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Material implication does not closely match the usage of conditional sentences in natural language. For example, even though material conditionals with false antecedents are vacuously true, the natural language statement "If 8 is odd, then 3 is prime" is typically judged false. Similarly, any material conditional with a true consequent is ...
In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- P {\displaystyle P} or Q {\displaystyle Q} and that either form can replace the other in ...
A material conditional formula is true unless is true and is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis had won World War Two, everybody would be happy" is vacuously true .
Import-export expresses a deductive argument form.In natural language terms, the formula states that the following English sentences are logically equivalent: [1] [2] [3]. If Mary isn't at home, then if Sally isn't at home, then the house is empty.
Material implication may refer to: Material conditional , a logical connective Material implication (rule of inference) , a rule of replacement for some propositional logic
Examples: The column-14 operator (OR), shows Addition rule : when p =T (the hypothesis selects the first two lines of the table), we see (at column-14) that p ∨ q =T. We can see also that, with the same premise, another conclusions are valid: columns 12, 14 and 15 are T.
The first premise is a conditional ("if-then") claim, such as P implies Q. The second premise is an assertion that Q, the consequent of the conditional claim, is not the case. From these two premises it can be logically concluded that P, the antecedent of the conditional claim, is also not the case. For example:
Material inference should not be confused with the following concepts, which refer to formal, not material validity: Material conditional — the logical connective "→" (i.e. "formally implies") Material implication (rule of inference) — a rule for formally replacing "→" by "¬" (negation) and "∨" (disjunction)