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  2. Substitution (logic) - Wikipedia

    en.wikipedia.org/wiki/Substitution_(logic)

    Where ψ and φ represent formulas of propositional logic, ψ is a substitution instance of φ if and only if ψ may be obtained from φ by substituting formulas for propositional variables in φ, replacing each occurrence of the same variable by an occurrence of the same formula. For example: ψ: (R → S) & (T → S) is a substitution ...

  3. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    However, in first-order logic, these two sentences may be framed as statements that a certain individual or non-logical object has a property. In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to ...

  4. S-box - Wikipedia

    en.wikipedia.org/wiki/S-box

    In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Shannon's property of confusion. Mathematically, an S-box is a nonlinear [1] vectorial Boolean function ...

  5. Unification (computer science) - Wikipedia

    en.wikipedia.org/wiki/Unification_(computer_science)

    For example, if ⊕ is associative, the unification problem { x ⊕ a ≐ a ⊕ x} has the solutions {x ↦ a}, {x ↦ a ⊕ a}, {x ↦ a ⊕ a ⊕ a}, etc., while the problem { x ⊕ a ≐ a} has no solution. For a given unification problem E, a set S of unifiers is called complete if each solution substitution is subsumed by some substitution ...

  6. Liskov substitution principle - Wikipedia

    en.wikipedia.org/wiki/Liskov_substitution_principle

    Liskov's notion of a behavioural subtype defines a notion of substitutability for objects; that is, if S is a subtype of T, then objects of type T in a program may be replaced with objects of type S without altering any of the desirable properties of that program (e.g. correctness).

  7. Change of variables - Wikipedia

    en.wikipedia.org/wiki/Change_of_variables

    Change of variables is an operation that is related to substitution. However these are different operations, as can be seen when considering differentiation or integration (integration by substitution). A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial:

  8. Corner solution - Wikipedia

    en.wikipedia.org/wiki/Corner_solution

    This diagram shows an example corner solution where the optimal bundle lies on the x-intercept at point (M,0). IC 1 is not a solution as it does not fully utilise the entire budget, IC 3 is unachievable as it exceeds the total amount of the budget. The optimal solution in this example is M units of good X and 0 units of good Y.

  9. Arene substitution pattern - Wikipedia

    en.wikipedia.org/wiki/Arene_substitution_pattern

    In meta-substitution, the substituents occupy positions 1 and 3 (corresponding to R and meta in the diagram). In para-substitution, the substituents occupy the opposite ends (positions 1 and 4, corresponding to R and para in the diagram). The toluidines serve as an example for these three types of substitution.