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The method uses Boolean theory to establish propositions essentially truth tables about necessary and sufficient 'conditions' and 'mechanisms' for an 'outcome' to occur across cases.
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According to the Boolean set theory, the membership of an element is described by exactly two crisp values.
The mathematical framework is based on a combination of set theory, Boolean operators and automata unfolding.
Several computational models on different cell signaling pathways using various mathematical methods are proposed till now, out of which the mathematical models using the Ordinary Differential Equations, Graph theory, Boolean model, Fuzzy logic, etc. are most popular and widely used (6, 49, 79 83).
Even the theory of Boolean algebras with a distinguished ideal is decidable.
A basic result of Tarski is that the elementary theory of Boolean algebras is decidable.
Since this approach is based on Boolean algebra (and probability theory), multiple state systems are unpractical.
Another interesting category of edge detectors is the logical/linear operators [21] which combine aspects of linear operators' theory and Boolean algebra.
In our study, we discovered several interesting relationships of inconsistency measurement to e.g. set theory and Boolean functions and we also report these findings.
These two processes are inverses of one another, and show that the theory of Boolean algebras and of rings with identity in which every element is idempotent are definitionally equivalent.
Based on well-established theory of Boolean random sets, this work provides scientists and engineers with simple and readily applicable results for matching combinations of Boolean random sets to observed microstructures.
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