On Logical Foundations of Active Databases

Perceptual representations – e.g., of objects or approximate magnitudes –are often invoked as building blocks that children combine with linguisticsymbols when they acquire the positive integers. Systems of numericalperception are either assumed to contain the logical foundations ofarithmetic innately, or to supply the basis for their induction. Here Ipropose an alternative to this general framework, and argue that theintegers are not learned from perceptual systems, but instead arise toexplain perception as part of language acquisition. Drawing oncross-linguistic data and developmental data, I show that small numbers(1-4) and large numbers (~5+) arise both historically and in individualchildren via entirely distinct mechanisms, constituting independentlearning problems, neither of which begins with perceptual building blocks.Specifically, I propose that children begin by learning small numbers(i.e., *one, two, three*) using the same logical resources that supportother linguistic markers of number (e.g., singular, plural). Several yearslater, children discover the logic of counting by inferring the logicalrelations between larger number words from their roles in blind countingprocedures, and only incidentally associate number words with perception ofapproximate magnitudes, in an *ad hoc* and highly malleable fashion.Counting provides a form of explanation for perception but is not causallyderived from perceptual systems.

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Logical Foundations of Computer Science

10.1007/3-540-58140-5 ◽

1994 ◽

Cited By ~ 1

Keyword(s):

Computer Science ◽

Logical Foundations

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Do Stimuli Elicit Behavior?--A Study in the Logical Foundations of Behavioristics

Philosophy of Science ◽

10.1086/287721 ◽

1960 ◽

Vol 27 (2) ◽

pp. 159-170 ◽

Cited By ~ 6

Author(s):

William W. Rozeboom

Keyword(s):

Logical Foundations

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Book Review: A Well-Reasoned, Poorly-Written Essay into the Logical Foundations of Scientific Research

Journal of Marketing Research ◽

10.1177/002224377401100336 ◽

1974 ◽

Vol 11 (3) ◽

pp. 350-351

Author(s):

Reavis Cox

Keyword(s):

Scientific Research ◽

Logical Foundations

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Special issue on ‘Program development’

Theory and Practice of Logic Programming ◽

10.1017/s1471068402001424 ◽

2002 ◽

Vol 2 (4-5) ◽

pp. 423-424 ◽

Cited By ~ 1

Author(s):

MAURICE BRUYNOOGHE ◽

KUNG-KIU LAU

Keyword(s):

Software Engineering ◽

Program Development ◽

Real World ◽

Development Process ◽

Logic Program ◽

Future Challenge ◽

Special Issue ◽

Logical Foundations ◽

The Past ◽

Specification Synthesis

This special issue marks the tenth anniversary of the LOPSTR workshop. LOPSTR started in 1991 as a workshop on Logic Program Synthesis and Transformation, but later it broadened its scope to logic-based Program Development in general.The motivating force behind LOPSTR has been a belief that declarative paradigms such as logic programming are better suited to program development tasks than traditional non-declarative ones such as the imperative paradigm. Specification, synthesis, transformation or specialisation, analysis, verification and debugging can all be given logical foundations, thus providing a unifying framework for the whole development process.In the past ten years or so, such a theoretical framework has indeed begun to emerge. Even tools have been implemented for analysis, verification and specialisation. However, it is fair to say that so far the focus has largely been on programming-in-the-small. So the future challenge is to apply or extend these techniques to programming-in-the-large, in order to tackle software engineering in the real world.

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