An argument (in propositional logic) is a sequence of
propositions. All but the final proposition are called premises. The last
proposition is the conclusion. The argument is valid iff the truth of all
premises implies the conclusion is true.
In this discussion, we are using a notation where, hypotheses
are written in a column, followed by a horizontal bar, followed by a line that
begins with the therefore symbol with the conclusion.
Addition
P
----------------
∴P∨Q
Disjunctive Syllogism
P∨Q
¬P
----------------
∴Q
Conjunction
P
Q
----------------
∴P∧Q
Hypothetical Syllogism
P→Q
Q→R
----------------
∴ P→R
Simplification
P∧Q
----------------
∴P
Constructive Dilemma
(P→Q)∧(R→S)
P∨R
----------------
∴Q∨S
Modus Ponens
P→Q
P
----------------
∴Q
Destructive Dilemma
(P→Q)∧(R→S)
¬Q∨¬S
----------------
∴¬P∨¬R
Modus Tollens
P→Q
¬Q
----------------
∴¬P
Resolution
P∨Q
¬P∨R
----------------
∴ Q∨R
How to build arguments using the rules of inference
1. I t is
not sunny this afternoon and it is colder than yesterday.
2. If we
go swimming it is sunny.
3. If we
do not go swimming then we will take a canoe trip.
4. If we
take a canoe trip then we will be home by sunset.
5. We
will be home by sunset
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