Joint Action of Binary Factors in the Sufficient Causes Theory and Its Classification
Julia V. Nagrebetskaya1, Vladimir G. Panov2

1Julia V. Nagrebetskaya, Department of Mathematics, Mechanics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg, Russia.
2Vladimir G. Panov*, Laboratory of Mathematical Modelling in Ecology and Medicine, Institute of Industrial Ecology Ural Branch of RAS, Ekaterinburg, Russia. 

Manuscript received on October 12, 2019. | Revised Manuscript received on 22 October, 2019. | Manuscript published on November 10, 2019. | PP: 2146-2153 | Volume-9 Issue-1, November 2019. | Retrieval Number: A4702119119/2019©BEIESP | DOI: 10.35940/ijitee.A4702.119119
Open Access | Ethics and Policies | Cite | Mendeley | Indexing and Abstracting
© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (

Abstract: We consider a problem of formal definition of joint action in the binary sufficient causes framework based on the theory of Boolean algebras. This theory is one of the general causality concepts in epidemiology, environmental sciences, medicine and biology. Its correct mathematical form allows us to regard the binary version of this theory as a specific application of Boolean functions theory. Within the formalism of Boolean functions, a strict definition of the joint action is given and various criteria for the presence of joint action of factors in a Boolean function are obtained. The methods previously developed for analyzing joint action in binary sufficient causes framework allows us to split all the Boolean functions into disjoint equivalence classes. The relationships among these classes however remain uncertain. In the present paper, an integer invariant is introduced which allows one to order joint action types in a certain way. We consider examples of two- and three-factor theories of sufficient causes with the ordinary epidemiological symmetry group. Estimation of the time complexity of determining the type of joint action are considered as well.
Keywords: Boolean Algebra, Boolean function, Joint Action, Group Action on a Set, Integer-valued Invariant, Sufficient Causes Theory, Time Complexity
Scope of the Article:  Classification