Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 7, Problem 13E
a.
Explanation of Solution
Clause
- P ⇒ Q is equivalent to ￢P ∨Q by implication elimination.
- ￢(P1 ∧· · · ∧ Pm) is equivalent to (￢P1 ∨ · ...
b.
Explanation of Solution
Clause
- A clause can have positive and negative literals.
- Let the negative literals have the form￢P1, . . . ,￢Pm and let the positive literals have the form Q1, . . . ,Qn, where the Pis and Qjs are symbols.
- Then the clause can be written as (￢P1 ∨· &#x...
c.
Explanation of Solution
Full resolution rule
- For atoms pi, qi, ri, si, then pj = qk:
- Then the full resolution rule is
p1 ∧ . . . pj . . . ∧ pn1 ⇒ r1 ∨ . . . rn2
s1 ∧ ...
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Does the fact ¬Spouse(George,Laura) follow from the facts Jim≠George and Spouse(Jim,Laura)? If so, give a proof; if not, supply additional axioms as needed. What happens if we use Spouse as a unary function symbol instead of a binary predicate?
Using resolution and proving by contradiction/refutation that "¬Cat(Sister)" is entailed by the knowledge base shown below.
Things in capital letters show that it is a constant/object, things in lower cases are variables. Convert to CNF first, then show steps using resolution and showing unifications at eat step. Be sure to reach the empty clause.
1. ∀x Cat(x) ⇒ Fluffy(x)
2. ∀x Fluffy(x) ⇒ Cute(x)
3. ∀x ∀p [Fluffy(x) ∧ Has(p,x)] ⇒ Care(x,p)
4. ∀x ∀y Careable(x) ⇒ ¬ Care(x,y)
5. Own(Claire,Sister)
Consider the wffs:φ1 ≡ p1 → (p2 → (p3 → p4))φ2 ≡ (p1 ∧ p2 ∧ p3) → p4(a) Technically speaking, neither φ1 nor φ2 is well-formed since neither is allowed by the formal syntaxof propositional logic. Correct them. Note, however, that we will freely make such trivial ’errors’ throughout this semester (as do most such courses).(b) Use truth tables (in the form defined in this course) to show that φ1 ↔ φ2.(c) After internalizing an intuitive understanding of this equality, propose an extension of it to n atoms.(d) State the number of rows in a truth table for proving the extension
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
Knowledge Booster
Similar questions
- Clearly explain the difficulty in defining terms that refer to natural kinds. Give an example to illustrate. In predicate logic, do we always know if a predicate is false if it is not true? What assumption are we making if we assume that if P is not in the knowledge base, then ¬ P is true?arrow_forwardA propositional knowledge-base KB consisting of five sentences is given below (note that "/\" is used to denote "logical and", and "\/" is used to denote "logical or", and "~" is used to denote "logical negation"): 1. (~P /\ ~Q ) -> R2. R -> S3. ~S4. P -> ~U5. U a) Explain in English (in Steps!) that KB |= Q. b) Show resolution steps that leads to KB |- Q. You should first convert the sentences in the KB into clauses.arrow_forwardGiven four propositions A, B, C, and D, how many models are there for the sentence “(C or D) and not A”?arrow_forward
- A propositional knowledge-base KB consisting of five sentences is given below (note that "/\" is used to denote "logical and", and "\/" is used to denote "logical or", and "~" is used to denote "logical negation"): 1. (~P /\ ~Q ) -> R2. R -> S3. ~S4. P -> ~U5. U (a). Explain in English that KB |= Q.(b). Show resolution steps that leads to KB |- Q. You should first convert the sentences in the KB into clauses.arrow_forwardDetermine whether or not the following statement is a tautology or not and give reasoning. If you need to, you can build a truth table to answer this question. (q→p)∨(∼q→∼p) A. This is a tautology because it is always true for all truth values of p and q. B. This is not a tautology because it is always false for all truth values of p and q. C. This is a tautology because it is not always false for all values of p and q. D. This is not a tautology becasue it is not always true for all truth values of p and q.arrow_forwardDo you see yourself using email in the not-too-distant future? The path of an email message starts with the sender and concludes with the receiver of the message. Take careful notes on everything you discover. Is there a rationale to the differences, and if so, what are they? Consider the possibility that there exist several models, each of which has a unique level of complexity (or abstraction).arrow_forward
- Determine whether these statement forms are logically equivalent. In each case, construct a truth table and include a sentence justifying your answer. Your sentence should show that you understand the meaning of logical equivalence. p ꓥ t and parrow_forwardLet p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence. a)¬q b)p∧q c)¬p∨q d)p→¬q e)¬q→p f)¬p→¬q g)p↔¬q h)¬p∧(p∨¬q)arrow_forwardDraw Semantic Network for the scenario of “The Horse and Camel are mammal, where all of them are animals can run and have eyes and the horse is brown and can jump and the camel can’t jump”.arrow_forward
- Suppose propositional sentences and knowledge-base here. We have a knowledge-base called KB. KBPrime is defined as an union of (1) KB and (2) the negation of a propositional predicate P. Answer true/false to the following questions. Note that "|=" is used to denote entailment, and "|-" is used to denote derivation through resolution. a) If KB |= P, then KB |- P. That is, if KB entails P, then KB derives (using resolution) P. b) If KB |- P, then KB |= P. c) If KBPrime |- [], then KBPrime is not satisfiable. d) If KBPrime is not satisfiable, then KBPrime |- [].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_forward1.4 Translate each of the following sentences into predicate calculus, conceptual dependencies, and conceptual graphs: 1.4.1 The student traveled to Cape Town in a university bus. 1.4.2 Students who study hard pass their exams.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education