Encoding and Decoding of Recursive Structures in Neural-Symbolic Systems

2021 ◽  
Vol 30 (1) ◽  
pp. 37-50
Author(s):  
A. Demidovskij
Keyword(s):  
Symbolic Systems ◽  
Recursive Structures

Numerical symbols as explanations of human perceptual experience

2018 ◽  
Author(s):  
David Barner
Keyword(s):  
Perceptual Experience ◽  
Number Words ◽  
The World ◽  
Symbolic Systems ◽  
Perceptual Systems

Why did humans develop precise systems for measuring experience, like numbers, clocks, andcalendars? I argue that precise representational systems were constructed by earlier generationsof humans because they recognized that their noisy perceptual systems were not capturingdistinctions that existed in the world. Abstract symbolic systems did not arise from perceptualrepresentations, but instead were constructed to describe and explain perceptual experience. Byanalogy, I argue that when children learn number words, they do not rely on noisy perceptualsystems, but instead acquire these words as units in a broader system of procedures, whosemeanings are ultimately defined by logical relations to one another, not perception.

Beyond the Fife and Drum: Northern Protestant Working Class Cultures

Public Voices ◽  
2017 ◽  
Vol 9 (1) ◽  
pp. 73
Author(s):  
Paul Burgess
Keyword(s):  
Northern Ireland ◽  
Working Class ◽  
World Order ◽  
Cultural Traditions ◽  
One Dimensional ◽  
Dimensional Image ◽  
The Troubles ◽  
Meaning Systems ◽  
The World ◽  
Symbolic Systems

The author contends that throughout the duration of the present conflict in NorthernIreland, the world has been repeatedly given a one-dimensional image of this culture depicting it as mainly a product of ethnicity and also a reflection of class sentiment and lived experience.As drummer and songwriter of Ruefrex, a musical band internationally renowned for its songs about the Troubles conflict in Northern Ireland, Burgess discusses the need to express Protestant cultural traditions and identity through words and music. Citing Weber’s argument that individuals need to understand the world and their environment and that this understanding is influenced by perceptions of world order and attitudes and interpretations of symbolic systems or structures, the author argues that losing the importance of symbolic structures in relation to actual events will result in failure to understand why communities embrace meaning systems that are centrally informed by symbol and ritual. In his mind, rather than seeking to promote an understanding of Protestant or Catholic reality, it is important to speculate how the practice of difference might be used in developing any kind of reality of co-operation and co-ordination

Preliminaries

2017 ◽  
Author(s):  
David J. Lobina
Keyword(s):  
Data Structures ◽  
Production Systems ◽  
Specific Data ◽  
Recursive Functions ◽  
Recursive Solution ◽  
Partial Recursive Functions ◽  
Recursive Structures ◽  
Recursive Data Structures ◽  
Recursive Data ◽  
The Relationship

Recursion, or the capacity of ‘self-reference’, has played a central role within mathematical approaches to understanding the nature of computation, from the general recursive functions of Alonzo Church to the partial recursive functions of Stephen C. Kleene and the production systems of Emil Post. Recursion has also played a significant role in the analysis and running of certain computational processes within computer science (viz., those with self-calls and deferred operations). Yet the relationship between the mathematical and computer versions of recursion is subtle and intricate. A recursively specified algorithm, for example, may well proceed iteratively if time and space constraints permit; but the nature of specific data structures—viz., recursive data structures—will also return a recursive solution as the most optimal process. In other words, the correspondence between recursive structures and recursive processes is not automatic; it needs to be demonstrated on a case-by-case basis.

Algebra

2018 ◽  
Author(s):  
Andrea Henderson
Keyword(s):  
Euclidean Geometry ◽  
Symbolic Logic ◽  
Associative Networks ◽  
Aristotelian Logic ◽  
Modern Algebra ◽  
Symbolic Systems ◽  
The Difference ◽  
Founding Principle ◽  
Conventional Symbol

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean geometry and the latter with algebra. Rather than trying to bridge this divide, practitioners of modern algebra and the pioneers of symbolic logic made it the founding principle of their work. Regarding the content of claims as a matter of “indifference,” they concerned themselves solely with the formal interrelations of the symbolic systems devised to represent those claims. In its celebration of artificial algorithmic structures, symbolic logician Lewis Carroll’s Sylvie and Bruno dramatizes the power of this new formalist ideal not only to revitalize the moribund field of Aristotelian logic but also to redeem symbolism itself, conceived by Carroll and his mathematical, philosophical, and symbolist contemporaries as a set of harmonious associative networks rather than singular organic correspondences.

Recursive Structures: Growing of Fractals and Plants

1992 ◽  
pp. 9-65
Author(s):  
Heinz-Otto Peitgen ◽  
Hartmut Jürgens ◽  
Dietmar Saupe
Keyword(s):  
Recursive Structures

scholarly journals Optimal Purely Functional Priority Queues

1996 ◽  
Vol 3 (37) ◽  
Author(s):  
Gerth Stølting Brodal ◽  
Chris Okasaki
Keyword(s):  
Data Structure ◽  
Higher Order ◽  
Priority Queues ◽  
Worst Case ◽  
Minimum Element ◽  
Asymptotically Optimal ◽  
Running Time ◽  
Recursive Structures ◽  
Functional Setting

Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time. These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt<br />Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other<br />priority queues. Each of these steps is expressed using ML-style functors. The last transformation, known as data-structural bootstrapping, is an interesting<br />application of higher-order functors and recursive structures.

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