Конференции ИВТ СО РАН

Abstracts

The peculiarity of some solutions acceptance problems is a bad formalization of problem field. Furthermore, sometimes the information of the field is uncertain and contradictory. Moreover, contradiction can be expressed by mutually exclusive information, which is received from different sources, and uncertainty - by absence or lack of such information. One of widespread approach to the solutions acceptance in this problem fields is usage of expert systems theory methods. However, these approaches require using of logical prove means. Classical proving based on accurate knowledge of “True” and “False” of propositions turns out unacceptable here or has limited possibilities. The reason is that the proving is based on principles of contradiction and exclusion of the third, which are unsuitable for this situation. In these cases, different variants of non-classical proving usually based on many-valued or fuzzy logics are traditionally used. It is enough in many cases. However, despite the refusal of mentioned logical principles in such logics, they are not free from the similar limitations. Particularly, a statement in many-valued logics must not have more than one meaning of truth and in these logics, there is the n’s excluding law instead of the third’s excluding law. In the fuzzy logics relationship between “True” and “False” in a statement is fixed etc.

The paper discusses one more approach to the description of incomplete and contradictory subject fields’ statement truthfulness. It is based on truthfulness notion by áTrue; Falseñ - vector, where both components (“aspect of truthfulness”) have value from the interval of [0, 1] [1]. It makes aspects “True” and “False” independent from each other, as well as it naturally admits existence of other aspects of truthfulness besides “True” and “False”. Fuzzy and some many-valued logics are special cases of such point of view. The classical logic is its special case too. The logical proving problems for such notion of truthfulness are considered here.

Литература
1. Многозначные логики с векторной семантикой/ Аршинский Л.В.; ВСИ МВД России.- Иркутск, 2003.- 46 с.: Рус.- Деп. в ВИНИТИ 13.02.03, № 281-В2003.

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