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tags:

• 🌱
• AI
• ComputerScience date: 23--Apr--2023

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$$\frac{prerequisite:justification}{conclusion}$$

• If prerequisite is true
  • All justifications are consistent
    • KB does not entail $\lnot beta(x)$
  • Conclusion is true

• $\Delta$ is set of default rules
• $\Phi$ set of facts

• Closed world assumption
  • What is not known to be true is assumed false
  • $\frac{:\lnot \beta}{\lnot \beta}$
• Default rules in $\Delta$ can be applied to a theory
  • If preconditions are entailed
  • And if justification are consistent
• Other default rules can be applied to a resulting theory
  • To extend $\Phi$ known facts
• An extension of a default theory
  • A theory has exhausted all default rules
  • A default theory can have 0, 1, or many extensions

• Beliefs $\Xi = \Phi$
• Guess $\exists \Xi^* = \Xi \cup \alpha(c)$
  • For every $\delta \in \Delta$
    • Check triggered and justified
    • Update beliefs if consistent
    • $\Xi = \Xi \cup \gamma(c)$
• Check if guess was valid

Default rules applied in different order can result in different extensions

• Sceptical
  • Formula is entailed by default theory if it is entailed by all extensions
• Credulous
  • Formula is entailed if it is entailed by at least one of its extensions
  • Can give rise to inconsistent belief depending on expansion order of default rule

• Each

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Links: Semantic - Logic - NTU Vault/Machine Learning/Inference