Propositional Logic

Propositional logic, also known as sentential logic or propositional calculus, is a branch of logic that deals with statements or propositions that can be either true or false. It focuses on the logical relationships between these propositions, using symbols and rules to represent and manipulate them. There are many logical systems, including predicate logic and other higher-order logics.

Propositional logic is the simplest form of logic and serves as the foundation for more complex logical systems. It is widely used in various fields such as mathematics, computer science, and philosophy to help analyze and evaluate arguments and draw valid conclusions. In this system, propositions are typically represented by variables, connected by logical operators such as AND, OR, and NOT. The rules of propositional logic allow us to derive new propositions from given premises. It enables us to reason and make inferences based on logical principles. Furthermore, propositional logic can be implemented in computer programs to allow automated reasoning. In summary, propositional logic is a valuable tool for both humans and computer systems alike.

Terms:

• Propositions: A statement that is true or false, but not both.
• Well-formed formulas (WFF): Also called formulas, a string of logical symbols combined according to some rules that can be evaluated to true or false.
• Atoms: simple proposition (in propositional logic). Intuitively, it is a proposition that cannot be broken down into anything simpler. It can be denoted by an upper case letter.
• Connectives: It is used to connect logical formulas and can be unary or binary, i.e., it takes one or two arguments.
• Negation: A unary connective representing the word “not” and denoted by “¬”.
• Conjunction: A binary connective representing the word “and” and denoted by “∧”.
• Disjunction: A binary connective representing the word “or” and denoted by “∨”.
• Implication: A binary connective representing the word “implies” and denoted by “→”.
• Equivalence: A binary connective representing “equivalent to” and denoted by “↔”.
• Atomic proposition : A proposition without connectives.
• Compound proposition: A proposition with connectives.
• Propositional variables: A placeholder for a wff, by convention Latin alphabet for atomic propositions and Greek letters for also allowing compound propositions. In theory, an infinite set of variables is possible.