The section of related work is organised in two streams namely, a section of first order logic calculus and a section of encryption algorithms.
Mathematical Logic
Definition 1: A Model is a set D and a function f such that:
The function f assigns each constant to a member of D.
The function f assigns each unary predicate to a subset of D.
The function f assigns each binary predicate to a subset D × D.
The basic idea is that a set of constants and predicates are paired with elements from the set of elements of the model. In other words, each constant can be paired directly with an element of the model. For, example, if our model includes an individual called John, then, we might pair the constant “a” with the individual John.
Let us consider predicates. An expression like G (a) is true just in case f (a) is in the subset of D that f assigns G to. For example, if “a” is paired with “John” and John is in the set of D that G is paired with, f (a) = John and John ∈ f(G), then G(a) is true.
In the same way, H (a, b) is true just in case “(a, b)” is in the subset of D × D that f assigns H to. For example, if we take D to be the set of words of English and we take H to be the relation has fewer letters than, then H (a, b) is true just in case the elements we pair constant “a” and constant “b” which are in the set of ordered pairs defined by f (H). For example, if f (a) = table and f (b) = vase, then (table, vase) ∈ f (H) and H (a, b) is true.
Note that there is not requirement that there be a single model. AQ logical system can be paired with any number of models. A more detailed description can be found in (Mendelson, 2009).