A tensor approach to higher order expectations of quantized chaotic trajectories. I. General theory and specialization to piecewise affine Markov systems

2000 ◽  
Vol 47 (11) ◽  
pp. 1571-1583 ◽  
Author(s):  
R. Rovatti ◽  
G. Mazzini ◽  
G. Setti
Keyword(s):  
General Theory ◽  
Higher Order ◽  
Markov Systems ◽  
Piecewise Affine

A general theory of generic modelling and paradigm shifts: part 3 – the extension

Kybernetes ◽  
2015 ◽  
Vol 44 (2) ◽  
pp. 311-328 ◽  
Author(s):  
Maurice Yolles ◽  
Gerhard Fink
Keyword(s):  
General Theory ◽  
Agency Theory ◽  
Higher Order ◽  
Living Systems ◽  
Paradigm Shifts ◽  
Content Type ◽  
Simplex Model ◽  
Complex Phenomena ◽  
Cultural Agency ◽  
Simplex Models

Purpose – Anticipating behaviour and responding to the needs of complexity and problematic issues requires modelling to facilitate analysis and diagnosis. Using arguments of anticipation as an imperative for inquiry, the purpose of this paper is to introduce generic modelling for living systems theory, and assigns the number of generic constructs to orders of simplex modelling. An nth simplex order rests in an nth order simplex cybernetic space. A general modelling theory of higher orders of simplexity is given, where each higher order responds to every generic construct involved, the properties of which determining the rules of the complex system being that is represented. Higher orders of simplexity also explain greater degrees of complexity relatively simply, and give rise to the development of new paradigms that are better able to explain perceived complex phenomena. Design/methodology/approach – This is Part 3 of three linked papers. Using principles that arise from Schwarz’s living systems set within a framework provided by cultural agency theory, and with a rationale provided by Rosen’s and Dubois’ concepts of anticipation, the papers develop a general modelling theory of simplex orders. They show that with the development of new higher orders, paradigm shifts can occur that become responsible for new ways of seeing and resolving stubborn problematic issues. Part 1 established the fundamentals for a theory of modelling associated with cybernetic orders. Using this, in this Part 2 the authors established the principles of cybernetic orders using simplex modelling. This included a general theory of generic modelling. In this Part 3 the authors extend this, developing a fourth order simplex model, and exploring the potential for higher orders using recursive techniques through cultural agency theory. The authors also explore various forms of emergence. Findings – Cultural agency theory can be used to generate higher simplex through principles of recursion, and hence to create a potential for the generation of families of new paradigms. The idea of conceptual emergence is also tied to the rise of new paradigms. Research limitations/implications – The use of higher order simplex models to represent complex situations provides the ability to condense explanation concerning the development of particular system behaviours, and hence simplify the way in which the authors analyse, diagnose and anticipate behaviour in complex situations. Illustration is also given showing how the theory can explain the emergence of new paradigms. Practical implications – Cultural agency can be used to structure problem issues that may otherwise be problematic, within both a top-down and bottom-up approach. It may also be used to assist in establishing behavioural anticipation given an appropriate modelling approach. It may also be used to improve and compress explanation of complex situations. Originality/value – A new theory of simplex orders arises from the new concept of generic modelling, illustrating cybernetic order. This permits the possibility of improved analysis and diagnosis of problematic situations belonging to complex situations through the use of higher order simplex models, and facilitates improvement in behavioural anticipation.

A general theory of generic modelling and paradigm shifts: part 1 – the fundamentals

Kybernetes ◽  
2015 ◽  
Vol 44 (2) ◽  
pp. 283-298 ◽  
Author(s):  
Maurice Yolles ◽  
Gerhard Fink
Keyword(s):  
General Theory ◽  
Agency Theory ◽  
Higher Order ◽  
Living Systems ◽  
Paradigm Shifts ◽  
Content Type ◽  
Simplex Model ◽  
Complex Phenomena ◽  
Cultural Agency ◽  
Simplex Models

Purpose – Anticipating behaviour and responding to the needs of complexity and the problematic issues that they can generate requires modelling to facilitate analysis and diagnosis. Using arguments of anticipation as an imperative for inquiry, the purpose of this paper is to introduce generic modelling for living systems theory, and assigns the number of generic constructs to orders of simplex modelling. An nth simplex order rests in an nth order simplex cybernetic space. A general modelling theory of higher orders of simplexity is given, where each higher order responds to every generic construct involved, the properties of which determining the rules of the complex system being that is represented. Higher orders of simplexity also explain greater degrees of complexity relatively simply, and give rise to the development of new paradigms that are better able to explain perceived complex phenomena. Design/methodology/approach – This is part 1 of three linked papers. Using principles that arise from Schwarz’s living systems set within a framework provided by cultural agency theory, and with a rationale provided by Rosen’s and Dubois’ concepts of anticipation, the papers develops a general modelling theory of simplex orders. It shows that with the development of new higher orders, paradigm shifts can occur that become responsible for new ways of seeing and resolving stubborn problematic issues. The paper is composed of two parts. Part 1 establishes the fundamentals for a theory of modelling associated with cybernetic orders. Using this, part 2 establishes the principles of cybernetic orders using simplex modelling. This will include a general theory of generic modelling. Part 3 extends this, developing a fourth order simplex model, and exploring the potential for higher orders using recursive techniques through cultural agency theory. Findings – Cultural agency theory can be used to generate higher simplex through principles of recursion, and hence to create a potential for the generation of families of new paradigms. The idea of conceptual emergence is also tied to the rise of new paradigms. Research limitations/implications – The use of higher order simplex models to represent complex situations provides the ability to condense explanation concerning the development of particular system behaviours, and hence simplify the way in which the authors analyse, diagnose and anticipate behaviour in complex situations. Illustration is also given showing how the theory can explain the emergence of new paradigms. Practical implications – Cultural agency can be used to structure problem issues that may otherwise be problematic, within both a top-down and bottom up approach. It may also be used to assist in establishing behavioural anticipation given an appropriate modelling approach. It may also be used to improve and compress explanation of complex situations. Originality/value – A new theory of simplex orders arises from the new concept of generic modelling, illustrating cybernetic order. This permits the possibility of improved analysis and diagnosis of problematic situations belonging to complex situations through the use of higher order simplex models, and facilitates improvement in behavioural anticipation.

scholarly journals Logical Combinatorialism

2020 ◽  
Vol 129 (4) ◽  
pp. 537-589
Author(s):  
Andrew Bacon
Keyword(s):  
General Theory ◽  
Fundamental Property ◽  
Logical Truth ◽  
Higher Order ◽  
Order Logic ◽  
Higher Order Logic ◽  
Fundamental Properties ◽  
Logical Operations ◽  
The World

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality.

Many-atom interactions in the theory of higher order elastic moduli: A general theory

2013 ◽  
Vol 55 (12) ◽  
pp. 2405-2412 ◽  
Author(s):  
I. A. Osipenko ◽  
O. V. Kukin ◽  
A. Yu. Gufan ◽  
Yu. M. Gufan
Keyword(s):  
General Theory ◽  
Elastic Moduli ◽  
Higher Order

scholarly journals Metacybernetics: Towards a General Theory of Higher Order Cybernetics

Systems ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 34
Author(s):  
Maurice Yolles
Keyword(s):  
General Theory ◽  
Agency Theory ◽  
Critical Realism ◽  
Uncertainty Reduction ◽  
Living System ◽  
Higher Order ◽  
The Relationship ◽  
Local Rationality

Metacybernetics refers to the higher cybernetic orders that arise in living system agencies. Agencies are complex, and for them to be viable and hence survive, they require both stability and uncertainty reduction. Metacybernetics is defined through a metasystem hierarchy, and is mostly known through 1st and 2nd order cybernetics. In this exploratory paper the purpose is to create a framework that can underpin metacybernetics and explain the relationship between different cybernetic orders. The framework is built on agency theory which has both substructural and superstructural dimensions. Substructure has an interest in stability, is concerned with the generation of higher cybernetic orders, and is serviced by horizontal recursion. Superstructure is concerned with uncertainty reduction by uncovering hidden material or regulatory relationships, and is serviced by vertical recursion. Philosophical aspects to the framework are discussed, making distinction between global rationality through critical realism, and local rationality that relates to different cybernetic orders that correspond to bounding paradigms like positivism and constructivism.

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