A Fundamental Tradeoff in Knowledge Representation and Reasoning Revised Version

1
A Fundamental Tradeoff in Knowledge
Representation and Reasoning (Revised Version)

• Hector J. Levesque and Ronald J. Brachman

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Main Points

• Automated Reasoning
• Difficulty varies according to language used
• As language expressiveness increase,
  computational tractability decreases and vice
  versa

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Representational Formalisms

• First-Order Logic (FOL)
• Databases
• Logic Program
• Semantic Networks
• Frames

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Knowledge Representation (KR) System

• Must have a knowledge base (KB)
• Structures represent propositions for systems
  knowledge
• Structures must play causal role in system
  behavior

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KR System Goals

• Select appropriate symbolic structures
• Select appropriate mechanism
• Answering questions
• Explicitly
• Implicitly
• Assimilating new knowledge
• Must conform to language truth theory

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FOL KR System

• Simple facts or observations
• Henrys friends are Dougs cousin
• Knowledge about terminology
• Brother is sibling restricted to males
• Procedural knowledge
• Advice on finding someones father

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Advantages of FOL

• Can express precisely conditions for answering
  yes, no or unknown
• Implicit inference reduced to theorem proving in
  FOL

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Problem of FOL KR

• Theorem proving in FOL is unsolvable (in worse
  case scenario)

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Two Pseudo-solutions

• Push computational barrier as far back as
  possible
• Advances in parallel computing and VLSI
• Improved automatic theorem proving techniques
• Lower the bar of correctness
• Guarantee obtaining answer in certain time frame
• Answer may not be correct

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Incomplete Knowledge

• ?Student(Doug)
• ? x Cousin (Bill, x) Male(x)
• ?x Friend (George, x) ? ?y Child(x,y)

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Incomplete Knowledge

• Observation Expressive power of FOL is
  determined by what can be left unsaid
• Therefore Restrict kinds of incompleteness in
  FOL
• Result More manageable inference procedure

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Database Form

• The idea is to restrict a KB to contain the kinds
  of information stored in a relation
• Interference reduces to calculations on model
• No negation, disjunction or existential
  quantifiers

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Course
 
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Database Form Example

• How many courses are offered by the CISE dept?
• Answer count Cs in course where c.dept. CISE
• Inferences is done by calculation on model

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Database Form Example

• We know csc 248 is a CISE course
• We also know No CISE course other than csc 373
  has odd id number
• We can determine there are at least two CISE
  courses but not by counting

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Database Form Conclusion

• Database a knowledge base whose limited form
  allows very special forms of inference

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Logic Program Form

• Executes logic program written in PROLOG, PLANNER
  etc. to reason
• Inference service consists of two components
• Retrieval Component
• Search Component
• Generally not decidable whats implicit in KB
  (worse case scenario)

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Benefits of Program Logic Form

• Gives different perspective for viewing KR
  inference service
• KR subsystems performs limited form of inference
• Then the KB system or user intelligently
  completes the inference

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Problems of Program Logic Form

• Determining the primitives that would allow logic
  program to extend reasoning of KR subsystem
• Defining the KR inference service.

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Semantic Network Form

• Only contains unary and binary predicates
• Types are organized into a taxonomy
• Generic KB consists of two basic kinds of
  sentences
• Sentences representing subsumption
• Sentences placing constraints on attributes

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Semantic Network Form Advantages

• Can be represented by labeled directed graph
• Graph searching techniques can be used to perform
  inferences

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Semantic Network Form Drawbacks

• It allows for default forms of reasons (for
  better or worse)

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Frames Description Form

• Mainly an elaboration on the semantic network
  form
• Types in semantic networks are now frames and
  attributes are slots
• Slots
• Values
• Restrictions
• Attached procedures (advice)

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Frames Description Form

• Like semantic network form, take liberties in
  representing logical form
• Unlike semantic network form, structures have
  properties of
• Subsumption
• Disjointedness

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Overall Conclusion

• Cannot conclude that one formalism is better than
  the other
• Utilize them for
• What the can represent
• The reasoning strategies they permit
• Much more to be learned about tradeoffs