Consecutive retrieval with redundancy: an optimal linear and an optimal cyclic arrangement and their storage space requirements

Information retrieval, file organization, consecutive retrieval property, consecutive retrieval with redundancy, storage space requirements 1

Information Compression, Intelligence, Computing, and Mathematics

This paper presents evidence for the idea that much of artificial intelligence, human perception and cognition, mainstream computing, and mathematics, may be understood as compression of information via the matching and unification of patterns. This is the basis for the "SP theory of intelligence", outlined in the paper and fully described elsewhere. Relevant evidence may be seen: in empirical support for the SP theory; in some advantages of information compression (IC) in terms of biology and engineering; in our use of shorthands and ordinary words in language; in how we merge successive views of any one thing; in visual recognition; in binocular vision; in visual adaptation; in how we learn lexical and grammatical structures in language; and in perceptual constancies. IC via the matching and unification of patterns may be seen in both computing and mathematics: in IC via equations; in the matching and unification of names; in the reduction or removal of redundancy from unary numbers; in the workings of Post's Canonical System and the transition function in the Universal Turing Machine; in the way computers retrieve information from memory; in systems like Prolog; and in the query-by-example technique for information retrieval. The chunking-with-codes technique for IC may be seen in the use of named functions to avoid repetition of computer code. The schema-plus-correction technique may be seen in functions with parameters and in the use of classes in object-oriented programming. And the run-length coding technique may be seen in multiplication, in division, and in several other devices in mathematics and computing. The SP theory resolves the apparent paradox of "decompression by compression". And computing and cognition as IC is compatible with the uses of redundancy in such things as backup copies to safeguard data and understanding speech in a noisy environment

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Computing and Information Science

Cornell University Courses of Study Vol. 98 2006/200

Abstract intelligence: Embodying and enabling cognitive systems by mathematical engineering

Basic studies in denotational mathematics and mathematical engineering have led to the theory of abstract intelligence (aI), which is a set of mathematical models of natural and computational intelligence in cognitive informatics (CI) and cognitive computing (CC). Abstract intelligence triggers the recent breakthroughs in cognitive systems such as cognitive computers, cognitive robots, cognitive neural networks, and cognitive learning. This paper reports a set of position statements presented in the plenary panel (Part II) of IEEE ICCI*CC’16 on Cognitive Informatics and Cognitive Computing at Stanford University. The summary is contributed by invited panelists who are part of the world’s renowned scholars in the transdisciplinary field of CI and CC

Computing and Information Science (CIS)

Cornell University Courses of Study Vol. 97 2005/200

The Noetic Prism

Definitions of ‘knowledge’ and its relationships with ‘data’ and ‘information’ are varied, inconsistent and often contradictory. In particular the traditional hierarchy of data-information-knowledge and its various revisions do not stand up to close scrutiny. We suggest that the problem lies in a flawed analysis that sees data, information and knowledge as separable concepts that are transformed into one another through processing. We propose instead that we can describe collectively all of the materials of computation as ‘noetica’, and that the terms data, information and knowledge can be reconceptualised as late-binding, purpose-determined aspects of the same body of material. Changes in complexity of noetica occur due to value-adding through the imposition of three different principles: increase in aggregation (granularity), increase in set relatedness (shape), and increase in contextualisation through the formation of networks (scope). We present a new model in which granularity, shape and scope are seen as the three vertices of a triangular prism, and show that all value-adding through computation can be seen as movement within the prism space. We show how the conceptual framework of the noetic prism provides a new and comprehensive analysis of the foundations of computing and information systems, and how it can provide a fresh analysis of many of the common problems in the management of intellectual resources