- [[Wason four-card selection task]], [[truth table]], [[logical implication]] - [[logical modeling]], [[predicate logic]], [[modal logics]], [[monadic logics]] # Idea Propositional logic is a branch of mathematics that deals with the study of logical systems, sometimes called *propositions*. It's a fundamental concept in computer science: programming, AI, formal verification, database systems, circuit design, theorem proving, compiler design, algorithms, graph theory, automata theory. It uses symbols and logical rules to analyze and understand the structure of arguments, which are a sequence of logical arguments that follow on from each other. We often use a [[truth table]] to analyze systems. We can use it to analyze arguments and identify their logical structure. Propositional logic is the backbone of [[computational thinking]]. It allows us to break down complex problems into simple statements that are easy to reason. It is like the DNA of [[computer science]]. A cognitive system that makes predictions about the world on the basis of known pieces of information. ## Proposition A proposition is a statement that is either true or false. It's a [[boolean]]: 0 or 1. Statements like "are you okay" are not propositions because they don't have a true or false value. When trying to decide if a statement is a proposition, ask yourself "Does it make sense to say the statement is true, or false?" We combine propositions to form [[compound propositions]]. ## Symbols and notation We often use $T$ to represent true and $F$ to represent false. We might use $p$ to represent one proposition and $q$ for another proposition. Operators and *logical connectives* - $\land$: and ([[conjunctive propositions]]; [[binary operator]]) - $\lor$: or ([[disjunctive propositions]]; binary operator) - $\oplus$: exclusive or ([[exclusive disjunctive propositions]]; binary operator) - $\neg$: negation ([[negation operator]]; [[unary operator]]) - $\to$: implication/implies ([[implication operator]]) These symbols, represent the *propositional variables*. The 5 *logical connectives* above are the basic building blocks using propositional logic effectively. ![[20231229123448.png]] # References - [Coursera | Online Courses & Credentials From Top Educators. Join for Free | Coursera](https://www.coursera.org/learn/an-introduction-to-logic-in-computer-science/supplement/GPpD9/what-is-propositional-logic)