An algebraic interpretation of 2-factor binary sufficient component cause theory

Панов, В Г; Нагребецкая, Юлия Вацлавовна

doi:10.15622/sp.26.19

Cited by 2 publications

(13 citation statements)

References 11 publications

(33 reference statements)

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“…A more rigorous formal presentation of the binary sufficient causes theory is possible on the basis of finite Boolean algebras theory. That was shown in [22,23] for two variables and in [24] for general case of n variables. An adequate mathematical apparatus is presented therein for studying a classification of factors joint action types in the binary theory of sufficient causes.…”

Section: Introductionmentioning

confidence: 71%

“…A complete description of the formalism of binary sufficient causes theory based on Boolean algebras theory is presented in [22][23][24]. The paper [24] also describes the relationship between the theory of sufficient causes and the Neyman-Holland-Rubin causality model [25].…”

Section: A Mathematical Frameworkmentioning

confidence: 99%

“…Briefly, the structure of the binary theory of sufficient causes can be described as follows [22][23][24]. The state space of a binary experiment forms a finite Boolean algebra consisting of the set of all binary vectors of length n. The response (outcome) is considered as a Boolean function on this space and the set of all responses forms the Boolean algebra of all Boolean functions defined on the state space.…”

Section: Introductionmentioning

confidence: 99%

“…Empirical symmetries [15,17,21] play an important role in the structure of a binary experiment. In the proposed formalization [22][23][24] these symmetries can be written as automorphisms on the algebra of Boolean functions.…”

Section: Introductionmentioning

confidence: 99%

“…In the usual epidemiological situation, these symmetries form a group of all symmetries of the n-dimensional cube [22][23][24]. As a result, it is impossible to distinguish the types of joint action which could be considered antagonistic (in a sense, weakening the total effect of agents) from the synergistic types (that are stronger than the sum of one-factor effects).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Joint Action of Binary Factors in the Sufficient Causes Theory and Its Classification

Nagrebetskaya¹,

Panov²

2019

IJITEE

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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.

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Section: Introductionmentioning

confidence: 71%

Section: A Mathematical Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Joint Action of Binary Factors in the Sufficient Causes Theory and Its Classification

Nagrebetskaya¹,

Panov²

2019

IJITEE

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Boolean Algebras and Classification of Interactions in Sufficient-Component Cause Model

Panov¹,

Nagrebetskaya²

2015

Int. J. of Pure and Appl. Math.

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A mathematical model of the sufficient-component cause framework is considered based on the theories of Boolean algebra. The model consists of the space of states of a binary experiment and a set of symmetries of the experiment. The space of states is a Boolean algebra of n Boolean variables where n is the number of the binary causes in the experiment. The set of symmetries of the experiment is a subgroup of the group of all automorphisms of Boolean algebra of the states of experiment. This subgroup is generated by transformations preserving a type of interaction. An experimenter should deduce these transformations from the peculiar properties of the experiment. Examples of such transformations are provided. Classification of interactions is obtained by the calculation of the orbits of action of the group of symmetries on the space of states of the experiment. It is shown that the classification of the interaction for the ordinary symmetries of sufficient causes is the same as reported in related works. Other symmetries of the binary experiment are considered as well. It is shown that the corresponding classification of the interaction types in a binary experiment depends substantially on the symmetries of the experiment. Statistical criteria of particular types of responses are proven and the problem

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An algebraic interpretation of 2-factor binary sufficient component cause theory

Cited by 2 publications

References 11 publications

Joint Action of Binary Factors in the Sufficient Causes Theory and Its Classification

Joint Action of Binary Factors in the Sufficient Causes Theory and Its Classification

Boolean Algebras and Classification of Interactions in Sufficient-Component Cause Model

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