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What does $\alpha_r\supset\beta_r$ mean in the tolerance definition of System Z?

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Problem Detail: 

I'm reading up on System Z introduced by Judea Pearl (in System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning). A central definition is that of tolerance of a subset $R'$ of a rule set $R$ for a rule $r = \alpha_r\to\beta_r$ (denoted by $T(r\ \vert\ R')$). Tolerance of $R'$ for $r$ is defined to be the set of satisfiable formulas $$(\alpha_r\land\beta_r)\bigcup_{r'\in R'}(\alpha_{r'}\supset\beta_{r'})$$ (see page 2 of the article by Pearl).

I don't understand what $\alpha_{r'}\supset\beta_{r'}$ is supposed to mean. Can anyone explain?

Asked By : FK82
Answered By : D.W.

In elementary logic, $A \supset B$ is notation for the formula $\neg A \lor B$ (for the implication "$A$ implies $B$"). In other words, $A \supset B$ is a formula; it is true if $A$ is false or if $B$ is true, and false otherwise. http://math.stackexchange.com/q/1106001/14578

How you could have figured this out on your own: Read the entire paper. For instance, a useful place would be to start would be reading the examples in Section 3, where from the examples one can reverse-engineer the probable meaning of the symbol.

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Question Source : http://cs.stackexchange.com/questions/48539

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