| Circumscription |
Articles about Circumscription |
Information AboutCircumscription |
| CATEGORIES ABOUT CIRCUMSCRIPTION | |
| logic programming | |
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The original problem considered by McCarthy was that of contains one such solution), but rather that of excluding conditions that are not explicitly stated. For example, the solution “go half a mile south and cross the river on the bridge” is intuitively not valid because the statement of the problem does not mention such a bridge. On the other hand, the existence of this bridge is not excluded by the statement of the problem either. That the bridge does not exist is a consequence of the implicit assumption that the statement of the problem contains everything that is relevant to its solution. Explicitly stating that a bridge does not exist is not a solution to this problem, as there are many other exceptional conditions that should be excluded (such as the presence of a rope for fastening the cannibals, the presence of a larger boat nearby, etc.) Circumscription was later used by McCarthy to formalize the implicit assumption of scenario. Other solutions to the frame problem that correctly formalize the Yale shooting problem exist; some use circumscription but in a different way (see Frame Problem for details). THE PROPOSITIONAL CASE While circumscription was initially defined in the first-order logic case, the particularization to the propositional case is easier to define. Given a propositional formula , its circumscription is the formula having only the models of with a minimal amount of variables assigned to true. Formally, propositional models can be represented by set of propositional variables; namely, each model is represented by the set of propositional variables it assign to true. For example, the model assigning true to , false to , and true to is represented by the set , because and are exactly the variables that are assigned to true by this model. Given two models and represented this way, the condition is equivalent to setting to true every variable that sets to true. In other words, models the relation of “setting to true less variables”. Circumscription is expressed by selecting only the models that assign to true a minimal amount of variables. It can therefore defined as follows: | ||
| :<math>CIRC(TP,Z) | \{ M ~~ M \models T \mbox{ and } |
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