Long and Garigliano make a concerted effort to develop a set-theoretic model of analogy and demonstrate its application in a natural language system. Their intentions are to provide a foundation for a consensus on the role and scope of certain forms of analogy, and to demonstrate the technique, giving evidence of its usefulness. The authors make lengthy and detailed arguments for the approach taken in this difficult and important area of research. Informally, a property holds of one term or concept (called the receiver) from the premises that the same property holds of another term or concept (called the origin) and that the two terms are alike in some relevant way. From this notion, the authors proceed using a software engineering methodology. Requirements are presented; a knowledge representation and analogical algorithm is specified; and the module is built, tested, and evaluated to determine whether the requirements are met.

The ten requirements for the analogical reasoning module are (1) produce results quickly, (2) identify the basis for analogy within a context of large amounts of extraneous and irrelevant information, (3) common properties between analogous terms, (4) relevance of common properties to transferred property, (5) add to the information of common properties, (6) incomplete information is adequate, (7) distinction from statistical argument and logical argument, (8)strengthening of conclusions is possible, (9) knowledge representation is usable for other purposes, and (10) conclusions can be compared with other reasoning techniques.

The basic knowledge representation is a semantic net with vertices representing concepts and properties and edges representing relationships. Relationships have two components, the first component distinguishing “defined” from “obtained” relationships and the second determining modality in the form of “necessity,” “expectancy,” “statistical,” and “observational.” Six of the eight combinations are used; for  example,  flying is a defined expectancy property of birds. The most important concepts are the origin, the receiver, and the crossover. Analogy asserts that the receiver has a property that the origin contains. The crossover is a concept that contains large amounts of both the origin (including the key property) and the receiver.

The basic algorithm for reasoning is: confirm that some of the concepts have the property for which the analogy is being drawn, construct a locality for the receiver in layers of decreasing inclusion of the receiver, identify candidate origins that are of similar size to the receiver and contain the desired property, construct candidate crossovers based on the amount of content of origin and receiver, and choose the best analogy based on crossovers that contain a large portion of both the origin and the receiver and that are of the same order of magnitude as the sum of the sizes of the origin and the receiver.

The module is built in the functional language Miranda. The system within which the module is tested is LOLITA, which does natural language processing. The testing is done on scanned newspaper articles, and the arguments for the requirements having been met are made based on both the reasoning and the testing.

A strength of the book is that it gives the complete code for the analogical reasoning module. Being written in Miranda makes it less accessible than if it were written in a more common language, however.

Another strength is that the module is incorporated into a larger system for natural language processing, LOLITA. Only one example is given, however, weakening the goal of demonstrating usefulness.

The goal of providing a foundation for a consensus is also compromised. Consensus is much harder to obtain when one does not incorporate the ideas of others and argues against a prominent approach.

Nor are the arguments for positioning the logic approach against other approaches, particularly the structure-mapping approach, convincing. Instead of depending on the structure of relationships in the knowledge representation, the authors’ approach depends on how many concepts and properties have been represented. By depending so much on counting concepts, the logic approach has the problem of convincing the critic that all concepts and properties have been included in the knowledge base, in the right places. The argument that quantity equals quality continues to be unresolved, and issues of correct and complete categorization become crucial[1,2].

Another weakness is overlooking the literature on computational theories of metaphor, particularly those that are similar in using a set-theoretic approach [3,4], using semantic nets and abstraction [5], or embedding the module within a larger system [1,6]. This omission is particularly unfortunate, since the application is in the domain of natural language processing. Consensus forming is more likely when new ideas are tied to the similar ideas of others.

The book is indeed valuable. Its basic strength is in continuing the research project of developing testable analogical reasoning algorithms within large useful projects. The results from the more extensive tests planned within the LOLITA system will be worth examining. The problem of building working computational models of analogical reasoning continues to be difficult and worthy of continued effort.