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sav08:definition_of_propositional_resolution [2008/03/12 17:08] vkuncak |
sav08:definition_of_propositional_resolution [2009/05/14 10:39] vkuncak |
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| * **clause** is a disjunction of literals | * **clause** is a disjunction of literals | ||
| - | ===== Clauses as Sets of Literlas ===== | + | |
| + | ===== Clauses as Sets of Literals ===== | ||
| The order and the number of occurrences of literals in clauses do not matter, because of these valid formulas: | The order and the number of occurrences of literals in clauses do not matter, because of these valid formulas: | ||
| Line 24: | Line 25: | ||
| Here $C,D$ are clauses and $p \in V$ is a propositional variable. | Here $C,D$ are clauses and $p \in V$ is a propositional variable. | ||
| - | Intuition: consider the form | + | Intuition: consider equivalent formulas |
| \[ | \[ | ||
| - | \frac{\lnot C \rightarrow \{\lnot p\}\ \ \ (\lnot p \rightarrow D)} | + | \frac{((\lnot C) \rightarrow (\lnot p))\ \ \ ((\lnot p) \rightarrow D)} |
| - | {\lnot C \rightarrow D} | + | {(\lnot C) \rightarrow D} |
| \] | \] | ||
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| ===== Applying Resolution Rule to Check Satisfiability ===== | ===== Applying Resolution Rule to Check Satisfiability ===== | ||
| Line 38: | Line 42: | ||
| - empty clause $\emptyset$ is derived | - empty clause $\emptyset$ is derived | ||
| - application of the resolution rule produces no new clauses | - application of the resolution rule produces no new clauses | ||
| + | |||
| + | [[sav09:Example of Using Propositional Resolution]] | ||
| ===== Soundness of Resolution Rule ===== | ===== Soundness of Resolution Rule ===== | ||