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A Brief Intro to Propositional Logic as the Foundation of Artificial Intelligence

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28th Aug, 2020
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A Brief Intro to Propositional Logic as the Foundation of Artificial Intelligence

Propositional logic in Artificial Intelligence is one of the many methods of how knowledge is represented to a machine so that its automatic learning capacity can be enhanced. Machine Learning (ML) and Knowledge Representation and Logic (KR&R) are imperative for building smart machines that can perform tasks that typically require human intelligence.

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Propositional Logic is the Foundation of Artificial Intelligence

If we want a machine to be intelligent enough to have a dialogue with us in natural language or do complex tasks like diagnosing a medical condition, or any problem-solving and decision making, then first the machine needs to become knowledgeable about the real word. Machine learning enables a machine to grow knowledgeable through automatic and experience-based learning without being explicitly programmed.

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But the ability of automatic learning is feasible only if the machine can rightly interpret the information of our real world. However, a machine can’t understand our language, so the knowledge of the real world needs to be represented to the machine in the right manner that is readable to a computer system. Propositional logic is one of the simplest methods of knowledge representation to a machine.

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The Basic Idea of Propositional Logic

Proposition means sentences. Propositional logic applies the Boolean logic to convert our real-world data into a format that is readable to the computer. For instance, if we say ‘It is hot and humid today’, the machine won’t understand. But if we can create propositional logic for this sentence, then, we can make the machine-read, and interpret our message.

Derived from Boolean logic, the heart of propositional logic is the idea that the final output (meaning) of all propositions are either true or false. It can’t be both. 

For example, ‘Earth is round’, the output for this proposition is TRUE. If we say, ‘Earth is square’, then the output is FALSE. Propositional logic applies to those sentences where the output can only be either TRUE or FALSE. But if we refer to the sentence like ‘Some children are lazy’ then here we have two possible outputs. This preposition is TRUE for those children who are lazy, but it is FALSE for those children who are not lazy. So, for such sentences/propositions where two or more outputs are possible, propositional logic doesn’t apply.

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How Propositional Logic in Artificial Intelligence Represents Data to Machine

There are two types of prepositions, atomic and complex, that can be represented through propositional logic. Atomic means a single preposition like ‘the sky is blue’, ‘hot days are humid’, water is liquid, etc.

Complex prepositions are those, which have been formed by connecting one, two, or more sentences. In propositional logic, there are five symbols to create the syntax to represent the connection of two or more sentences. Syntax means a proper structure to represent information. Representing a propositional logic with a wrong structure is a syntax error. For example, 1+3=4 but if this information is represented has 13+=4, then it is the wrong syntax. So, the prime requirement is to represent data in the right syntax. 

Refer to the image shown below:


P.s: There are widely accepted alternative symbols as different authors can use different symbols

Propositional logic in Artificial Intelligence treats sentences as a variable, and in case of complex sentences, the first step is to break a sentence into different variables.

Example: How complex propositions can be represented through propositional logic in artificial intelligence so that a machine can understand or interpret the meaning of the propositions

Ram can play tennis (let’s take it as variable X)

Ram cannot play tennis – There is a negation in the sentence, so symbolic representation will be ˜ X

Ram can play tennis and badminton – Note, there is a new addition ‘Badminton’, let’s take it as variable Y. Now, this sentence has a Conjunction, so symbolic representation will be X ˄ Y

Ram can play tennis or badminton – Here is a Disjunction, so symbolic representation will be X ˅ Y

If Ram can play tennis then he can play badminton – There is a condition, so symbolic representation will be X → Y

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Ram can play tennis if and only if he can play badminton – It is a biconditional sentence, so symbolic representation will be X ↔ Y

Once the machine reads the massage, it applies the Boolean logic-based formulas to create the TRUE and FALSE chart to interpret the final output of a complex proposition.

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Knowledge is a key factor in machine learning. Thus propositional logic in artificial intelligence is crucial for unleashing the true potential of ML. 

If you’re interested to learn more about artificial intelligence examples, machine learning, check out IIIT-B & upGrad’s PG Diploma in Machine Learning & AI which is designed for working professionals and offers 450+ hours of rigorous training, 30+ case studies & assignments, IIIT-B Alumni status, 5+ practical hands-on capstone projects & job assistance with top firms.


Pavan Vadapalli

Blog Author
Director of Engineering @ upGrad. Motivated to leverage technology to solve problems. Seasoned leader for startups and fast moving orgs. Working on solving problems of scale and long term technology strategy.
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Frequently Asked Questions (FAQs)

1What is propositional logic in artificial intelligence?

Propositional logic is a branch of the field of logic in artificial intelligence. It is one of the two earliest branches of AI, the other being symbolic logic. Propositional logic is the study of reasoning with statements represented as propositions with a truth value. It is a logic-based approach to representation of knowledge and its processing. Propositional Logic is a mathematical representation of (human) reasoning performed by computers. It is thus a formal means to represent logical statements, such as I am a man or The table is red.

2How is propositional logic used in artificial intelligence?

Propositional logic is the foundation of artificial intelligence. It is the idea that statements can be true or false (1 or 0) and that relationships between the statements can be discovered by logical and mathematical rules. Given certain statements and their interrelatedness, AI can be used to drive computers and detect fraud, determine validity in a legal case, and make predictions based on certain assumptions.

3What are the limitations of propositional logic?

Propositional logic has a limited amount of formalisms and language, it is used in computer theory and in mathematics, but it is not suitable for natural languages. It cannot be applied in natural language since it is a formal system and it cannot be used as an underlying structure. So it is a formal system applied in a limited area of study.

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