rules-of-inference

Rules Of Inference

Propositional rules are still applicable in FOL. In addition there are two more rules in FOL.

Universal Instantiation

$$\frac{\forall xP(x)}{P(a),a\in C}$$

It says that if for all $x$ on $P(x)$ is $true$ then $P(a)$ also holds $true$. That is, if for all values for $x$, if the formula turns out to be $true$, then formula for $a$ in $P(a)$ will also holds $true$.

For instance,

$$\text{displaylines}\frac{\forall x(Man(x)\to Mortal(x))}{Man(Socrats)\to Mortal(Socrats)}$$

Generalisation

$$\frac{P(a)}{\exists xP(x)}$$

It says that if, $P(a)$ is true, then some of $x$ for $P(x)$ also holds true.

For instance,

$$\text{displaylines}\frac{Student(Hemant)\wedge Bully(Hemant)}{\exists xStudent(x)\wedge Bully(x)}$$