3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is.

Slides:

Advertisements

Similar presentations

Inference in First-Order Logic

Advertisements

Artificial Intelligence 8. The Resolution Method

Inference Rules Universal Instantiation Existential Generalization

ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM] Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information.

Standard Logical Equivalences

UIUC CS 497: Section EA Lecture #2 Reasoning in Artificial Intelligence Professor: Eyal Amir Spring Semester 2004.

We have seen that we can use Generalized Modus Ponens (GMP) combined with search to see if a fact is entailed from a Knowledge Base. Unfortunately, there.

Methods of Proof Chapter 7, second half.. Proof methods Proof methods divide into (roughly) two kinds: Application of inference rules: Legitimate (sound)

For Friday No reading Homework: –Chapter 9, exercise 4 (This is VERY short – do it while you’re running your tests) Make sure you keep variables and constants.

Logic Use mathematical deduction to derive new knowledge.

13 Automated Reasoning 13.0 Introduction to Weak Methods in Theorem Proving 13.1 The General Problem Solver and Difference Tables 13.2 Resolution.

Methods of Proof Chapter 7, Part II. Proof methods Proof methods divide into (roughly) two kinds: Application of inference rules: Legitimate (sound) generation.

Quiz Propositional Logic. 1. Let A,B,C be propositions, i.e. they can take values False (F) or True (T). a) How many possible worlds are there.

Resolution in Propositional and First-Order Logic.

Normal Forms and Resolution in FOL

Resolution Proof Example Prateek Tandon, John Dickerson.

Predicate Calculus Russell and Norvig: Chapter 8,9.

First-Order Logic ECE457 Applied Artificial Intelligence Spring 2007 Lecture #7.

RESOLUTION: A COMPLETE INFERENCE PROCEDURE. I Then we certainly want to be able to conclude S(A); S(A) is true if S(A) or R(A) is true, and one of those.

PAI Recitation 3 – Logic Yuxin Chen Inference Truth tables Modus ponens Resolution …

1 Resolution in First Order Logic CS 171/271 (Chapter 9, continued) Some text and images in these slides were drawn from Russel & Norvig’s published material.

Outline Recap Knowledge Representation I Textbook: Chapters 6, 7, 9 and 10.

Inference in FOL Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 9 Spring 2004.

1 Automated Reasoning Introduction to Weak Methods in Theorem Proving 13.1The General Problem Solver and Difference Tables 13.2Resolution Theorem.

Inference and Resolution for Problem Solving

Methods of Proof Chapter 7, second half.

Knoweldge Representation & Reasoning

Inference in First-Order Logic

Inference in FOL Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 9 Fall 2004.

Artificial Intelligence

Inference in FOL Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 9 Spring 2005.

Start with atomic sentences in the KB and apply Modus Ponens, adding new atomic sentences, until “done”.

Cooperating Intelligent Systems Inference in first-order logic Chapter 9, AIMA.

CS1502 Formal Methods in Computer Science Lecture Notes 10 Resolution and Horn Sentences.

Proof Systems KB |- Q iff there is a sequence of wffs D1,..., Dn such that Dn is Q and for each Di in the sequence: a) either Di is in KB or b) Di can.

Inference in First-Order logic Department of Computer Science & Engineering Indian Institute of Technology Kharagpur.

CS1502 Formal Methods in Computer Science

Logical Agents Logic Propositional Logic Summary

1 Knowledge Representation. 2 Definitions Knowledge Base Knowledge Base A set of representations of facts about the world. A set of representations of.

ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM] Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information.

Tasks Task 41 Solve Exercise 12, Chapter 2.

ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM] Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information.

Homework #3-1: predicate logic (20%)

1CS3754 Class Notes 14B, John Shieh, Figure 2.5: Further steps in the unification of (parents X (father X) (mother bill)) and (parents bill.

Unification Algorithm Input: a finite set Σ of simple expressions Output: a mgu for Σ (if Σ is unifiable) 1. Set k = 0 and  0 = . 2. If Σ  k is a singleton,

CS Introduction to AI Tutorial 8 Resolution Tutorial 8 Resolution.

Logical Agents Chapter 7. Knowledge bases Knowledge base (KB): set of sentences in a formal language Inference: deriving new sentences from the KB. E.g.:

Intelligent Systems Predicate Logic. Outline Motivation Technical Solution – Syntax – Semantics – Inference Illustration by Larger Example Extensions.

Computing & Information Sciences Kansas State University Lecture 14 of 42 CIS 530 / 730 Artificial Intelligence Lecture 14 of 42 William H. Hsu Department.

1 Logical Inference Algorithms CS 171/271 (Chapter 7, continued) Some text and images in these slides were drawn from Russel & Norvig’s published material.

CPSC 386 Artificial Intelligence Ellen Walker Hiram College

Kansas State University Department of Computing and Information Sciences CIS 730: Introduction to Artificial Intelligence Lecture 15 of 41 Friday 24 September.

First-Order Logic ECE457 Applied Artificial Intelligence Fall 2007 Lecture #7.

Reasoning using First-Order Logic

For Wednesday Finish reading chapter 10 – can skip chapter 8 No written homework.

CS.462 Artificial Intelligence SOMCHAI THANGSATHITYANGKUL Lecture 05 : Knowledge Base & First Order Logic.

Resolution Theorem Proving in Predicate Calculus Lecture No 10 By Zahid Anwar.

Logical Agents. Outline Knowledge-based agents Logic in general - models and entailment Propositional (Boolean) logic Equivalence, validity, satisfiability.

Topics Covered since 1st midterm…

Propositional Logic Session 3

Propositional Logic Resolution

Logic Use mathematical deduction to derive new knowledge.

Artificial Intelligence

CS 416 Artificial Intelligence

PROPOSITIONAL LOGIC - SYNTAX-

Quiz Nov Logic.

Quiz Nov Logic.

Quiz Propositional Logic.

Presentation transcript:

3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is happy. 2. Anyone who studies or is lucky can pass all his exams. 3. John did not study but John is lucky. 4. Anyone who is lucky wins the lottery. (b) Convert them to conjunctive normal form (CNF). [6p] (c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is happy. 2. Anyone who studies or is lucky can pass all his exams. 3. John did not study but John is lucky. 4. Anyone who is lucky wins the lottery. (b) Convert them to conjunctive normal form (CNF). [6p] (c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is happy. 2. Anyone who studies or is lucky can pass all his exams. 3. John did not study but John is lucky. 4. Anyone who is lucky wins the lottery. (b) Convert them to conjunctive normal form (CNF). [6p] (c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is happy. 2. Anyone who studies or is lucky can pass all his exams. 3. John did not study but John is lucky. 4. Anyone who is lucky wins the lottery. (b) Convert them to conjunctive normal form (CNF). [6p] (c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

3 Logic Translate the following four English sentences to first order logic (FOL). [4p] 1. Anyone passing his history exams and winning the lottery is happy. 2. Anyone who studies or is lucky can pass all his exams. 3. John did not study but John is lucky. 4. Anyone who is lucky wins the lottery. (b) Convert them to conjunctive normal form (CNF). [6p] (c) Answer the query “Is John happy?”. Use the resolution refutation algorithm. [5p]

CNF First: Implication elimination

CNF Then: drop the ”for all” quantifiers

CNF Then: move the negation inwards

CNF Then: distribute the ”ors”

CNF Then: separate the ”and” sentences into individual sentences

Query and resolution refutation Knowledge Base (KB)

Query and resolution refutation The negation of our query

Query and resolution refutation {x/John}

Query and resolution refutation {x/John}

Query and resolution refutation {x/John; y/HistoryExam}

Query and resolution refutation {x/John; y/HistoryExam}

Query and resolution refutation {x/John}

Query and resolution refutation {x/John}

Query and resolution refutation

Query and resolution refutation