Determining the Scope of English Quantifiers

How can one represent the meaning of English sentences in a formal logical notation such that the translation of English into this logical form is simple and general? This report answers this question for a particular kind of meaning, namely quantifier scope, and for a particular part of the translation, namely the syntactic influence on the translation. Rules are presented which predict, for example, that the sentence: Everyone in this room speaks at least two languages. has the quantifier scope AE in standard predicate calculus, while the sentence: At lease two languages are spoken by everyone in this room. has the quantifier scope EA. Three different logical forms are presented, and their translation rules are examined. One of the logical forms is predicate calculus. The translation rules for it were developed by Robert May (May 19 77). The other two logical forms are Skolem form and a simple computer programming language. The translation rules for these two logical forms are new. All three sets of translation rules are shown to be general, in the sense that the same rules express the constraints that syntax imposes on certain other linguistic phenomena. For example, the rules that constrain the translation into Skolem form are shown to constrain definite np anaphora as well. A large body of carefully collected data is presented, and used to assess the empirical accuracy of each of the theories. None of the three theories is vastly superior to the others. However, the report concludes by suggesting that a combination of the two newer theories would have the greatest generality and the highest empirical accuracy.

A Multiple-Context Equality-Based Reasoning System

Expert systems are too slow. This work attacks that problem by speeding up a useful system component that remembers facts and tracks down simple consequences. The redesigned component can assimilate new facts more quickly because it uses a compact, grammar-based internal representation to deal with whole classes of equivalent expressions at once. It can support faster hypothetical reasoning because it remembers the consequences of several assumption sets at once. The new design is targeted for situations in which many of the stored facts are equalities. The deductive machinery considered here supplements stored premises with simple new conclusions. The stored premises include permanently asserted facts and temporarily adopted assumptions. The new conclusions are derived by substituting equals for equals and using the properties of the logical connectives AND, Or, and NOT. The deductive system provides supporting premises for its derived conclusions. Reasoning that involves quantifiers is beyond the scope of its limited and automatic operation. The expert system of which the reasoning system is a component is expected to be responsible for overall control of reasoning.

Internal Camera Calibration Using Rotation and Geometric Shapes

This paper describes a simple method for internal camera calibration for computer vision. This method is based on tracking image features through a sequence of images while the camera undergoes pure rotation. The location of the features relative to the camera or to each other need not be known and therefore this method can be used both for laboratory calibration and for self calibration in autonomous robots working in unstructured environments. A second method of calibration is also presented. This method uses simple geometric objects such as spheres and straight lines to The camera parameters. Calibration is performed using both methods and the results compared.

Relative Contributions of Internal and External Features to Face Recognition

The central challenge in face recognition lies in understanding the role different facial features play in our judgments of identity. Notable in this regard are the relative contributions of the internal (eyes, nose and mouth) and external (hair and jaw-line) features. Past studies that have investigated this issue have typically used high-resolution images or good-quality line drawings as facial stimuli. The results obtained are therefore most relevant for understanding the identification of faces at close range. However, given that real-world viewing conditions are rarely optimal, it is also important to know how image degradations, such as loss of resolution caused by large viewing distances, influence our ability to use internal and external features. Here, we report experiments designed to address this issue. Our data characterize how the relative contributions of internal and external features change as a function of image resolution. While we replicated results of previous studies that have shown internal features of familiar faces to be more useful for recognition than external features at high resolution, we found that the two feature sets reverse in importance as resolution decreases. These results suggest that the visual system uses a highly non-linear cue-fusion strategy in combining internal and external features along the dimension of image resolution and that the configural cues that relate the two feature sets play an important role in judgments of facial identity.