1. Knowledge Representation & Logic
Concepts: Semantic Nets & propositional logic
Readings: Semantic Nets (Winston chap. 2)
Readings: Russell & Norvig (Chap 6)
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2. Knowledge representation?
We will discuss knowledge representation from two aspects:
- knowledge representation and semantic nets
- knowledge representation that is concerned with the syntax
and semantics of the language of propositional logic
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3. Knowledge Representation
Core problem in developing an intelligent system:knowledge representation: express knowledge in a computer-tractable form
Knowledge representation: a description that incorporates information about a problem, environment, entity, ...
Primary focus of knowledge representation is two fold; -
- How to represent the knowledge one has about a problem domain
- How to reason using that knowledge in order to answer questions
or make decisions
Knowledge representation deals with the problem of how to model the world sufficiently for intelligent action
Knowledge-based agents know something about their environment and they use their knowledge together with an inference engine to reason about their environment.
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4. How essential is KR ?
A ‘problem’ involves relationships between concrete objects, abstract concepts
relationship: dependencies, constraints, independencies,...
an appropriate KR makes these explicit, and clarifies them so as to model them succinctly and without unnecessary details
once the KR is designed, then the essence of the problem is clear
good representation is key to good problem solving
once an appropriate KR is arrived at for a given problem, the problem is almost solved
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5. KR
If we didn’t have a useful KR, the problem solving algorithm would have to incorporate the problem details within itself
result (at best): unwieldy, complex algorithm
worse result (probably): cannot solve problem, because the problem definition is unclear and abstruse
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6. How do you know that a particular KR is good?
Evaluating KR
How do you know that a particular KR is good?
Explicitness:clarity is important in expressing state of problem at a glance
constraints: expressing how objects, relations influence each other
suppress irrelevant detail
transparency: easy to understand
completeness: all problem variations can be handled
concise: compact and clear
fast: quick access for reads, writes, updates
computable: their creation can be automated
A problem can be represented in more than one way
which is preferrable depends on the goals for the problem solving task and above goals
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7. Semantic Nets and Knowledge Representation
A representation can be viewed as having four components:
1. Lexical: what symbols are used (vocabulary or lexicon)
labels for objects, links
e.g.. chess pieces, board positions, board move links
e.g.. duck, farmer, moose, boat trip links
2. structural: constraints describing how symbols can be arranged
structure of KR: how are nodes and links connected?
3. semantic: the meaning or interpretation of the lexical and structural components
what are they denoting wrt the problem at hand?
4. procedural: the means to use the KR to solve a problem
may be many; likely there is one that uses that particular KR to best advantage
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8. Semantic Nets
semantic net: a representation in which nodes represent objects, links displays relations between objects, and link labels denote the particular relations
syntactically, semantic nets are labeled graphs
more than merely a data structure: the representations that nodes and links denote are important --> the semantics
due to their generality, semantic nets are the foundation of many KR schemes
they are often specialized according to the application
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9. Semantic Nets
A farmer, fox, goose and grain needs to move across a river in a boat.
Constraint: boat can only carry the farmer and one other occupant at a time.
Condition: Fox should not be left unattended with goose and goose should not be left with grains.
What should the farmer do?
Figure 2.1:(Winston P17) Problem of Farmer
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10. Semantic nets lexical: nodes, links, link labels
structural: nodes interconnected with labeled links
semantics: depends on application
procedural: include procedures to read, write, update the net
eg. Farmer problem in text
lexical:
nodes: represent configurations of farmer, goose, fox, grain, and river bank orientation
links: canoe trips
link labels: not too critical here (“canoe trip”), arrows important
structural: the connections that do not result in an eaten entity
semantic: we ascribe the semantic net our “intended interpretation” wrt the problem as a whole
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11. Example
Lintel
Right
post
left
is-supported by
GO258
G088
G083
g0075
g0034
Equivalence semantics: relates description in the representation to descriptions
in other representations with meaning
Procedural semantics: set of programs (defined) operates on descriptions
in representation
Descriptive semantics: explanations of what descriptions mean in a language we
understand (e.g above example)
Note: equivalence semantics & procedural semantics  Descriptive semantics
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12. Semantic nets
note the similarity between KR / semantic nets in AI problem solving, and data structures and computer programs
especially how an appropriate net / data structure simplifies problem solving / program
note that we can find mappings between representations
hence there is no “most powerful” net
but one net might be clearer than another
Homework: Read on taxonomy of nets described in
Winston (p.21, fig 2.2)
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13. Using semantics nets 1. matching Describe and match method:
We will look at a few examples of the use of Semantic nets
1. matching
Describe and match method:
(i) describe object using a suitable representation (i.e. in the ‘language’ you understand)
(ii) look it up in your library of known objects for
a match or until no more library descriptions found
(iii) announce success if found, or failure.
fig 2.4 Winston (p.23) see next slide
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14. Example:Matching Library object Description Rejects identify
identify object
by describing it
Rejects
identify
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15. Illustration of describe Matching and Match
Feature-based object identifier has:
(1) feature extractor: describe main characteristics of object to be identified (eg. shape, size, colour, ...)
these characteristics are used to construct a semantic net representation for this object
becomes a feature point - an abstract ‘coordinate’ in a multi-dimensional feature space
(2) feature evaluator measures feature point distance from known objects in feature space
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16. Example Area Fig 2.5: Winston p.24 4 3 2 unknown 1 8 No. of holes 16
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17. 1. feature-based identification in analogy problems
geometric analogy net:
nodes: geometric primitives (dots, circles, squares,...)
links: (i) relations between primitives (above, inside, left of, ...)
(ii) transformations: addition, deletion, expansion, contraction, rotation, reflection, and combinations of these
We then use this net representation to denote analogies: how one picture is related to another
See Fig 2.6 p.25 Winston
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18. Analogy problems
Fig 2.7
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19. Feature ID and analogy problems
in this rule, the transformation links are the key: when doing an analogy problem, we want to find an instance which duplicates these transformations (may be more than 1 transformation!)
the problem solver can create these transformations and relations automatically, using tricks from computer graphics (see figs 2.8, 2.9)
then, once we ascribe rules for all the transformations, we find the one that matches the problem specification the best
note that there many be more than one transformation per analogy
we may need to choose the best of many: need a way to judge
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