The Use of Equality in Deduction and Knowledge Representation

This report describes a system which maintains canonical expressions for designators under a set of equalities. Substitution is used to maintain all knowledge in terms of these canonical expressions. A partial order on designators, termed the better-name relation, is used in the choice of canonical expressions. It is shown that with an appropriate better-name relation an important engineering reasoning technique, propagation of constraints, can be implemented as a special case of this substitution process. Special purpose algebraic simplification procedures are embedded such that they interact effectively with the equality system. An electrical circuit analysis system is developed which relies upon constraint propagation and algebraic simplification as primary reasoning techniques. The reasoning is guided by a better-name relation in which referentially transparent terms are preferred to referentially opaque ones. Multiple description of subcircuits are shown to interact strongly with the reasoning mechanism.

The Definition and Implementation of a Computer Programming Language Based on Constraints

The constraint paradigm is a model of computation in which values are deduced whenever possible, under the limitation that deductions be local in a certain sense. One may visualize a constraint 'program' as a network of devices connected by wires. Data values may flow along the wires, and computation is performed by the devices. A device computes using only locally available information (with a few exceptions), and places newly derived values on other, locally attached wires. In this way computed values are propagated. An advantage of the constraint paradigm (not unique to it) is that a single relationship can be used in more than one direction. The connections to a device are not labelled as inputs and outputs; a device will compute with whatever values are available, and produce as many new values as it can. General theorem provers are capable of such behavior, but tend to suffer from combinatorial explosion; it is not usually useful to derive all the possible consequences of a set of hypotheses. The constraint paradigm places a certain kind of limitation on the deduction process. The limitations imposed by the constraint paradigm are not the only one possible. It is argued, however, that they are restrictive enough to forestall combinatorial explosion in many interesting computational situations, yet permissive enough to allow useful computations in practical situations. Moreover, the paradigm is intuitive: It is easy to visualize the computational effects of these particular limitations, and the paradigm is a natural way of expressing programs for certain applications, in particular relationships arising in computer-aided design. A number of implementations of constraint-based programming languages are presented. A progression of ever more powerful languages is described, complete implementations are presented and design difficulties and alternatives are discussed. The goal approached, though not quite reached, is a complete programming system which will implicitly support the constraint paradigm to the same extent that LISP, say, supports automatic storage management.

The Representation of Image Texture

This thesis explores how to represent image texture in order to obtain information about the geometry and structure of surfaces, with particular emphasis on locating surface discontinuities. Theoretical and psychophysical results lead to the following conclusions for the representation of image texture: (1) A texture edge primitive is needed to identify texture change contours, which are formed by an abrupt change in the 2-D organization of similar items in an image. The texture edge can be used for locating discontinuities in surface structure and surface geometry and for establishing motion correspondence. (2) Abrupt changes in attributes that vary with changing surface geometry ??ientation, density, length, and width ??ould be used to identify discontinuities in surface geometry and surface structure. (3) Texture tokens are needed to separate the effects of different physical processes operating on a surface. They represent the local structure of the image texture. Their spatial variation can be used in the detection of texture discontinuities and texture gradients, and their temporal variation may be used for establishing motion correspondence. What precisely constitutes the texture tokens is unknown; it appears, however, that the intensity changes alone will not suffice, but local groupings of them may. (4) The above primitives need to be assigned rapidly over a large range in an image.