Propositional logic
- 1. Propositional logic Prof. Neeraj Bhargava Kapil Chauhan Department of Computer Science School of Engineering & Systems Sciences MDS University, Ajmer
- 2. Introduction Propositional logic (PL) is the simplest form of logic where all the statements are made by propositions. A proposition is a declarative statement which is either true or false. It is a technique of knowledge representation in logical and mathematical form.
- 3. Example: a) It is Wednesday. b) The Sun rises from West (False proposition) c) 3+3= 7(False proposition) d) 5 is a prime number.
- 4. basic facts about propositional logic: Propositional logic is also called Boolean logic as it works on 0 and 1. In propositional logic, we use symbolic variables to represent the logic, and we can use any symbol for a representing a proposition, such A, B, C, P, Q, R, etc. Propositions can be either true or false, but it cannot be both.
- 5. Cont.. Propositional logic consists of an object, relations or function, and logical connectives. These connectives are also called logical operators. The propositions and connectives are the basic elements of the propositional logic. Connectives can be said as a logical operator which connects two sentences.
- 6. Syntax of propositional logic: The syntax of propositional logic defines the allowable sentences for the knowledge representation. There are two types of Propositions: Atomic Propositions Compound propositions
- 7. Atomic Proposition Atomic Proposition: Atomic propositions are the simple propositions. It consists of a single proposition symbol. These are the sentences which must be either true or false. Example: a) 2+2 is 4, it is an atomic proposition as it is a true fac t. b) "The Sun is cold" is also a proposition as it is a false fact.
- 8. Compound proposition Compound proposition: Compound propositions are constructed by combining simpler or atomic propositions, using parenthesis and logical connectives. Example: a) "It is raining today, and street is wet." b) "Ankit is a doctor, and his clinic is in Mumbai."
- 9. Assignment Explain Propositional logic and their types with example