A sentence is a tautology if and only if every row of the truth table for it evaluates to true. A statement is a declaratory sentence which is true orfalse but not both. 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. All men are mortal. De nition 5. ! Propositional logic 1. Two sentences are logically equivalent if they have the same truth value in each row of their truth table. Some trees have needles. 2.3 Negation Our last basic logical operator is negation, a fancy way to say \not." We also need variables to represent propositions: propositional variables. This is just one of many examples where the semantics of expressions in natural language is NOT properly modeled by the semantics of classical propositional logic. ! In those examples, \(x\) and \(y\) probably stand for numbers. PREPOSITIONal LOGIC 2. Let p be a proposition. e.g. X > 3. ! Propositional Logic: Contents Syntax and Semantics of Propositional Logic Satisfiability (SAT) Tableau Algorithm for SAT Structural induction Semantic consequence and logical equivalence Conjunctive and disjunctive normal form (CNF and DNF) Logic in Computer Science 2 The negation of p, denoted :p, is a proposition that is true when p is false, and false when p is true. Typically use letters \(p,q,r,s,\ldots\) for propositional variables. In other words , a statement is adeclarative sentence which has a definate truth table. Predicate Logic ! This Demonstration uses truth tables to verify some examples of propositional calculus. Predicate logic can express these statements and make inferences on them. Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).. 3. understanding of propositional logic. For a proposition \(p\), we can ask if \(p\) is true or false. Some statements cannot be expressed in propositional logic, such as: !

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