Term
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Definition
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Term
CONJUNCTION ELIMINATION (&E) |
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Definition
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Term
CONJUNCTION INTRODUCTION (&I) |
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Definition
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Term
CONDITIONAL ELIMINATION (⊃E) |
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Definition
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Term
CONDITIONAL INTRODUCTION (⊃I) |
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Definition
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Term
NEGATION ELIMINATION (~E) |
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Definition
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Term
NEGATION INTRODUCTION (~I) |
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Definition
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Term
DISJUNCTION ELIMINATION (V E) |
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Definition
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Term
DISJUNCTION INTRODUCTION (V I) |
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Definition
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Term
BICONDITIONAL ELIMINATION (≡E) |
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Definition
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Term
BICONDITIONAL INTRODUCTION (≡I) |
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Definition
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Term
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Definition
It is not the case that P
-P |
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Term
p and q
p but q
p however q
p although q
p nevertheless q
p nonetheless q
p moreover q |
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Definition
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Term
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Definition
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Term
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Definition
both either p or q and it is not the case that both p and q
(P v Q) & -(P & Q) |
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Term
if p then q
p only if q
q if p
q provided that p
q given p |
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Definition
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Term
p if and oly if q
p if but only if q
p just in case q |
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Definition
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Term
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Definition
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)
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Term
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Definition
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 |
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Term
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Definition
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 |
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Term
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Definition
Sentence P of SL is derivable in SD from a set Γ iff there is a derivation in SD in which all the primary assumptions are members of Γ and P occurs within the scope of the primary assumptions. |
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Term
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Definition
Argument of SL is valid in SD iff the conclusion of the argument is derivable in SD from the set consisting of the premises. |
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Term
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Definition
: Argument of SL is invalid in SD iff it is not valid in SD.
Truth-functional validity
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Valid in SD
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Term
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Definition
Sentence P of SL is a theorem in SD iff P is derivable in SD from the empty set.
Truth-functional truth
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Theorem in SD
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Term
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Definition
Sentences P and Q are equivalent in SD iff Q is derivable in SD from {P} and P is derivable in SD from {Q}.
Truth-functional equivalence
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Equivalence in SD
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Term
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Definition
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.
Truth-functional consistency
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Consistency in SD
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Term
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Definition
A set Γ of sentences of SL is consistent in SD iff it is not inconsistent in SD
Truth-functional consistency
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Consistency in SD
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