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Default Logic.md

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Default Logic
2022-11-08
2022-11-21

Default Logic

Definitions

Reiter Extension

Makinson Approach

Process Tree Algorithm

A closed default is one that has been instantiated The In-set contains all the consequences from applying a default The Out-set contains all the negations of the justifications from applying a default: these are the predicates which cannot be proven true by the In-Set for the extension to be consistent

  1. Start with the root node: Out is initialized to $\emptyset$ while In is set to the current knowledge base
  2. For every node, check for direct applicability of defaults (If no defaults are directly applicable: we arrived at a closed process) direct applicability must satisfy 2 conditions:
    1. Default must be triggered: In-set contains the prerequisite
    2. Default must be justified: negation of justifications cannot be proven True from the current In-set
  3. If the new In-set becomes inconsistent ($In \cap Out \neq \emptyset$ or $In\cup \delta .consq \ \vdash Out$) : process is unsuccessful

We arrive at an extension for every closed and successful process.