FANDOM

179 Pages

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.
Natural Deduction Transformation Rules
Rules of inference
Rules of Transformation