Test-score semantics provides a representational scheme for statements such as, “Over the past few years, Stan made a lot of money.” Because of the presence of terms such as “few” and “a lot,” it is better to assign a level of truth, rather than a truth value. In test-score semantics, the truth of a proposition is determined by a test procedure that collects and composes partial test scores, determined by matching the underlying elements in a proposition against an explanatory database of fuzzy relations. A number of examples are analyzed, including “Joan is young and attractive,” “Most Frenchmen are neither very tall nor very fat,” “By far the richest man in France is bald,” “Berkeley has a temperate climate,” “On the average, Virginia smokes at least a few cigarettes a day,” and “Most young men like mostly young women.” These examples show how to handle negation, quantification, intensification, and so on.
Here’s an early example. To construct the test-score test procedure for the second-order fuzzy predicate “many large balls,” assume the explanatory database contains three sets of relations--POPULATION[Ball; Size], LARGE[Size; &mgr;], and MANY[Number; &mgr;]--where the POPULATION pairs give the sizes of the balls, the LARGE pairs give the degree (&mgr;) to which a size is “large,” and the MANY pairs give the degree to which a number of things are “many.” The test procedure for determining how true “many large balls” is for a given database is as follows: Find the size of each ball, according to the POPULATION pairs; add up the degrees to which each size is “large,” according to the LARGE pairs; finally, return the degree to which this sum is “many,” according to the MANY pairs.
The major question that I felt was left unanswered was how someone using this approach could tell if the semantics was doing “the right thing.” For example, the “many large balls” test procedure appears to give the same answer for a large set of slightly large balls and a smaller set of very large balls. Is this right? I’m not sure. There are two difficulties with evaluating a test procedure’s correctness. First, what behavior do we actually want? Second, given a particular test procedure, how do we characterize exactly what a test procedure does?
Despite this concern, I recommend this paper to anyone interested in a fuzzy logic approach to semantics. This is a good overview of test-score semantics; it is a little technical, but very clear, with numerous examples.