AI3391 Artificial Intelligence session 24 knowledge representation.pptx

1. AI3391 ARTIFICAL INTELLIGENCE
(II YEAR (III Sem))
Department of Artificial Intelligence and Data
Science
Session 24
by
Asst.Prof.M.Gokilavani
NIET
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2. TEXTBOOK:
• Artificial Intelligence A modern Approach, Third Edition,
Stuart Russell and Peter Norvig, Pearson Education.
REFERENCES:
• Artificial Intelligence, 3rd Edn, E. Rich and K.Knight
(TMH).
• Artificial Intelligence, 3rd Edn, Patrick Henny Winston,
Pearson Education.
• Artificial Intelligence, Shivani Goel, Pearson Education.
• Artificial Intelligence and Expert Systems- Patterson,
Pearson Education.
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3. Topics covered in session 24
• Logical Reasoning: Knowledge-Based Agents
• Propositional Logic
• Propositional Theorem Proving
• Effective Propositional Model Checking
• Agents Based on Propositional Logic
• First order logic
• Syntax and semantics
• Knowledge representation and engineering
• Inference and first order logic
• Forward and backward chaining
• Inference
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4. What is Ontology?
• Ontology can be defined as “the science or
study of being” and it deals with the nature of
reality.
• It is a system of belief that reflects an
interpretation of an individual about what
constitutes a fact.
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5. Ontological Engineering
• Ontologies are constructed using knowledge representation
languages and logics. An ontology consists of a set of
concepts, axioms, and relationships that describe a domain of
interest .
– Create more general and flexible representations.
– Concepts like actions, time, physical object and beliefs
– Define general framework of concepts
– Upper ontology
– Limitations of logic representation
• Red, green and yellow tomatoes: exceptions and
uncertainty
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6. Ontological Engineering
• Representing a general-purpose ontology is a
difficult task called ontology engineering
• Existing GP Ontologies have been created in
different ways:
• By team of trained oncologists
• By importing concepts from database(s)
• By extracting information from text documents
• By inviting anybody to enter commonsense knowledge
• Ontological engineering has only been partially
successful, and few large AI systems are based on
GP ontologies (use special purpose ontologies).
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7. • Each link indicates that the lower concept is a
specialization of the upper one. Specializations are not
necessarily disjoint; a human is both an animal and an
agent, for example.
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8. Categories and objects
Two choices for representation:
• Predicate
– Basketball(b)
• Object
– Basketballs
– Member(b, Basketballs)
– Subset(Basketballs, Balls)
• Categories - Organizing
Inheritance:
– All instances of the category Food are edible
• Fruit is a subclass of Food
• Apples is a subclass of Fruit
– Therefore, Apples are edible
• The Class/Subclass relationships among Food, Fruit and Apples is a
taxonomy.
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9. Categories- partitioning
• Disjoint: The categories have no members in common
– Disjoint(s)⇔(∀ c1,c2 c1 ∈ s ∧ c2 ∈ s ∧ c1 ≠ c2 ⇒ Intersection(c1,c2)
={})
– Example: Disjoint({animals, vegetables})
• Exhaustive Decomposition: Every member of the category is
included in at least one of the subcategories
– E.D.(s,c) ⇔ (∀ i i ∈ c ⇒ ∃ c2 c2 ∈ s ∧ i ∈ c2)
– Example: Exhaustive Decomposition( {Americans, Canadian,
Mexicans}, North Americans).
• Partition: Disjoint exhaustive decomposition
– Partition(s,c) ⇔ Disjoint(s) ∧ E.D.(s,c)
– Example: Partition({Males, Females},Persons).
– Is ({Americans, Canadian, Mexicans},North Americans) a partition?
– No! There might be dual citizenships.
• Categories can be defined by providing necessary and sufficient
conditions for membership
– ∀ x Bachelor(x) ⇔ Male(x) ∧ Adult(x) ∧ Unmarried(x)
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10. Categories and Objects Natural Kinds
• Many categories have no clear-cut definitions (chair, bush,
book).
• Tomatoes: sometimes green, red, yellow, black, mostly round.
• One solution: category Typical(Tomatoes)
– ∀x x ∈ Typical(Tomatoes) ⇒ Red(x) ∧ Spherical(x)
• We can write down useful facts about categories without
providing exact definitions
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11. Physical composition
• Physical composition
– One object may be part of another:
• PartOf(Seoul, South koarea)
• PartOf(South korea, East Asia)
• PartOf(East Asia, Asia)
• The PartOf predicate is transitive (and reflexive)
• so we can infer that PartOf(Seoul, Asia)
• More generally:
– ∀ x PartOf(x,x)
– ∀ x,y,z PartOf(x,y) ∧ PartOf(y,z) ⇒ PartOf(x,z)
• Often characterized by structural relations among parts.
• E.g. Biped(a) ⇒
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12. Categories and Objects Measurements
• Objects have height, mass, cost, ....
• Values that we assign to these are measures
• Combine Unit functions with a number:
– Length(L1) = Inches(1.5) = Centimeters(3.81).
• Conversion between units:
– ∀ i Centimeters(2.54 x i)=Inches(i).
• Some measures have no scale:
• Beauty, Difficulty, etc. •
– Most important aspect of measures: they are orderable.
– Don't care about the actual numbers.
– (An apple can have deliciousness .9 or .1.)
• Measures can be used to describe objects as follows:
– Diameter(Basketball 12) = Inches(9.5) .
– ListPrice (Basketball 12) = $(19) .
– d ∈ Days ⇒ Duration(d) = Hours(24) .
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13. Events
• Facts are treated as true independent of time
• Events: need to describe what is true, when something is happening
• For instance: Flying event
• E ∈ Flying's
• Flyer(E, Shankar)
• Origin(E, SanFrancisco)
• Destination(E, Baltimore)
• We will consider two kinds of time intervals: moments and extended
intervals. The distinction is that only moments have zero duration:
• Partition({Moments, Extended Intervals}, Intervals)
• i ∈ Moments ⇔ Duration(i) = Seconds(0) .
• The function Duration gives the difference between the end time and the
start time.
• Interval(i) ⇒ Duration(i) = (Time(End(i)) Time(Begin(i))) .
• Time(Begin(AD1900)) = Seconds(0) .
• Time(Begin(AD2001)) = Seconds(3187324800) .
• Time(End(AD2001)) = Seconds(3218860800) .
• Duration(AD2001) = Seconds(31536000) .
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14. Events
• Two intervals Meet if the end time of the first equals the star
time of the second. The complete set of interval relations
logically below:
• Meet(i, j) ⇔ End(i) = Begin(j)
• Before(i, j) ⇔ End(i) < Begin(j)
• After(j, i) ⇔ Before(i, j)
• During(i, j) ⇔ Begin(j) < Begin(i) < End(i) < End(j)
• Overlap(i, j) ⇔ Begin(i) < Begin(j) < End(i) < End(j)
• Begins(i, j) ⇔ Begin(i) = Begin(j)
• Finishes(i, j) ⇔ End(i) = End(j)
• Equals(i, j) ⇔ Begin(i) = Begin(j) ∧ End(i) = End(j)
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15. • Graphically Predicates on time intervals.
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16. • Physical objects can be viewed as generalized events, in the
sense that a physical object is a chunk of space–time.
• George Washington was president throughout 1790
• T (Equals (President(USA), George Washington), AD1790)
Events A schematic view of the object President(USA) for the
first 15 years of its existence.
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17. Mental events and objects
• So far, KB agents can have beliefs and deduce new beliefs
• What about knowledge about beliefs? What about knowledge about
the inference process?
– Requires a model of the mental objects in someone’s head and
the processes that manipulate these objects.
• Relationships between agents and mental objects: believes, knows,
wants,
– Believes(Lois, Flies(Superman)) with Flies(Superman) being a
function . . . a candidate for a mental object (reification).
– Agent can now reason about the beliefs of agents.
• Modal logic solves some tricky issues with the interplay of
quantifiers and knowledge.
– particular someone who Bond knows is a spy ∃ x Kbond Spy(x)
– Bond just knows that there is at least one spy
– Kbond ∃ x Spy(x)
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18. Reasoning system for categories
• Semantic Networks
• Logic vs. semantic networks
• Many variations
– All represent individual objects, categories of
objects and relationships among objects.
– persons have two legs—that is
– ∀ x x ∈ Persons ⇒ Legs(x, 2)
• Allows for inheritance reasoning
– Female persons inherit all properties from person.
– OO programming.
• Inference of inverse links
– Sister Of vs. Has Sister
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19. Topics to be covered in next session 25
• Proportional logic
Thank you!!!
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