Artificial Intelligence
CS 165A
Thursday, November 15, 2007
 Knowledge Representation (Ch 10)
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Notes
• HW assignments
– HW#4 due Wednesday (11/21), HW#5 due 12/4
• Schedule
– Three weeks left
– Knowledge representation (Ch. 10), probabilistic reasoning (Ch.
13, 14)
– What else?
 Planning
 Perception (speech, language, vision)
 Robotics
 Examples of AI research and/or applications
• Precedence of AND, OR
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Correction to 10/30 Lecture notes, slide #9
Precedence of operators (logical connectives)
•
Levels of precedence, evaluating left to right
1.  (NOT)
2.  (AND, conjunction)
3.  (OR, disjunction)
4.  (implies, conditional)
5.  (equivalence, biconditional)
•
PQR
– (P  (Q))  R
•
PQR
– P  (Q  R)
•
PQ  RS
– P  ((Q  R)  S)
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Forward and Backward Chaining
• Forward chaining
– Data driven or data directed
– New version of TELL(KB, p)
 Add the sentence p, then apply inference rules to the updated
KB until no more rules apply (“chaining” – “chain reaction”)
• Backward chaining
–
–
–
–
What form would you want your KB to be
in to best support backward chaining?
Goal oriented
ASK(KB, q)
If SUBST(, q) is in KB, return q' = SUBST(, q)
Else, find implication sentences p  q then set p as a subgoals
 Keep doing this, working “backwards”
 If p is not in KB, look for r  p, then set r as a subgoal
 Etc…..
– Backward chaining is the basis for logic programming (e.g., Prolog)
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Forward chaining example
KB = { }
1. TELL(KB, Buffalo(x)  Pig(y)  Outrun(x,y))
2. TELL(KB, Pig(x)  Slug(y)  Outrun(x,y))
3. TELL(KB, Outrun(x,y)  Outrun(y,z)  Outrun(x,z))
4. TELL(KB, Buffalo(Bob))
5. TELL(KB, Pig(Pat))
6. TELL(KB, Slug(Steve))
What happens at every step?
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Backward chaining example
KB:
Pig(y)  Slug(z)  Faster(y,z)
Slimy(z)  Creeps(z)  Slug(z)
Pig(Pat)
Slimy(Steve)
Creeps(Steve)
ASK(KB, Faster(Pat, Steve))
q
Is q in KB? No
So look for p  q
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At this point we have…
• A powerful logic (FOL) in which we can express many or
most things of interest
• Two powerful inference rules and their normal forms
– Generalized Modus Ponens
– Generalized Resolution
 Both use unification
• Ways to convert any FOL sentences (a KB) into normal
form (CNF or INF)
• Inference strategies: data-driven and goal-driven
– Forward chaining
– Backward chaining
• Search methods and a problem formulation method
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We have AI, more or less
• We can now build rational agents that receive percepts,
reason about their world and implicit goals, and act upon
their world
– Problem-solving agents
• We could also consider how to set goals and subgoals for
our agents; how to construct and execute plans that achieve
the agent’s goals
– Planning agents

Not covering in this course
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Applications of logical reasoning systems
• Logical reasoning systems often referred to as
– Knowledge-based systems
– Rule-based systems
• Two common kinds of reasoning systems
– Expert systems
Knowledge-based systems
– Production systems
Expert
systems
Production
systems
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Expert systems
• Expert system: a computer program embodying knowledge
and ability of expert in task domain
– Built with the help and guidance of human experts
– Seek to perform as well as or better than human experts on specific
tasks
– Historically rule-based (but less so now – could be probabilistic)
– Many in use in business, science, engineering, and the military
– Basic underlying theory: Horn KBs with resolution refutation
• Some examples
– Medical diagnosis (MYCIN)
– Science (DENDRAL –
chemical spectral analysis)
– Mathematics theorem proving
– Geological exploration
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–
–
–
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System repair
VLSI chip layout
Help desk
Computer system configuration
Chess
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Production systems
• A production is a condition-action rule
– An “if-then” rule: if condition then action is valid
• A production system is a knowledge-based system that
uses productions to match the state of the KB with
applicable actions
– p  q  action1
– r  action2
• Aspects of a production system
–
–
–
–
ADD(KB, p) with forward chaining
Match phase
Conflict resolution phase
Choice of action
Perceive
Reason
Act
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Production systems (cont.)
• Match phase: Which rules have left-hand sides
(“conditions”) that match the KB?
– Rules (productions) are stored separately from knowledge
– May have heuristic rules for ordering rule application
• Conflict resolution phase: Which of the matching rules
should be executed?
– I.e., which applicable action should be taken?
• Notes
– Examples of early system: R1 for configuring VAX 780s
– Led to early versions of expert systems
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Limitations of formal logic
• Formal logic sometimes doesn’t perform well in the real world
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–
–
–
“brittle” if have (hidden) contradiction in KB
Most categories have fuzzy boundaries
Most rules have exceptions
Cause/effect is usually not completely straightforward
• Examples:
– Modus ponens and science
– Medical diagnosis
PQ
Q
If a patient has the flu, the patient will have a fever.
The patient has a fever. What can be concluded?
• Issues:
–
–
–
–
–
Answer: Logically, nothing
Handling of arbitrary logical expressions
Complex semantics
Uncertainty
Computational efficiency
Human interaction
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Logic and uncertainty
• For example, consider the rule “Raining(t)  WetGrass(t)”
– Is this always true
 Can [T,F] be applicable in real world?
 What if it’s not raining?
– We’d rather know the full relationship between Raining and
WetGrass
• FOL deals with all, not all, some, none
– The real world is not so simple
• Complexity is often manifested as uncertainty
– Rather than a very large number of rules that cover every case, we
may have a few rules that capture most of the cases
– This may be a result of ignorance or laziness
• We need ways to reason about or in the presence of
uncertainty [coming soon, Ch. 13 and 14]
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Knowledge
• We’ve also mostly finessed the issues regarding what
knowledge to represent and how
– What is the domain of objects?
– How do we represent more complex knowledge than simple
predicates?
– We can describe object properties and relations between objects,
but how to describe actions, situations, and events?
– What if the state of the world changes?
– Can we reason about categories of objects?
• Chapter 10 raises these kinds of issues under the topic of
knowledge representation
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Thursday quiz
Give an English description of the following sentence in FOL
using situation calculus:
 x, s Studying(x, s)  Failed(x, Result(TakeTest, s))
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Knowledge engineering
• The process of knowledge base construction (either
special-purpose or general-purpose KBs) is called
knowledge engineering
• The knowledge engineering process:
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–
–
–
–
–
–
Identify the task
Assemble the relevant knowledge
Decide on a vocabulary of predicated, functions, and constants
Encode general knowledge about the domain
Encode a description of the specific problem instance
Pose queries to the inference procedure and get answers
Debug the knowledge base
See the electronic circuits domain example in Section 8.4
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Ontological engineering
• Ontology – a theory of the nature of being or existence
– What exists, what can be known (in a particular domain)?
• Ontological engineering builds a formal ontology for a
particular domain
– Defines categories and their relations (e.g., inheritance)
 Taxonomy of categories and subcategories
– Defines/limits what can possibly be stated, and reasoned about, in
the domain
• Would like to reason about actions, events, and situations
– Need a way to efficiently consider time, or time sequences
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Reification
• Category  Object
– Can represent basketballs using the predicate Basketball(x) or by
reifying the category as an object, Basketballs
 Member (x, Basketballs)
– Object x is a member of the category Basketballs
 Subset(Basketballs, Balls)
– Basketballs is a subcategory of Balls
– Class properties apply to specific class objects
 x must be spherical, must bounce, etc.
– “isa” (member or subclass) relationship
 subcategory isa category
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Semantic networks
• A semantic network is a directed graph consisting of
– Vertices – representing concepts
– Edges – representing semantic relations between the concepts
• “Visual logic”
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The Frame Problem
• The frame problem is the problem of expressing a dynamic
domain in logic without explicitly specifying which
conditions are not affected by an action
– If the light is on at time t1, do we have to explicitly say it’s on at
time t2?
– This can become very burdensome....
• The frame problem can be addressed (partially) with
– Including situations (Si) that describe the state of the environment
at particular points in time
 S0  S1  S2  ...
 Doesn’t have to represent equally spaced units of time
– Representing the results of actions from Si to Sj
– Having an ontology of time
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Situation Calculus – actions, events
• “Situation Calculus” is a way of describing change over
time in first-order logic
– Fluents: Functions or predicates that can vary over time have an
extra argument, Si (the situation argument)
 Predicate(args, Si)
 Location of an agent, aliveness, changing properties, ...
– The Result function is used to represent change from one situation
to another resulting from an action (or action sequence)
 Result(GoForward, Si) = Sj
 “Sj is the situation that results from the action GoForward
applied to situation Si
 Result() indicates the relationship between situations
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Situation Calculus
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Represents the world in different “situations” and the relationship between situations
Situation Calculus
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Represents the world in different “situations” and the relationship between situations
Examples
• How would you interpret the following sentences in FirstOrder Logic using situation calculus?
 x, s Studying(x, s)  Failed(x, Result(TakeTest, s))
If you’re studying and then you take the test, you will fail.
(or) Studying a subject implies that you will fail the test for that subject.
 x, s TurnedOn(x, s)  LightSwitch(x)  TurnedOff(x,
Result(FlipSwitch, s))
If you flip the light switch when it is turned on, it will then be turned off.
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