Spatial inference with geometric proportional analogies

2021

Spatial reasoning is an important part of common-sense reasoning but has most often been examined in isolation from other areas of common sense knowledge representation. Spatial reasoning also has been a prominent area of research in linguistic semantics. In this work, we aim to create a corpus of common sense reasoning problems formalized in the context of a large and comprehensive theory of world knowledge, in the hopes that it will be more generally reusable on a wide variety of practical reasoning problems. An additional goal is to demonstrate the computational sufficiency of this work by employing automated reasoning to solve the problems. Finally, we also state the problems first in natural language, to provide a set of test cases for theories of linguistic semantics and computational linguistics, with a computational representation that can help to validate whether any method or process of interpreting language into a computational logic representation is correct or sufficien...

1998

This research continues with current innovative geocomputational research trends that aim to provide enhanced spatial analysis tools. The coupling of case-based reasoning (CBR) with GIS provides the focus of this paper. This coupling allows the retrieval, reuse, revision and retention of previous similar spatial cases. CBR is therefore used to develop more complex spatial data modelling methods (by using the CBR modules for improved spatial data manipulation) and provide enhanced exploratory geographical analysis tools (to find ...

4 th AGILE Conference on Geographic …, 2001

In this paper we describe the application of analogical structure matching techniques to the domain of Geographic Information Systems (GIS). Automatic categorisation of map data into roads, buildings etc. is currently based on isolated objects. We describe how identifying analogous clusters of objects can categorise ambiguous polygons by introducing context into the categorisation process. We describe a number of GIS classification tasks that can be performed by analogical structure matching, resulting in a useful classification tool that operates in a cognitively plausible manner.

2002

Four experiments examined whether spatial reasoning about non-spatial concepts is based on mapping concepts to space according to similarities in relational structure. Six-and 7-year-old children without any prior graphing experience were asked to reason with graph-like diagrams. In Experiments 1 and 2, children were taught to map time and quantity to vertical and horizontal lines, and then were asked to judge the relative value of a second-order variable (rate) or a first-order variable (quantity) represented in a function line.

Lecture Notes in Computer Science, 2012

Graphical depictions of complex interactions pose a challenge to spatial reasoning. In this research, we tested whether analogical processes can be harnessed to help students learn to solve complex graphical reasoning problems. Specifically, we asked whether a brief training experience using spatial analogies could help students learn about stock-and-flow graphs. The basic idea of our intervention was to juxtapose contrastive graphs and encourage students to compare them. In two studies, we test the following predictions derived from structural alignment theories of analogy: (1) comparing contrastive graphs during training will lead to better performance in a graph-understanding task than will studying the same exemplars sequentially; and (2) comparing highsimilarity pairs will lead to better performance than will comparing low similarity pairs. The results support both of these predictions, indicating that even a brief analogical comparison task can confer relational insight. Further, these results corroborate prior evidence that a structural alignment process underlies analogical comparison.

Cognitive Science, 2004

Three experiments investigated whether the similarity of relational structures influences the interpretation of spatial representations. Adults were shown diagrams of hand gestures paired with simple statements and asked to judge the meaning of new gestures. In Experiment 1 the gestures were paired with active declarative statements. In Experiment 2, the gestures were paired with conjunctive and disjunctive relations. Experiment 3 used statements similar to those used in Experiment 1, but eliminated the initial object-to-object mapping provided in Experiments 1 and 2. In all three experiments, most participants chose an interpretation that set up a parallel relational structure between the gesture and its meaning: spatial elements were paired with conceptual elements and spatial relations were paired with conceptual relations. These results are consistent with the hypothesis that similarity of relational structures influences spatial reasoning, and have implications for analogical reasoning, diagrammatic reasoning, and language processing.

argument, 2002

Spatial Information Theory, 2001

One of the central questions of spatial reasoning research is whether the underlying processes are inherently visual or spatial. The article reports a dual-task experiment that was conducted to explore the visual and/or spatial nature of human spatial reasoning. The main tasks were inferences based on a spatial version of the interval calculus introduced by Allen (1983). The secondary tasks were presented visually or acoustically, and were either spatial or non-spatial. The results indicate that spatial reasoning is mainly based on the construction and inspection of spatial layouts, whereas no evidence of the involvement of visual representations and processes was found.

2000

Searching for alternative solutions of an indeterminate reason- ing task is an important and necessary step in order to draw certain inferences as in the case of deduction. To elucidate the underlying mental representations and processes of the search for alternatives in spatial reasoning, an experiment was con- ducted that used specific material stemming from AI research of Qualitative Spatial

2008

In recent years a number of empirical results indicate that humans tend to use mental models during the reasoning process. This theory claims that humans represent and reason about spatial information by constructing, inspecting, and generating alternative models to check for a putative conclusion. New results about preferred models and local transformations made it necessary to refine the classical theory. From a formal perspective , however, a number of technical questions w.r.t. the explicit details of the theory are still unanswered. In this paper we formally ground the preferred mental model theory with the help of formal logic. This formalization allows to show inherent differences between formal and human reasoning and allows to identify a source of human errors in reasoning.