Mathematical theory for this equation was presented in [2, 3] and the references therein.
Łukasiewicz's verdict on Aristotle's categorical syllogistic is, that despite its narrowness, it is "a system the exactness of which surpasses even the exactness of a mathematical theory, and this is its everlasting merit".
The authors offer "a mathematical theory for how this brain region may achieve this feat, arguing that it operates in much the same way as artificial deep networks," writes Matteo Carandini, a professor at University College London.
We argue that such a theory needs to account for the semantics of agent interaction, and propose the first mathematical theory which does this.
This very short chapter gives brief biographies of two people who made seminal contributions to the mathematical theory that underlies this book.
Both aspects of the interaction between logic and language are demonstrated in the book i.e. firstly, how logical systems are designed and modified in response to linguistic needs and secondly, how mathematical theory arises in this process and how it affects subsequent linguistic theory.
A mathematical theory can perform this function so long as it is conservative, where a mathematical theory T is conservative if, roughly, for every nominalistic theory N, T+N has no consequences for the ontology of N that are not consequences of N alone.
The deteriorating process described above is consistent with claim #3 in section 2. The mathematical theory introduced in this paper unveils an underlying mechanism that may explain the deterioration and disruption occurring massively in sentimental relationships that were initially planned to last forever.
This mathematical theory allows for explanation of mechanical interactions at the micro structural observation scales of the Hydroxyapatite (HA) biomaterials.
This "mathematical theory" relied heavily on statistical analysis, and in the process Shannon also developed a measure of the efficiency of a communications system, which he called its entropy.
