FANDOM


Modis Ponens, also known as Conditional Elimination and Modus ponendo ponens [1][2], is a rule of inference in propositional logic that states that if we have a material condtional that has a true antecedent, then we may infer the consequent of the antedent. In other words, if P implies Q is true and P is true, then we may infer that Q is true. This is often stated symbolically in rule form as:


\frac{P \rightarrow Q, P}{\therefore Q.}

In sequent notation, it could be expressed as:

P \rightarrow Q, P \vdash Q.

As a theorem of propositional logic, it is expressed as: ((P \rightarrow Q)\wedge P) \rightarrow Q).

In all three expressions above, P and Q are metasyntactic variables representing well-formed formulas of propositional logic.

ReferencesEdit

  1. Ikenaga, B. "Rules of Inference and Logic Proofs". Retrieved from http://sites.millersville.edu/bikenaga/math-proof/rules-of-inference/rules-of-inference.htmlhttp://sites.millersville.edu/bikenaga/math-proof/rules-of-inference/rules-of-inference.html.
  2. Margaris, A. (1967). First Order Mathematical Logic. Blaisdell Publishing Company.

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.