On logical foundations of the ATMS

2006 ◽  
pp. 125-135 ◽  
Author(s):  
Yasushi Fujiwara ◽  
Shinichi Honiden
Keyword(s):  
Logical Foundations

Logical Foundations of Proof Complexity

2009 ◽  
Author(s):  
Stephen Cook ◽  
Phuong Nguyen
Keyword(s):  
Proof Complexity ◽  
Logical Foundations

Language, procedures, and the non-perceptual origin of natural number concepts

2016 ◽  
Author(s):  
David Barner
Keyword(s):  
General Framework ◽  
Ad Hoc ◽  
Building Blocks ◽  
Number Words ◽  
Linguistic Markers ◽  
Logical Foundations ◽  
Large Numbers ◽  
Perceptual Representations ◽  
Positive Integers ◽  
Perceptual Systems

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.

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

1960 ◽  
Vol 27 (2) ◽  
pp. 159-170 ◽  
Author(s):  
William W. Rozeboom
Keyword(s):  
Logical Foundations

scholarly journals Special issue on ‘Program development’

2002 ◽  
Vol 2 (4-5) ◽  
pp. 423-424 ◽  
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.

scholarly journals Logical information theory: new logical foundations for information theory

2017 ◽  
Vol 25 (5) ◽  
pp. 806-835 ◽  
Author(s):  
David Ellerman
Keyword(s):  
Information Theory ◽  
Logical Foundations ◽  
Logical Information

scholarly journals The Logical Foundations of Scientific Theories

2016 ◽  
Author(s):  
Decio Krause
Keyword(s):  
Scientific Theories ◽  
Logical Foundations
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