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When most people say 'logic', they mean either propositional logic or first-order predicate logic. • However, the precise definition is quite broad, and literally hundreds of logics have been studied by philosophers, computer scientists and mathematicians. • Any 'formal system' can be considered a logic if it has:.
Propositional Logic, Truth Tables, and. Predicate Logic. (Rosen, Sections 1.1, 1.2, 1.3). TOPICS. • Propositional Logic. • Logical Operations. • Equivalences. • Predicate Logic
[Side Note. This tautology, called the law of excluded middle, is a direct consequence of our basic assumption that a proposition is a statement that is either true or false. Thus, the logic we will discuss here, so-called Aristotelian logic, might be described as a “2-valued" logic, and it is the logical basis for most of the theory of
This chapter is dedicated to one type of logic, called propositional logic. The world logic refers to the use and study of valid reasoning. Logic contains rules and techniques to formalize statements, to make them precise. Logic is studied by philosophers, mathematicians and computer scientists. Logic appears in different
Which ones of the following sentences are propositions? Ottawa is the capital of Canada. Buenos Aires is the capital of Brazil. 2+2=4. 2+2=5 if it rains, we don't need to bring an umbrella. x +2=4 x + y = z. When does the bus come? Do the right thing. CSI2101 Discrete Structures Winter 2010: Propositional Logic.
A proposition is a declarative sentence that is either true or false. Examples of propositions: The Moon is made of green cheese. Trenton is the capital of New Jersey. Toronto is the capital of Canada. 1+0=1. 0+0=2. Examples that are not propositions. Sit down! What time is it? x+1=2 x+y=z. Richard Mayr (University of
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
More precisely, in this first chapter you will be introduced to propositional logic, the logical system behind the reasoning with 'not', 'and', 'or', 'if, then' and other basic sentence-combining operators. You will get acquainted with the notions of formula, logi- cal connective, truth, valid consequence, information update, formal
2 Propositional Logic. Exercises. 2.1 Which of the following are propositions: (a) If I am wrong, then I am an idiot. (b) Choose a number between 5 and 10. (c) Have I already arrived at the town of True? (d) 7 is the largest number. (e) Numbers are odd. 2.2 The Language of Discourse. Consider the propositions 'I am carrying
Lecture 1: Propositional Logic. Syntax. Semantics. Truth tables. Implications and Equivalences. Valid and Invalid arguments. Normal forms. Davis-Putnam Algorithm. 1
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