An algebraic interpretation of the λβK-calculus and a labelled λ-calculus

An algebraic interpretation of multilayer networks is introduced in relation to conscious experience, brain and body. The discussion is based on a network model for undirected multigraphs with coloured edges whose elements are time-evolving multilayers, representing complex experiential brain-body networks. These layers have the ability to merge by an associative binary operator, accounting for biological composition. As an extension, they can rotate in a formal analogy to how the activity inside layers would dynamically evolve. Under consciousness interpretation, we also studied a mathematical formulation of splitting layers, resulting in a formal analysis for the transition from conscious to non-conscious activity. From this construction, we recover core structures for conscious experience, dynamical content and causal efficacy of conscious interactions, predicting topological network changes after conscious layer interactions. Our approach provides a mathematical account of coupling and splitting layers co-arising with more complex experiences. These concrete results may inspire the use of formal studies of conscious experience not only to describe it, but also to obtain new predictions and future applications of formal mathematical tools.

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Product of Two Commutators as a Square in a Free Group

Canadian Mathematical Bulletin ◽

10.4153/cmb-1990-032-4 ◽

1990 ◽

Vol 33 (2) ◽

pp. 190-196

Author(s):

Jonell A. Comerford ◽

Y. Lee

Keyword(s):

Free Group ◽

Mapping Class Group ◽

Class Group ◽

Mapping Class ◽

Algebraic Interpretation

AbstractWe show that, if [s,t][u, v] = x2 in a free group, x need not be a commutator. We arrive at our example by use of a result of D. Piollet which characterizes solutions of such equations using an algebraic interpretation of the mapping class group of the corresponding surface.

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Algebraic Interpretation of Image Analysis Operations

Pattern Recognition and Image Analysis ◽

10.1134/s105466181903009x ◽

2019 ◽

Vol 29 (3) ◽

pp. 389-403 ◽

Cited By ~ 2

Author(s):

I. B. Gurevich ◽

V. V. Yashina

Keyword(s):

Image Analysis ◽

Algebraic Interpretation

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Integrating Type Theory and Distributional Semantics: A Case Study on Adjective–Noun Compositions

Computational Linguistics ◽

10.1162/coli_a_00264 ◽

2016 ◽

Vol 42 (4) ◽

pp. 703-725 ◽

Cited By ~ 5

Author(s):

Nicholas Asher ◽

Tim Van de Cruys ◽

Antoine Bride ◽

Márta Abrusán

Keyword(s):

Type Theory ◽

Semantic Information ◽

Semantic Theory ◽

Formal Semantic ◽

Distributional Semantics ◽

Semantic Approach ◽

Lexical Meaning ◽

Semantic Framework ◽

Algebraic Interpretation

In this article, we explore an integration of a formal semantic approach to lexical meaning and an approach based on distributional methods. First, we outline a formal semantic theory that aims to combine the virtues of both formal and distributional frameworks. We then proceed to develop an algebraic interpretation of that formal semantic theory and show how at least two kinds of distributional models make this interpretation concrete. Focusing on the case of adjective–noun composition, we compare several distributional models with respect to the semantic information that a formal semantic theory would need, and we show how to integrate the information provided by distributional models back into the formal semantic framework.

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MORITA'S THEORY FOR THE SYMPLECTIC GROUPS

International Journal of Number Theory ◽

10.1142/s1793042111004952 ◽

2011 ◽

Vol 07 (08) ◽

pp. 2115-2137 ◽

Cited By ~ 1

Author(s):

ZHI QI ◽

CHANG YANG

Keyword(s):

Symplectic Group ◽

Discrete Series ◽

Principal Series ◽

Symplectic Groups ◽

Holomorphic Discrete Series ◽

Algebraic Interpretation ◽

Series Representations ◽

Discrete Series Representations ◽

Principal Series Representations

We construct and study the holomorphic discrete series representations and the principal series representations of the symplectic group Sp (2n, F) over a p-adic field F as well as a duality between some sub-representations of these two representations. The constructions of these two representations generalize those defined in Morita and Murase's works. Moreover, Morita built a duality for SL (2, F) defined by residues. We view the duality we defined as an algebraic interpretation of Morita's duality in some extent and its generalization to the symplectic groups.

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