Session on Analogy in Reasoning and Construction

Conference: ACA'2009, June 25-28, 2009, Montreal, Quebec, Canada

Abstract:

The study of analogy is vast. It permeates every field of scholarship and research.
Symbolic calculation software provides powerful tools for exploring the mechanized use of analogy in reasoning and construction.
This session addresses:

1. symbolic calculations that have involved analogy,
2. models on which future software can be based,
3. the selection of further topics for mechanization, from the overwhelming field of possibilities,
4. the development of strategies to study these.

Invited talks:

1. Professor Paul Thagard, (Philosophy, University of Waterloo). How brains compute analogies. Abstract: In our 1996 book, Mental Leaps, Keith Holyoak and I presented a psychological theory of how people perform analogical thinking. We argued that retrieval, mapping, and transfer of analogical information involve 3 constraints: similarity, structure, and purpose. In the past decade, much has been learned about the neural processes that underlie these constraints. This talk will offer a computational account of how neural networks compute similarity, structure, and purpose.


2. Professor Godfried Toussaint, (Computer Science and Center for Interdisciplinary Research In Music Media and Technology, McGill University). Analysis and Generation of Symbolically Represented Musical Rhythm. Abstract: Tools for analyzing musical rhythms that are represented symbolically are reviewed. Such tools include measuring the complexity and similarity of rhythms, as well as characterizing what makes a "good" rhythm good. These characterizations lead to simple algorithms for automatic generation of "good" rhythms. Analogy plays an important role throughout this work.


3. Devin Griffiths, (Center for Cultural Analysis, Rutgers University) The Semantic Analysis of Analogy in Darwin's Origin of Species. Abstract: I discuss the role of analogy in Darwin’s "Origin of Species" using textual analysis. One of his key contributions was to redefine "evolution", "species" and other basic concepts. I analyze single-sentence analogical constructions over the course of his work using Latent Semantic Analysis (LSA) in novel ways that include Fisher testing, leading to a discussion of analogy and its relationship to the coherence of sentence-to-sentence meaning. Analogies transfer characteristics between semantic systems and I reflect upon what this implies.


4. Professor Pierre Bouchard, (Mathematics, University of Quebec at Montreal). The Chemistry of Modern Combinatorics -- "Species' -- a Tool for Analogical Discussion Abstract: Category theory is a flourishing branch of mathematics that has the exploration of analogy as one of its major uses. I will give a very brief and naive introduction to the concepts of "category" and "functor". Then I will give simple definitions of a "species of structure F" and a "structure of species F over a finite set U", illustrated by numerous examples. I will then show what a "molecular" species is, give all examples of molecular species on a small number of elements, and use an example to show how every species can be decomposed into a "sum" of molecular species. From there I will show how to count the number of molecular species that there can be on a given finite set of n elements, and what two chemists found about that in 1929. To conclude, I will mention what an atomic species is, and show how any molecular species can be decomposed into a "product" of atomic species. Where can we go from there, particularly in regard to analogy? The answer during the talk!


5. Professor Michael Barnett, (Computer and Information Science, City University of New York, Emeritus). Using analogy in symbolic calculation.
Abstract: I have reduced the human effort in several recent symbolic calculations of chemical valence theory by the mechanized use of analogy. I explain the basic principles by (analogous) text processing examples, state the benefits of my mathematical applications of these methods, and show some diagrammatic depictions of certain laboratory experiments constructed in analogous ways.

Suggested Scope for Further Talks:

1. Representation and classification of analogies of general application.


2. Representation and classification of analogies in mathematics.


3. Representation and classification of analogies in experimental and theoretical science.


4. Representation and classification of analogies in humanities, e.g. textual analysis, visual arts, music.


5. Using analogy in symbolic calculation of mathematical formulas.


6. Using analogy in symbolic calculation of text and other non-mathematical material.


7. Analogy in mathematics, language and other education, with (potential) computer support.


8. Mechanical recognition of analogy.


9. Other topics that relate to the recognition and use of analogy.

Call for Submissions: