Symbolic Translation Research Articles

Acquiring and managing knowledge using a conceptual structures approach: introduction and framework

One powerful representational system-conceptual structures that continue the trend towards knowledge programming-is examined. J.F. Sowa's conceptual structures approach (Conceptual Structures: Information Processing in Mind and Machine, Addison-Wesley, NY, 1984), a graph-based semantic network, is a general representational system with a natural-language expressivity. This allows problem-domain issues to be readily captured and expressed at several levels of granularity. Conceptual graph (CG) propositions can also act as a flexible intermediate form for the more common representations used in implementing many AI systems-frames, production rules, conceptual dependency, and logic systems. Thus, CG knowledge models are capable of symbolic translation into forms that are more familiar. Issues of expressively capturing the semantics of problem domains are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A many-valued logic for approximate reasoning

A new system of many-valued logic, the Extended Post system of order p, p ≥ 2, is proposed as a system of logic supporting reasoning with facts and rules which are reliable to a specified extent. In an Extended Post system there are as many operations of logical disjunction and logical conjunction as there are truth values. The truth value associated with a particular operation of disjunction (conjunction) acts as a threshold value controlling the behavior of the operation. The availability of an extended set of logical operations provides improved flexibility in the symbolic translation of sentences from the ordinary word-language. Extended Post systems are equipped with a semantics in which graded rather than crisp sets correspond to predicates. The system exhibits a rich algebraic structure. The p operations of disjunction form a distributivity cycle. To each disjunction there corresponds a dual operation of conjunction, the two operations being distributive to one another. The p conjunctions form a dual distributivity cycle. Both propositional calculus and first-order predicate calculus of EP systems are developed. The application to approximate reasoning is described. It is shown that there exist distinct isomorphic copies of fuzzy logic, each corresponding to a distinct level of approximation and being complete to resolution.

The Relationship between Sex and Learning Style and Graphicacy in 14‐year‐old Children

Abstract Two aspects of learning style in 14‐year‐old children were determined and compared with map reading performance. The two styles were: (1) field‐dependence‐independence which was assessed by means of a test of embedded figures; and (2) verbal imagery learning style which, since there is evidence that it is related to the extraversion‐introversion dimension of personality, was assessed by the Junior Eysenck Personality Inventory. Map reading performance was measured on a three‐part test. The sections were: (a) map‐aerial photograph correlation, (b) symbol translation and (c) view identification. An analysis of variance indicated two significant results: (1) being field‐independent rather than field‐dependent resulted in better performance on all aspects of map reading for boys but made no difference for girls; (2) there was no difference between boys and girls on symbol translation, but on map‐photograph correlation extrovert boys did better than extrovert girls, and on view identification ambivert girls were superior to ambivert boys. The results suggest that map reading performance depends on the learning style and sex of the pupil and on the type of task.

Specifications, models, and implementations of data abstractions

We consider the specification and verification of modules in hierarchically structured programs, as proposed by Parnas and Hoare. We argue that a specification for such a module is a set of sentences in some logical language in which the names to be exported by the module appear as nonlogical symbols. We further argue that an implementation of one module in terms of another module is a translation of the nonlogical symbols of the first specification into the language of the second. Equality must also be interpreted. We proposed necessary conditions which any such notion of ‘correct implementation’ ought to satisfy. These criteria provide a basis for judging the logical adequacy of any proposed specification language and definition of implementation. We then study DLP, a specification language obtained by adding uninterpreted procedure symbols to Pratt's first order dynamic logic. We present a definition of ‘implementation’ for DLP, and we show it satisfies these conditions. The main theorem, called the implementation Theorem, extends the Interpretation Theorem from first-order logic to DLP. The proof of this theorem is complicated by the necessity of dealing with modalities, parameters to procedures, interpretations of equality, and interpretations of sorts as tuples.

A systems analog mime for color vision disorders in humans

A multiunit processing system mime for human color vision is presented. This processing system is composed of a sequence of black box units which encode the visual field and subsequently decode the visual field in the following manner. A “primary retinal encoder” performs an internal digitization of the visual field in both color and intensity. A “fundamental symbol translating unit” encodes the color and intensity patterns into a new pattern containing the fundamental symbols. This encoding is done via a Gödel transformation of the fundamental symbol patterns. The symbols needed to execute this transformation are found in an encoded table called the “symbol translation table.” Finally, the “Gödel signal generator” translates the fundamental symbol pattern into an electrical signal which is sent to a decoding region in the visual cortex and lateral geniculate body. This region is also tied to the symbol translation table, and is then used to decode the electrical signal back to the visual field. It is shown that various errors/failures in these black box units may lead to a wide variety of visual problems which mimic human disorders. These disorders include color blindness, color weakness, dyslexic problems, and a new disorder called visual field fluctuation.

What Mathematical Subjects Should be Included in the Curriculum of the Secondary Schools? From the Point of View of the Industrial Establishments

The most important of all branches of learning is the ability to read. The translation of symbols, figures, letters, words, understandingly and meaningly to the brain by the eye, stands first in importance of “the three R’s.” The ability to express thoughts in characters or symbols for the edification of others, the art of inscribing such thought or words on paper or parchment — the ability to write, stands second of “the three R’s.” And then we have arithmetic, the third of “the three R’s.” Arithmetic, the lowest branch, the primer of mathematics, is the most useful and most applicable of all our branches of mathematics.