Rules of Inferences-Definition & Types of Inference Rules-Discrete Maths |Math for Computer Science
Rule of Inference
A key idea in mathematics, logic, and computer science are rules of inference. They offer a set of guidelines that enable us to draw logical inferences from a collection of presumptions. Artificial intelligence, computer programming, and computer systems analysis all heavily rely on Rules of Inference in the subject of computer science. Students studying computer science should be aware of the Rules of Inference since it will aid in the development of their critical thinking abilities and their understanding of how to create strong arguments and proofs. The terms "Logic," "Propositional Logic," "Deductive Reasoning," "Logical Reasoning," "Mathematics," "Philosophy," and "Critical Thinking" are among the most popular ones when it comes to Rules of Inference.
Let us consider the following example.
Example 1: Read the following “obvious” statements:
All Greeks are philosophers.
Socrates is a Greek.
Therefore, Socrates is a philosopher.
This conclusion seems to be perfectly correct, and quite obvious to us. However, we cannot justify
it rigorously since we do not have any rule of inference. When the chain of implications is more
complicated, as in the example below, a formal method of inference is very useful.
Example 2: Consider the following hypothesis:
1. It is not sunny this afternoon and it is colder than yesterday.
2. We will go swimming only if it is sunny.
3. If we do not go swimming, then we will take a canoe trip.
4. If we take a canoe trip, then we will be home by sunset.
From this hypothesis, we should conclude:
We will be home by sunset.
We shall come back to it in Example 5.
The above conclusions are examples of a syllogisms defined as a “deductive scheme of a formal
argument consisting of a major and a minor premise and a conclusion”.
Syllogism, a mode of argument that forms the core of the body of Western logical thought.
Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years.
We shall now discuss rules of inference for propositional logic. These
rules provide justifications for steps that lead logically to a conclusion from a set of hypotheses.
Because the emphasis is on correctness of arguments, these rules, when written as a proposition, are tautologies. Recall that a tautology is a proposition that is always true.
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