Recovering Information from Inconsistent KB with Bilattice Approach

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Recovering Information from Inconsistent KB with
Bilattice Approach

• Lin Zhangang
• zglin_at_is.pku.edu.cn

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Introduction

• Drawbacks of classical logic
• Any conclusion can be drawn from an inconsistent
  KB a single contradiction will destroy the
  meaningful data in a KB.
• Monotonicity insufficient to model human
  commonsense.

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Introduction(2)

• The approach of recovering data from an
  inconsistent KB
• Characteristics
• Paraconsistent
• In the framework of bilattice
• Without changing the syntax
• The process
• Switch to framework of bilattice
• Develop a mechanism of paraconsistent inferences
  (most consistent inference)
• Computing the support set of the KB

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Step 1

• The multi-valued framework

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Bilattice

• Definition (Ginsberg)
• A property

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Bifilter (designated value)

• Definition
• Two candidates for the set of designated value
• Logical bilattice

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• Inconsistency set

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Step 2

• Paraconsistent reasoning

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Logic in the framework of bilattice

• The language
• Notations
• the set of atomic formulae in KB
• the set of literals in KB
• Multi-valued Semantics

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Logic in the framework of bilattice(2)

• Notation
• Enhancing the logic
• The logic described above is weak (disjunctive
  syllogism)

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Logic in the framework of bilattice(3)

• Epistemic entailment
• Notation
• If scon(KB), then for
• If smin(KB), then for

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Normal form of KB

• Extended clause
• A normalized KB is a set of extended clauses

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Step 3

• Recovering consistent information

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Classification of atomic formulae

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Spoiled Literals

• The core of the inconsistency in KB
• Not included in the recovering set, easy to
  detect (See below)

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Recoverable literals

• The robust part of an inconsistent KB
• Can be associated with a consistent subset, which
  preserves information about recoverable literals

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Support sets of recoverable literals

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Support sets of recoverable literals (2)

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Damaged literals

• Literals that a consistent truth value can not
  reliably attached to them.
• Some observations
• The existence of a support set for a damaged
  literal is not assured
• Even if there is a support set for a damaged
  literal, there may be other SS supports its
  negation
• A literal can be damaged not only because of over
  information, but a lack of data as well

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Minimal MCM

• If one is only interested in recovering an
  inconsistent KB, it suffices to consider only the
  k-mimimal models of the mcms.
• Notation for k-minimal models of the mcms
  of KB

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Example

• The KB
• The k-minimal mcms
• Support sets

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• The End
• Happy National Day!