Computing Information Sciences Kansas State University CIS 530 / 730: Artificial Intelligence...

Computing & Information SciencesKansas State UniversityCIS 530 / 730: Artificial Intelligence

Lecture 09 of 42

Wednesday, 17 September 2008

William H. HsuDepartment of Computing and Information Sciences, KSU

KSOL course page: http://snipurl.com/v9v3Course web site: http://www.kddresearch.org/Courses/Fall-2008/CIS730

Instructor home page: http://www.cis.ksu.edu/~bhsu

Reading for Next Class:Section 7.5 – 7.7, p. 211 - 232, Russell & Norvig 2nd edition

Logical Agents and Propositional LogicDiscussion: Logic in AI

http://snipurl.com/v9v3

http://www.kddresearch.org/Courses/Fall-2008/CIS730

http://www.cis.ksu.edu/~bhsu

http://www.cis.ksu.edu/~bhsu


Lecture Outline Reading for Next Class: Sections 7.5 – 7.7, R&N 2e

Today: Logical Agents Classical knowledge representation Limitations of the classical symbolic approach Modern approach: representation, reasoning, learning “New” aspects: uncertainty, abstraction, classification paradigm

Next Week: Start of Material on Logic Representation: “a bridge between learning and reasoning” (Koller) Basis for automated reasoning: theorem proving, other inference

Computing & Information SciencesKansas State University

Type of Training Experience Direct or indirect? Teacher or not? Knowledge about the game (e.g., openings/endgames)?

Problem: Is Training Experience Representative (of Performance Goal)? Software Design

Assumptions of the learning system: legal move generator exists Software requirements: generator, evaluator(s), parametric target

function Choosing a Target Function

ChooseMove: Board Move (action selection function, or policy) V: Board R (board evaluation function) Ideal target V; approximated target Goal: operational description (approximation) of V

V̂

Example:Learning to Play Checkers


A Target Function forLearning to Play Checkers

Possible Definition

If b is a final board state that is won, then V(b) = 100 If b is a final board state that is lost, then V(b) = -100 If b is a final board state that is drawn, then V(b) = 0 If b is not a final board state in the game, then V(b) = V(b’) where b’ is the

best final board state that can be achieved starting from b and playing optimally until the end of the game

Correct values, but not operational Choosing a Representation for the Target Function

Collection of rules? Neural network? Polynomial function (e.g., linear, quadratic combination) of board features? Other?

A Representation for Learned Function

bp/rp = number of black/red pieces; bk/rk = number of black/red kings;

bt/rt = number of black/red pieces threatened (can be taken next turn)

bwbwbwbwbwbww bV 6543210 rtbtrkbkrpbp ˆ


Training Procedure for Learning to Play Checkers

Obtaining Training Examples the target function the learned function the training value

One Rule For Estimating Training Values:

Choose Weight Tuning Rule Least Mean Square (LMS) weight update rule: REPEAT

Select a training example b at randomCompute the error(b) for this training exampleFor each board feature fi, update weight wi as follows:

where c is a small, constant factor to adjust the learning rate

bV̂ bV

bVtrain

bVbV Successortrainˆ

bVbV berror ˆ train

berrorfcww iii


Design Choices forLearning to Play Checkers

Completed Design

Determine Type ofTraining Experience

Gamesagainst experts

Gamesagainst self

Table ofcorrect moves

DetermineTarget Function

Board valueBoard move

Determine Representation ofLearned Function

Polynomial Linear functionof six features

Artificial neuralnetwork

DetermineLearning Algorithm

Gradientdescent

Linearprogramming


Knowledge Bases

Adapted from slides by S. RussellUC Berkeley


Simple Knowledge-Based Agent

Figure 6.1 p. 152 R&NAdapted from slides by S. RussellUC Berkeley

Computing & Information SciencesKansas State UniversityFriday, 14 Sep 2007CIS 530 / 730: Artificial Intelligence

Overview Today’s Reading

Sections 7.1 – 7.4, Russell and Norvig 2e Recommended references: Nilsson and Genesereth (Logical Foundations of

AI) Previously: Logical Agents

Knowledge Bases (KB) and KB agents Motivating example: Wumpus World Logic in general Syntax of propositional calculus

Today Propositional calculus (concluded) Normal forms Production systems Predicate logic Introduction to First-Order Logic (FOL): examples, inference rules (sketch)

Next Week: First-Order Logic Review, Resolution


Knowledge Representation (KR) forIntelligent Agent Problems

Percepts What can agent observe? What can sensors tell it?

Actions What actuators does agent have? In what context are they applicable?

Goals What are agents goals? Preferences (utilities)? How does agent evaluate them (check environment, deliberate,

etc.)? Environment

What are “rules of the world”? How can these be represented, simulated?


Review:Simple Knowledge-Based Agent

Adapted from slides by S. Russell, UC Berkeley Figure 6.1 p. 152 R&N


Review:Types of Logic

Adapted from slides by S. Russell, UC Berkeley Figure 6.7 p. 166 R&N


Adapted from slides by S. Russell, UC Berkeley

Propositional Logic: Semantics



Propositional Inference:Enumeration (Model Checking) Method



Normal Forms:CNF, DNF, Horn



Validity and Satisfiability



Proof Methods



Inference (Sequent) Rules forPropositional Logic


Logical Agents:Taking Stock



The Road Ahead:Predicate Logic and FOL

Predicate Logic Enriching language

PredicatesFunctions

Syntax and semantics of predicate logic First-Order Logic (FOL, FOPC)

Need for quantifiers Relation to (unquantified) predicate logic Syntax and semantics of FOL

Fun with Sentences Wumpus World in FOL



Syntax of FOL:Basic Elements



FOL: Atomic Sentences(Atomic Well-Formed Formulae)



Summary Points Logical Agents Overview (Last Time)

Knowledge Bases (KB) and KB agents Motivating example: Wumpus World Logic in general Syntax of propositional calculus

Propositional and First-Order Calculi (Today) Propositional calculus (concluded)

Normal forms Inference (aka sequent) rules

Production systems Predicate logic without quantifiers Introduction to First-Order Logic (FOL)

Examples Inference rules (sketch)

Next Week: First-Order Logic Review, Intro to Theorem Proving


Fun with Sentences:Family Feud


Brothers are Siblings

x, y . Brother (x, y) Sibling (x, y) Siblings (i.e., Sibling Relationships) are Reflexive

x, y . Sibling (x, y) Sibling (y, x) One’s Mother is One’s Female Parent

x, y . Mother (x, y) Female (x) Parent (x, y) A First Cousin Is A Child of A Parent’s Sibling

x, y . First-Cousin (x, y) p, ps . Parent (p, x) Sibling (p, ps) Parent (ps, y)


“Every Dog Chases Its Own Tail”

d . Chases (d, tail-of (d)) Alternative Statement: d . t . Tail-Of (t, d) Chases (d, t) Prefigures concept of Skolemization (Skolem variables / functions)

“Every Dog Chases Its Own (Unique) Tail”

d . 1 t . Tail-Of (t, d) Chases (d, t) d . t . Tail-Of (t, d) Chases (d, t) [ t’ Chases (d, t’) t’ = t]

“Only The Wicked Flee when No One Pursueth”

x . Flees (x) [¬ y Pursues (y, x)] Wicked (x) Alternative : x . [ y . Flees (x, y)] [¬ z . Pursues (z, x)] Wicked (x)

Offline Exercise: What Is An nth Cousin, m Times Removed?

Jigsaw Exercise:First-Order Logic Sentences


Terminology Logical Frameworks

Knowledge Bases (KB) Logic in general: representation languages, syntax, semantics Propositional logic First-order logic (FOL, FOPC) Model theory, domain theory: possible worlds semantics, entailment

Normal Forms Conjunctive Normal Form (CNF) Disjunctive Normal Form (DNF) Horn Form

Proof Theory and Inference Systems Sequent calculi: rules of proof theory Derivability or provability Properties

Soundness (derivability implies entailment) Completeness (entailment implies derivability)

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