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In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P → Q {\displaystyle P\rightarrow Q} , the inverse refers to the sentence ¬ P → ¬ Q {\displaystyle \neg P\rightarrow \neg Q} .
3 Αυγ 2024 · The converse of the conditional statement is “If Q then P.”. The contrapositive of the conditional statement is “If not Q then not P.”. The inverse of the conditional statement is “If not P then not Q.”. We will see how these statements work with an example.
Introduction to Logic. The inverse of an implication is an implication with the antecedent and consequent negated. For example, the inverse of (p ⇒ q) is (¬ p ⇒ ¬ q). Note that the inverse of an implication is not logically equivalent to the implication.
18 Μαΐ 2022 · inversion. Conversion refers to the formulation of a new proposition by way of interchanging the subject and the predicate terms of an original proposition, while retaining the quality of the original proposition. The original proposition is called the convertend, while the new proposition is called the converse. Let us consider the example below.
Inversion 15-317: Constructive Logic Frank Pfenning Lecture 12 October 12, 2017 1 Introduction The contraction-free sequent calculus can be seen as describing a decision procedure for intuitionistic propositional logic. Great! But as soon as we have a sequent with many antecedents, there are many choices of rules to apply.
30 Αυγ 2022 · The Fallacy of the Inverse. The fallacy of the inverse occurs when a conditional and the negation of its antecedent are given as premises, and the negation of the consequent is the conclusion. The general form is: \(\begin{array} {ll} \text{Premise:} & p \rightarrow q \\ \text{Premise:} & \sim p \\ \text{Conclusion:} & \sim q \end{array}\)
The inverse of the conditional \(p \rightarrow q\) is \(\neg p \rightarrow \neg q\text{.}\) The contrapositive of this new conditional is \(\neg \neg q \rightarrow \neg \neg p\text{,}\) which is equivalent to \(q \rightarrow p\) by double negation.
