Inference logic example

 

Example of Inference in Logic

Scenario:

Let’s say we have the following premises:

1. Premise 1: If it rains, the ground will be wet.
   • (Symbolically: $P \rightarrow Q$)
2. Premise 2: It is raining.
   • (Symbolically: $P$)

Inference (Modus Ponens):

From these premises, we can logically infer:

Conclusion: The ground will be wet.

• (Symbolically: $Q$)

Explanation:

This follows the Modus Ponens rule of inference, which states:

$$\text{If } P \rightarrow Q \text{ and } P \text{ is true, then } Q \text{ must also be true.}$$

Generalization:

Inference in logic is the process of deriving new statements from given premises using valid rules such as:

• Modus Ponens: $P \rightarrow Q, P \Rightarrow Q$
• Modus Tollens: $P \rightarrow Q, \neg Q \Rightarrow \neg P$
• Disjunctive Syllogism: $P \lor Q, \neg P \Rightarrow Q$
• Hypothetical Syllogism: $P \rightarrow Q, Q \rightarrow R \Rightarrow P \rightarrow R$

This logical inference method is fundamental in mathematics, computer science, and AI reasoning systems.