REITERATION (R)

CONJUNCTION ELIMINATION (&E) 

CONDITIONAL ELIMINATION (⊃E) 

CONDITIONAL INTRODUCTION (⊃I) 

NEGATION ELIMINATION (~E)

NEGATION INTRODUCTION (~I)

DISJUNCTION ELIMINATION (V E) 

or

BICONDITIONAL INTRODUCTION (≡I)

It is not the case that P

-P

p and q

p but q

p however q

p although q

p nevertheless q

p nonetheless q

p moreover q

Both p and q

P&Q

p or q

either p or q

P v Q

both either p or q and it is not the case that both p and q

(P v Q) & -(P & Q)

if p then q

p only if q

q if p

q provided that p

q given p

if p then q

P > Q

p if and oly if q

p if but only if q

p just in case q

p if and only if q

P = Q

neither p nor q

both it is not the case that p and it is not the case that q it is not the case that either p or q

-P & -Q

-(P V Q)

not both p and q

it is not the case that both p and q 

-(P & Q)

either it is not the case that p or it is not the case that q

-P V -Q

either p or q

P v Q

if it is not the case that p then q

-P > Q

if it is not the case that q then p

-Q > P

: Argument of SL is invalid in SD iff it is not valid in SD.

Sentence P of SL is a theorem in SD iff P is derivable in SD from the empty set.

Sentences P and Q are equivalent in SD iff Q is derivable in SD from {P} and P is derivable in SD from {Q}. 

A set Γ of sentences of SL is inconsistent in SD iff there is a sentence P such that both P and

~P are derivable in SD from Γ.

A set Γ of sentences of SL is consistent in SD iff it is not inconsistent in SD