## LOGICAL SYNTAXLogic, like ordinary language,
has a syntax, a set of rules determining which strings of symbols are meaningful
within a particular language. When a string of symbols satisfies the syntax
rules, that string is said to be Definitions:
With these definitions we can now define a WFF
NO other formula is a WFF!
*We will, for the sake of simplicity, allow a formula which Each compound WFF is a .statement
formRemember, our 5 basic statement forms are:
Remember, in a statement form
the lower case letters are , they do not change.
constants
A compound WFF Φ is a
substitution instance of the statement form Ψ if, but only if,
Φ can be obtained by replacing each Here's how it works: The compound WFF (P → Q) (if you doubt that this is a WFF, check it using the formal definition above) is a substitution instance of p → q because if we replace the p in p → q with P and the q with Q we get (P → Q) in which the constant (in red) remains the same, but each sentential variable (in green and blue, respectively) are replaced by WFF's of the appropriate color. To take a more complex example, the compound WFF [(P → Q) → (~R ● S)] is a substitution instance of p → q because if we replace the p in p → q with (P → Q) and the q with (~R ● S) we get [(P → Q) → (~R ● S)]. Finally,
~((P
→ (Q
▼ ~R)) ↔ ((Q ● P)
→
P)) is a substitution instance of ~p.
In this example the negated WFF, ((P
→ (Q
▼ ~R)) ↔
((Q ● P)
→
P)) is a substitution instance of
p
↔
q.
The left hand side of the biconditional,
(P
→
of the second conditional,
(Q
●
P),
is a substitution instance of
p ●
qantecedent |

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