Mon, Mar 4, 2019
Kleene, “Representation of Nerve Nets…”
In this paper, Kleene writes about how an organism or robot is analogized to human beings by way of certain stimuli and actions.
Kleene references much of the work from McCulloch and Pitts, who in their fundamental paper on logical analysis of nervous activity formulate assumptions about how to interpret the neurophysiology of certain human species. These abstractions are effective in the way they identify an “all-or-nothing” firing.
The firing of neurons is also presented as a logic gate. For example, $N_1$ and $N_2$ both firing at time p is distinct from $N_2$ only firing. Depending on the circumstances and occurrence of these events, the all-or-nothing feature of these neurons firing may be necessary for understanding the broader usage.
Kleene should restrict the different events to be represented by a matrix, in which the lag and the events are represented in time series, for certain t.
The logic of certain AND, OR, and BUT are apparent in how te neural nets are created and accepted in due course. Symbolic logic is a good way o systematize the neural network, and such diagrams drawn by Hilbert-Ackermann describe these events.
The method of treating a principal conjunctive normal form depends on disjunction between various factors. For example, if the principal disjunctive normal form has n terms, the principal conjunctive normal form has $2^kx - n$ factors and vice versa.
Is there a certain simplicity in how we are to model the human brain and the human cognitive system? How does this simplicity compare to other forms of human actions and reasoning?
Chomsky, “Three Models for the Description of Language”
Chomsky, the father of human linguistics is known for his model of language, particularly, the way he identifies central problems in descriptive study of language.
Chomsky writes that the grammar of language is best viewed as a theory of structure of language and that grammar is based on finite number number of observed sentences, known as the linguist’s corpus. If a large corpus of English does not contain either sentence 1 or sentence 2, we will decide for ourselves that grammar taken in isolation provides a very strong test for understand the whole branch of linguistics. A finite-state grammar G is a system with a finite number of states.
Finite-state language L is the set of sentences generated by some finite-state grammar G. In English, that means our sentences are largely structured around grammatical relationships that depend on certain structures more than other structures.
A language is best viewed as a “kernel” of basic sentences with a set of transformations applied to kernel sentences or earlier transforms to produce new and more complicated sentences from elementary components. This reduces the immense complexity of actual language and furthers the understanding of language.