2. Causes of nonmonotonicity

To identify the root cause of the" loss of knowledge", which was demonstrated in Chapter 1, it is necessary, first, to note that these arguments about the monotony of the growth of knowledge or Vice versa, its losses, suggest a linear process consisting of stages, each of which is attributed to the current expression of some knowledge, meaning.

But example 1 shows a tree structure where the most interest is the transition from b to C.

To make the elements of a complex expression correspond to the specified stages of knowledge growth, you can consider the nodes on the way from the sheet to the root of the tree, by which this expression is complicated in the process of assembling from its sub-expressions.

These (sub-)expressions here everywhere mean a number of different degrees of knowledge about the facts of "reality" (Fig.1).

For such an obvious complication of expression, it is now possible to raise questions about a new, modified understanding of monotony with the growth of knowledge-would it be useful? is it expected? which contradicts that expectation in the first-order predicate language.

Obviously, the reason we understand nemonotonnost lies in the standard procedure of interpretation, which:

there is a procedure, algorithm

generates knowledge, meaning, corresponding to the expression as a whole, because it is the main link between the world of signs and the world of non-linguistic facts

makes a true assessment of this expression, that is, indicates whether it is the correct formula or not (Fig.One)

Valid expression Invalid expression

The incoherence property of interest can be formulated as a conclusion as follows: the use of the standard interpretation procedure does not imply any connection between the facts corresponding to the whole formula and the facts described by its sub-formulas.

This means that the above reasoning about mapping podvernulas some of the facts generally inappropriate in standard logic.

However, the need to work with increasing knowledge makes it necessary to distinguish in logic the original and derived facts, as well as methods for establishing a correspondence between them, but only under the assumption of full availability and the same clarity of each participant in the reasoning process, which can be called a requirement of completeness of understanding:

introducing the standard procedure of interpretation, the logic achieves the semantic uniqueness of all the individual "views" that defines the terms of their adequacy to "reality".

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