The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be mode...The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be modeled using the Maximum Ordinality Principle and its associated formal language, known as the “Incipient” Differential Calculus (IDC).展开更多
On the basis of formal grammar, this paper introduces operation set θ (e.g.,vector point multiply ·, vector couple multiply * , vector set multiply X, substitution H,function F, set plus ∪, et al.) and set of s...On the basis of formal grammar, this paper introduces operation set θ (e.g.,vector point multiply ·, vector couple multiply * , vector set multiply X, substitution H,function F, set plus ∪, et al.) and set of set' s types L (e.g., ordered set, continuous(descending) ordered set, unordered set, coupled set, coordinate, et al.), and generalizes them toother word types of natural language, thus presenting the generative grammar for words―anextensible 6-element formal system {V_T, V_N, θ, L, S, P}, and takeing time words in naturallanguage as example for detailed discussion. With the colorfulness of time words of naturallanguage, time words for different natural languages assume different meaning. Generative grammarfor time words can generate not only different time words, but also their semantics (Generativegrammar of Chomsky can only produce all right sentences instead of semantics), and then, generalizesthem to other word types, e.g., accurate measure words, adjectives, etc.展开更多
文摘The main objective of this paper is to demonstrate that the internal processes of Self-Organizing Systems represent a unique and singular process, characterized by their specific generativity. This process can be modeled using the Maximum Ordinality Principle and its associated formal language, known as the “Incipient” Differential Calculus (IDC).
文摘On the basis of formal grammar, this paper introduces operation set θ (e.g.,vector point multiply ·, vector couple multiply * , vector set multiply X, substitution H,function F, set plus ∪, et al.) and set of set' s types L (e.g., ordered set, continuous(descending) ordered set, unordered set, coupled set, coordinate, et al.), and generalizes them toother word types of natural language, thus presenting the generative grammar for words―anextensible 6-element formal system {V_T, V_N, θ, L, S, P}, and takeing time words in naturallanguage as example for detailed discussion. With the colorfulness of time words of naturallanguage, time words for different natural languages assume different meaning. Generative grammarfor time words can generate not only different time words, but also their semantics (Generativegrammar of Chomsky can only produce all right sentences instead of semantics), and then, generalizesthem to other word types, e.g., accurate measure words, adjectives, etc.
