HNRS 190
Freshman Honors Symposium
Index
Blog
Inference Rules
Rules for \(\wedge\)
\[\frac{X,Y}{X\wedge Y}, \frac{X\wedge Y}{X}, \frac{X\wedge Y}{Y}\]
Rules for \(\vee\)
\[\frac{X}{X\vee Y}, \frac{X\vee Y,X\vdash Z,Y\vdash Z}{Z}\]
Rules for \(\Rightarrow\)
\[\frac{X\vdash Y}{X\Rightarrow Y}, \frac{X,X\Rightarrow Y}{Y}\]
Rules for \(\Leftrightarrow\)
\[\frac{X\Rightarrow Y,Y\Rightarrow X}{X\Leftrightarrow Y}, \frac{X\Leftrightarrow Y}{X\Rightarrow Y}, \frac{X\Leftrightarrow Y}{Y\Rightarrow X}\]
Note that \(X \Leftrightarrow Y\) and \(X = Y\) are the same thing in
propositional logic.
Rules for \(\neg\)
\[\frac{X\vdash\mathsf{FALSE}}{\neg X}, \frac{\neg\neg X}{X}\]
Rules for \(\mathsf{FALSE}\)
\[\frac{X,\neg X}{\mathsf{FALSE}}\]