ISSN 0032-9460, Problems of Information Transmission, 2011, Vol. 47, No. 4, pp. 353–363.
Pleiades Publishing, Inc., 2011.
Original Russian Text
A.V. Zhozhikashvili, V.L. Stefanuk, 2011, published in Problemy Peredachi Informatsii, 2011, Vol. 47, No. 4,
Properties of a Folded Category Constructed
from a Category and a Lattice
A. V. Zhozhikashvili and V. L. Stefanuk
Kharkevich Institute for Information Transmission Problems,
Russian Academy of Sciences, Moscow
Received January 26, 2010; in ﬁnal form, August 9, 2011
Abstract—Previously, employing the apparatus of category theory for abstract description
of knowledge in production-type systems was shown to be reasonable. Interest towards ap-
plying the obtained techniques to so-called dynamic expert systems, which allow for variation
of data and knowledge in the course of system functioning, required a certain generalization
of previously developed category theory apparatus related to consideration of so-called folded
categories. The paper is devoted to the study of some properties of such categories.
A production system is an information processing system allowing to deal with aggregative
information units, which are referred to as knowledge in the literature. The authors of the present
paper have been studying such systems for many years, and ﬁnally they came to a much more
general interpretation of a production than what is generally accepted in the literature devoted to
such systems. Under this extended interpretation, many systems which are traditionally reckoned
among other types of knowledge-related systems can be attributed as production systems.
Many researchers who developed production systems proposed various ways of formal description
of such systems. However, all of them are intended for particular structures of data that the
corresponding systems work with, and cannot be extended to productions in a wide interpretation
as understood by the authors of the present paper. To construct a formalism describing productions
in the most general form, the authors address to the language of category theory . The language
of CT productions created by them [2–6] makes it possible to formulate rather vague concepts
occurring in the description of functioning of production system, such as, for instance, “a production
is applicable in some situation.”
Another incentive for the research (the present paper being a part of this research) was the
authors’ many years of study of so-called dynamic expert systems, ﬁrst introduced in . Opera-
tion of such systems allows for revision of previously obtained data, which might lead to rejecting
previously made logical conclusions and replacing them with others. In particular, in  there is
proposed a quasi-static realization of a dynamic expert system in which a static expert system is
“restarted,” which makes it possible to revise data previously introduced and knowledge thereby
For some time, these two lines of our research—development of a universal enough language for
description of intelligent systems and description of functioning of dynamic expert systems —did
Supported in part by the Russian Foundation for Basic Research, project nos. 07-07-00391 and 09-07-
00233, and Presidium of the Russian Academy of Sciences, Program no. 211.