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Unit 6: Formalized Symbolic Logics
Disjunctive Syllogism Notes
ϕ∨ ψ
¬ϕ
ψ
ϕ∨ ψ
¬ψ
ϕ
Rules for Biconditionals
Biconditional Introduction
ϕ→ ψ
ψ→ ϕ
ϕ↔ ψ
Biconditional Elimination
ϕ↔ ψ
ϕ
ψ
ϕ↔ ψ
ψ
ϕ
ϕ↔ ψ
¬ϕ
¬ψ
ϕ↔ ψ
¬ψ
¬ϕ
ϕ↔ ψ
ψ∨ϕ
ψ∧ϕ
ϕ↔ ψ
¬ψ ∨ ¬ϕ
¬ψ ∧ ¬ϕ
Rules of Classical Predicate Calculus
In the following rules, ϕ(β/α) is exactly like ϕ except for having the term β everywhere ϕ has the
free variable α.
Universal Introduction (or Universal Generalization)
ϕβ )
( α
∀α ϕ
Restriction 1: β does not occur in ϕ.
Restriction 2: β is not mentioned in any hypothesis or undischarged assumptions.
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