoughts on the applicability of our methods to scenarios in the real world, beyond the simulation environment of a game, and on how the learned associations can be represented and queried by a simple question-answer type system.     

Influence of estimation errors on wayfinding-decisions in unknown street networks – analyzing the least-angle strategy

The least-angle strategy is a common wayfinding method that can be applied in unknown environments if the target direction is known. The strategy is based on the navigator's heuristic to select the street segment at an intersection which is most in line with the target direction. To use this strategy, the navigator needs to know the angles between the target direction and the street segments leading out from the intersection. If the direct view to the target is blocked and the target vector cannot be perceived, the target direction that is needed for the decision process is based on the agent's believed position and orientation (estimated through path integration). The agent's believed position and target direction are distorted by human errors in estimation of distances and directions, mainly affecting the path integration process. In this paper we examine how human estimation errors of distance and rotation influence the decision behavior in the wayfinding process in an unknown street environment. To demonstrate the geometrical consequences for a specific test case, we use a simulated software agent which navigates in a simulated street environment.     

On Embedding a Qualitative Representation in a Two-Dimensional Plane

Abstract

This paper discusses embedding in a two-dimensional plane a symbolic representation for spatial data using the simple objects, points (P), lines (L), circuits (C), and areas (A). We have proposed PLCA as a new framework for a qualitative spatial reasoning. In a PLCA expression, the entire figure is represented in a form in which all the objects are related. We investigate the conditions for two-dimensional realizability of a PLCA expression, and derive the relation that the numbers of objects in a PLCA expression should have. In this process, we use the well-known Euler's formula. We also give an algorithm for drawing the figure of the PLCA expression that satisfies this condition in a two-dimensional plane and prove its correctness. The algorithm generates a quantitative expression from qualitative expression.     

Qualitative Spatial Reasoning for Topological Map Learning

Abstract

In this paper we investigate the application of qualitative spatial reasoning methods for learning the topological map of an unknown environment. We develop a topological mapping framework that achieves robustness against ambiguity in the available information by tracking all possible graph hypotheses simultaneously. We then exploit spatial reasoning to reduce the space of possible hypotheses. The considered constraints are qualitative direction information and the assumption that the map is planar. We investigate the effects of absolute and relative direction information using two different spatial calculi and combine the approach with a real mapping system based on Voronoi graphs.     

In Memoriam: Herbert L. Pick,Jr. (1930–2012)

ABSTRACT

Fictive motion in language (as in “the ridge went north”) is claimed to reflect the attention focus of the observer on the extension and spatial layout of an entity. This paper investigates fictive motion in alpine narratives, which describe the experience of moving in a very specifically structured space. We examine space properties that are highlighted through fictive motion in this specific context and describe how they go beyond spatial extension. We further report the communicative motivation behind the use of fictive motion, ranging from conveying the sense of place to encoding the full spatial footprint of a motion event.     

Spatial Reorientation: Effects of Verbal and Spatial Shadowing

ABSTRACT

Spatially disoriented adults flexibly conjoin geometric information (macroscopic shape) and nongeometric information (e.g., the color of a wall) to re-establish their bearings. It has been proposed that non-geometric information is incorporated into a geometric frame of reference through the use of spatial language. Support for this assumption comes from dual-task studies in which participants failed to use non-geometric features when they shadowed a verbal message concurrent to the reorientation task. These studies were performed in small rectangular spaces. In contrast, our study was performed in a large square room. Experiment 1 showed that verbal shadowing did not disrupt non-geometric feature use in this environment. In Experiment 2, we found that a spatial shadowing task that required the encoding of frequently changing spatial directions impaired reorientation behavior. Our study shows that nongeometric information can be used for reorientation without recourse to linguistic processes, and suggests that the use of non-geometric features is dependent upon a spatial coding process.     

Impact of Regionalization and Detour on Ad-hoc Path Choice

Abstract

Regionalization has been found to impact human route planning, both when the planning is based on a previously learned environment encoded in memory and when maps are used. This paper presents an experiment in a virtual desktop environment and examines how the length of the path in the start region or goal region impacts ad-hoc route choice, i.e., in situations where the decision is made right after perceiving the decision situation. More specifically, this research aims at quantifying the trade-off value between short travel distances and leaving the start as well as reaching the goal region quicker, respectively.     

Effects of Basic Path Properties on Human Path Integration

Abstract

We investigated how path integration performance can be influenced by five basic path properties in a Virtual Reality Cube. Participants performed path-completion tasks in hallway paths with up to 12 segments. Distance information was visual, whereas turning angles were specified through vision and body senses. The ridge regression analyses suggested that path integration was affected by the number of segments, overall path length/turning angles, and the correct homing distance. Moreover, an un-correlation paradigm showed that path completion performance might be affected by participants' expectations for the correct homing distance of different paths. Implications on models of path integration were discussed.     

Topologically Characterized Movement Patterns: A Cognitive Assessment

Abstract

In this paper, we discuss the role of topology as a predictor for the conceptualization of dynamically changing spatial configurations (referred to as movement patterns). We define meaningful units of movement patterns as paths through a topologically defined conceptual neighborhood graph. Topology plays a central role in formal approaches to human cognition and in predicting cognitive similarity ratings—although primarily for static spatial configurations. Formal specifications of the role of topology for characterizing movement patterns do exist, yet there is paucity of behavioral validation. To bridge this gap, we conducted an experiment based on the grouping paradigm to assess factors that underlie conceptualizations of movement patterns. The experiment was designed such that paths through the conceptual neighborhood graph were distinguished by topologically differentiated ending relations. We believe topology can make an important contribution in explaining movement conceptualizations. One recently formulated topology-based contribution is the endpoint hypothesis, asserting that a cognitive focus is placed on event ending relations. We discuss the results of our experiment in relation to previous experiments targeted toward a framework for modeling the cognitive conceptualization of dynamically changing spatial relations.     

A Neuro-Cognitive Theory of Deductive Relational Reasoning with Mental Models and Visual Images

Abstract

Many neuro-imaging studies have provided evidence that the parietal cortex plays a key role in reasoning based on mental models, which are supposed to be of abstract spatial nature. However, these studies have also shown concurrent activation in vision-related cortical areas which have often been interpreted as evidence for the role of visual mental imagery in reasoning. The aim of the paper is to resolve the inconsistencies in the previous literature on reasoning and imagery and to develop a neurally and cognitively plausible theory of human relational reasoning. The main assumption is that visual brain areas are only involved if the problem information is easy to visualize and when this information must be processed and maintained in visual working memory. A regular reasoning process, however, does not involve visual images but more abstract spatial representations—spatial mental models—held in parietal cortices. Only these spatial representations are crucial for the genuine reasoning processes.     

Analyzing Qualitative Spatio-Temporal Calculi using Algebraic Geometry

Abstract

Qualitative spatial reasoning is based on calculi which comprise relations and operation tables that encode operations like relation composition. Designing a calculus involves determining these tables and analyzing reasoning properties—a demanding task that is susceptible to errors if performed manually. This paper is concerned with automating computation of operation tables and analysis of qualitative calculi over real-valued domains like the plane ². We present an approach to specify qualitative relations using polynomial equations that allows methods from algebraic geometry to be applied. This paper shows how reasoning with qualitative relations can be posed algebraically and demonstrates algebraic reasoning using Gröbner base analysis. We evaluate this approach and describe our implementation, which is freely available as part of the spatial reasoning toolbox SparQ.     

Spatial Influence of Environmental Axes in a Baseball Field

Abstract

We investigated the influence of environmental axes in a baseball field. In Experiment 1, participants walked either a path in the prototypical orientation (home plate to second base) or one which was rotated 225°. Recall for object locations was best when participants imagined themselves aligned with axes salient from the experienced orientation. In Experiment 2, when learning was through a route text, there was less of an influence of environmental axes. In Experiment 3, when participants walked both paths, memories were good for the atypical orientation, suggesting that task-specific spatial cues can be more influential than a prior conceptual north.