Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 11E
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Sentence in CNF
- Each possible world can be written as a conjunction of literals.
- Asserting that a possible world is not the case can be written by negating that...
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Use the laws of propositional logic (logical equivalences) to show the following equivalency by choosing to change one, and only one, side of the equivalence expression.
(¬p→q)∨¬q ≡ T
What is the difference between ‘⊢’ and ‘⊨’. In giving your answer, briefly describe the two (equivalent) notions of validity we have given for truth-functional logic. (2-4 sentences
Artifical Intelligence
Suppose you are given some facts in First-Order Logics:
a) Andi is a professor
b) All professors are people.
c) Ani is the dean.
d) All Deans are professors.
e) All professors consider the dean a friend or don’t know him.
f) Everyone is a friend of someone.
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h) Andi criticized Ani.
Prove that: Ani is not Andi’s friend
Chapter 7 Solutions
Artificial Intelligence: A Modern Approach
Ch. 7 - Suppose the agent has progressed to the point...Ch. 7 - (Adapted from Barwise and Etchemendy (1993).)...Ch. 7 - Prob. 3ECh. 7 - Which of the following are correct? a. False |=...Ch. 7 - Prob. 5ECh. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - We have defined four binary logical connectives....Ch. 7 - Prob. 9ECh. 7 - Prob. 10E
Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - A sentence is in disjunctive normal form (DNF) if...Ch. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27E
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- Propositional logic lacks a general mechanism for deriving facts from other facts. A) True B) Falsearrow_forwardWith illustrations explain the various connectives used in propositional logic. Translate the following Propositional Logic to English sentences. Let: E=Laron is eating H=Laron is hungry E ⇒ ¬H E ∧ ¬H ¬(H ⇒ ¬E)arrow_forwardLogic's potential uses need to be taken into account (propositional and predicate).arrow_forward
- . Use truth tables to prove the following distributive properties for propositional logic. (a) p ∧ (q ∨ r) is logically equivalent to (p ∧ q) ∨ (p ∧ r). (b) p ∨ (q ∧ r) is logically equivalent to (p ∨ q) ∧ (p ∨ r).arrow_forwardSimplify using the Logical Equivalence Laws or Algebra of Propositions. Do not simplify by indicating the binaries. 22. (~P -> (P -> Q)) -> (Q -> (P -> P))arrow_forwardIn the context of Propositional Logic, using letters to denote sentences components, translate the following compound sentences into symbolic notation. In the translation indicate clearly the meaning of each propositional letter: A. Roses are red and violets are blue. B. Whenever violets are blue, roses are red and sugar is sweet. C. Roses are red only if the violets are not blue and the sugar is sour. D. Roses are red and if sugar is sour then violets are not blue or sugar is sweetarrow_forward
- prove that every compound proposition is logically equivalent to one whose only operation is NOR.(follow Rosen's outline)arrow_forwardWrite this English sentence in propositional logic: - It’s raining whenever I carry an umbrella.arrow_forwardIn modal logic, what is the duality between necessity and possibility? Provide examples of modal dualities.arrow_forward
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