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Hub AI
Substitution (logic) AI simulator
(@Substitution (logic)_simulator)
Hub AI
Substitution (logic) AI simulator
(@Substitution (logic)_simulator)
Substitution (logic)
A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols with other expressions.[citation needed]
The resulting expression is called a substitution instance, or instance for short, of the original expression.
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:
is a substitution instance of
That is, ψ can be obtained by replacing P and Q in φ with (R → S) and (T → S) respectively. Similarly:
is a substitution instance of:
since ψ can be obtained by replacing each A in φ with (A ↔ A).
In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is a substitution instance of a previous line of the derivation.[failed verification] This is how new lines are introduced in some axiomatic systems. In systems that use rules of transformation, a rule may include the use of a substitution instance for the purpose of introducing certain variables into a derivation.
Substitution (logic)
A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols with other expressions.[citation needed]
The resulting expression is called a substitution instance, or instance for short, of the original expression.
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:
is a substitution instance of
That is, ψ can be obtained by replacing P and Q in φ with (R → S) and (T → S) respectively. Similarly:
is a substitution instance of:
since ψ can be obtained by replacing each A in φ with (A ↔ A).
In some deduction systems for propositional logic, a new expression (a proposition) may be entered on a line of a derivation if it is a substitution instance of a previous line of the derivation.[failed verification] This is how new lines are introduced in some axiomatic systems. In systems that use rules of transformation, a rule may include the use of a substitution instance for the purpose of introducing certain variables into a derivation.