Common inference rules

Brunel University London

12 October 2026

CS1602: Logic and Computation 12

Rule of inference FORM Example

The “If – Therefore” rule

(Modus Ponens)

P→Q

P

∴Q

If Nara is in London, then she is in England.

Nara is in London.

Therefore, Nara is in England.

The “Not This, So Not That” rule

(Modus Tollens)

P→Q

¬Q

∴¬P

If I studied, I’d pass the test.

I didn’t pass the test.

So, I must not have studied.

The “Chain of Events” rule

(Hypothetical Syllogism)

P→Q

Q→R

∴P→R

If I wake up early, I’ll have time for breakfast.

If I have time for breakfast, I’ll be more focused.

So, if I wake up early, I’ll be more focused.

The “Process of Elimination” rule

(Disjunctive Syllogism)

P Q∨

¬P

∴Q

Either it’s raining or snowing.

It’s not raining.

So, it must not be snowing

The “Putting Things Together” rule

(Conjunction)

P

Q

∴P Q∧

I like pizza.

I like Ice cream.

So, I like both pizza and Ice cream.

The “Breaking Things Apart” rule

(Simplification)

P Q∧

∴P

It’s sunny and warm.

So, it’s sunny.

The “Adding Options” Rules

(Addition)

P

∴P Q∨ I have a dog.

So, I have either a dog or a cat.