Default Logic Rule
A Default Logic Rule is a production rule [math]\displaystyle{ delta }[/math] of the form [math]\displaystyle{ \frac{\alpha : \beta_1, ..., \beta_n}{\gamma} }[/math] where [math]\displaystyle{ \alpha, \beta_1, ..., \beta_n, \gamma }[/math] are first order formulae and [math]\displaystyle{ n \ge 1 }[/math], [math]\displaystyle{ alpha }[/math] is called the default prerequisite, [math]\displaystyle{ \beta_1, ..., \beta_n }[/math] are the default justifications, and [math]\displaystyle{ \gamma }[/math] is the default consequent.
- AKA: Assumption-based Default Rule.
- Context:
- It can be interpreted to as: if [math]\displaystyle{ \alpha }[/math] is known, and if it is consistent to assume [math]\displaystyle{ \beta_1, ..., \beta_n }[/math] then conclude [math]\displaystyle{ \gamma }[/math].
- It can range from being an Open Default Rule to being a Closed Default Rule, depending on whether [math]\displaystyle{ \alpha, \beta_1, ..., \beta_n, \gamma }[/math] have [[Free
Variable]]s.
- It can be used to draw Plausible Conclusions in the face of Incomplete Information.
- …
- Example(s):
- a Default Subsumption Relation (which are only transitive by default).
- See: Default Theory.
References
2012
- http://en.wikipedia.org/wiki/Default_logic#Syntax_of_default_logic
- QUOTE: [math]\displaystyle{ D }[/math] is a set of default rules, each one being of the form: :[math]\displaystyle{ \frac{\text{Prerequisite : Justification}_1, \dots , \text{Justification}_n}{\text{Conclusion}} }[/math] According to this default, if we believe that [math]\displaystyle{ Prerequisite }[/math] is true, and each of [math]\displaystyle{ Justification_i }[/math] is consistent with our current beliefs, we are led to believe that [math]\displaystyle{ Conclusion }[/math] is true.
The logical formulae in [math]\displaystyle{ W }[/math] and all formulae in a default were originally assumed to be first-order logic formulae, but they can potentially be formulae in an arbitrary formal logic. The case in which they are formulae in propositional logic is one of the most studied.
- QUOTE: [math]\displaystyle{ D }[/math] is a set of default rules, each one being of the form: :[math]\displaystyle{ \frac{\text{Prerequisite : Justification}_1, \dots , \text{Justification}_n}{\text{Conclusion}} }[/math] According to this default, if we believe that [math]\displaystyle{ Prerequisite }[/math] is true, and each of [math]\displaystyle{ Justification_i }[/math] is consistent with our current beliefs, we are led to believe that [math]\displaystyle{ Conclusion }[/math] is true.