Understanding Propositional Logic Fundamentals

May 21, 2024

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A proposition is a statement that can be true or false, forming the basis of propositional logic. Different types of propositions, logical operators, and truth tables are explored, along with key concepts like tautologies, contradictions, satisfiability, equivalence, and normal forms. Examples and explanations elucidate conjunctions, disjunctions, negations, implications, and other logical rules, essential for constructing proofs in logic. The content covers essential terminology, rules of inference, and methods for logical reasoning using propositions.

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Understanding Propositional Logic Fundamentals

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Propositional Logic

Propositional Logic. Reading: C. 7.4-7.8, C. 8. Logic: Outline. Propositional Logic Inference in Propositional Logic First-order logic. Agents that reason logically. A logic is a: Formal language in which knowledge can be expressed A means of carrying out reasoning in the language

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Propositional Logic

Computational Logic Lecture 2. Propositional Logic. Michael Genesereth Autumn 2009. Ambiguity. There’s a girl in the room with a telescope. Complexity. The cherry blossoms in the spring … sank. Misleading Representation. Champagne is better than soda.

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Propositional Logic

Propositional Logic. Propositions. 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

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PROPOSITIONAL LOGIC

PROPOSITIONAL LOGIC. Most of the definitions of formal logic have been developed so that they agree with the natural or intuitive logic. But the need to put it scientifically is to avoid ambiguity.

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Propositional Logic. Russell and Norvig: Chapter 6 Chapter 7, Sections 7.1—7.4. sensors. environment. ?. agent. actuators. Knowledge base. Knowledge-Based Agent. Types of Knowledge. Procedural , e.g.: functions Such knowledge can only be used in one way -- by executing it

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Propositional Logic. Sec. 1.1-1.3 12-May. 1. Is the reasoning in your argument valid?. All MSU students are brilliant. You are an MSU student. Therefore, you are brilliant.

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Propositional Logic

Computational Logic Lecture 2. Propositional Logic. Michael Genesereth Spring 2005. Grammatical Complexity. The dog chased the cat. The dog that ate the rat chased the cat. The cherry blossoms in the spring … sank . Ambiguity. Leland Stanford Junior University

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Propositional Logic. School of Athens Fresco by Raphael Wikimedia Common s. Discrete Structures (CS 173) Madhusudan Parthasarathy, University of Illinois. Mathematical logic (symbolic logic).

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Propositional Logic. Common Argument Forms. “a shape or outline”. The many meanings of “form”. a way of being that gives something it’s character. “democracy” is a form of government. “Her form in serving tennis is very good.”. A way of doing something. Argument “form”.

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Propositional Logic

Propositional Logic. Russell and Norvig: Chapter 6 Chapter 7, Sections 7.1—7.4 Slides adapted from: robotics.stanford.edu/~latombe/cs121/2003/home.htm. sensors. environment. ?. agent. actuators. Knowledge base. Knowledge-Based Agent. Types of Knowledge.

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Propositional Logic. Lecture 2: Sep 9. Conditional Statement. If p then q. p is called the hypothesis ; q is called the conclusion. The department says:. “If your GPA is 4.0, then you don’t need to pay tuition fee.”. When is the above sentence false?.

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Propositional Logic

Propositional Logic. 6.1 Symbols and Translation. Symbols and Translation. In Propositional Logic the basic elements are statements and operators (also called connectives). Letters are assigned to simple statements only.

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Propositional Logic

Propositional Logic. Propositional Logic. A proposition is a statement that is either true or false. We give propositions names such as p , q , and r . E.g. p = “pigs have wings” q = “Obama is U.S. president” In this world anyway, p is false and q is true. Truth Tables. −.

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Propositional Logic. Sentence Restrictions. Precise use of natural language is difficult . Want a notation that is suited to precision . Restrict discussion to sentences that are: declarative either true or false but not both. Such sentences are called propositions.

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Propositional Logic. Proposition. A proposition is a statement that is either true or false, but not both. Atlanta was the site of the 1996 Summer Olympic games. 1+1 = 2 3+1 = 5 What will my CS1050 grade be?. Table 1. The Truth Table for the Negation of a Proposition.

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Propositional Logic. Propositional Language Translations Truth Tables Propositional Proofs Appendix: Model Theory. Introduction. Propositional logic studies arguments whose validity depends on “if-then,” “and,” “or,” “not,” and similar notions.

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Propositional Logic

Propositional Logic. Section 1.1. Definition. A proposition is a declarative sentence that is either true or false but not both nor neither Any proposition has a truth value {T, F}. Examples. Examples. Proposition Types. A proposition could be either simple or compound.

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PROPOSITIONAL LOGIC

PROPOSITIONAL LOGIC. Logic : Language for reasoning Propositional logic Proposition is either true or false Grass is green 2 + 5 = 5 Truth value: truth(T) or Falsity (F) of a propositon Simple porpositions: single statement Compound propositions: combination of simple propositions

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Propositional Logic

Propositional Logic. Rosen 5 th ed., § 1.1-1.2. Foundations of Logic: Overview. Propositional logic: Basic definitions. Equivalence rules & derivations. Predicate logic Predicates. Quantified predicate expressions. Equivalences & derivations. Propositional Logic.

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CMSC 471. Propositional Logic. Chapter 7.4-7.5, 7.7. Adapted from slides by Tim Finin and Marie desJardins. Some material adopted from notes by Andreas Geyer-Schulz and Chuck Dyer. Propositional logic. Logical constants : true, false

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Propositional Logic. USEM 40a Spring 2006 James Pustejovsky. Evaluation of Deductive Arguments. argument A is a deductive argument =df. A is an argument in which the conclusion is supposed to follow from the premises with necessity / with certainty deductive argument A is valid =df.

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