Cantor was led to the study of arbitrary, abstract sets in his effort to understand the structure of some specific sets of real numbers or pointsets, and the theory which he created still exhibits today these tw
Along with systematical studying proper algebraic structure of formal axiology of nature, the axiomatic (hypothetic-deductive) method is used in this research as well. The investigation accomplishments are the followings. Galileo Galilei principle of relativity of motion has been represented in a two-...
Like Hilbert he characterized the structure of a two-dimensional manifold F by a system of neighbourhoods Up, each of which, U ⊂ F would contain p and be supplemented by a bijective map ψ: U→ V∈ ℂ, with V an open disk with center ψ(p). The totality of neighbourhoods was ...
The pretrained large language model has made significant progress in intelligent question-answering, reading comprehension, and other aspects. This paper refers to a rule-based mathematical model-the multidimensional axiomatic fuzzy set (AFS) model and e
Nonetheless, we can safely conclude that in adopting the causal interpretation of counterfactuals, together with the representational and algorithmic machinery of modi - able structural equation models, we are not introducing any restrictions on the structure of counterfactual statements in recursive systems...
It gives a comprehensive approach to quality. Implementing this system could prove challenging in specific industries but the earlier it is introduced in your company or organization, the sooner and better will be the results as well. Structure of the Course This course gives guidance for producing...
Many computer scientists advocate using axiomatic methods (such as algebraic specification) to specify a program data domain—the universe of abstract... R Cartwright - Acm Conference on Lisp & Functional Programming 被引量: 49发表: 1980年 Establishing the Riemannian structure of space-time by means...
definition of the natural numbers and their fulfillment of the Peano axioms. Also the concept of recursion is discussed. Although the presentation is axiomatic the results shall match the mathematical usage. Therefore the set theoretic axiom system of A. P. Morse and J. L. Kelley ...
Our abstract system has many models, including both classical and quantum examples. Keywords: axiomatic thermodynamics; information; entropy; Maxwell's demon 1. Introduction Axiomatic approaches to physics are useful for exploring the conceptual basis and logical structure of a theory. One classic ...
The great advantage of the axiomatic method is that it makes totally explicit just what our initial assumptions are. It is sometimes said that “mathematics can be embedded in set theory.” This means that mathematical objects (such as numbers and differentiable functions) can be defined to be ...