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sav08:satisfiability_of_sets_of_formulas [2008/03/11 18:21] vkuncak |
sav08:satisfiability_of_sets_of_formulas [2008/03/11 18:21] vkuncak |
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| ====== Satisfiability of Sets of Formulas ====== | ====== Satisfiability of Sets of Formulas ====== | ||
| - | We next introduce sets of formulas as a way of talking about potentially infinite conjunctions of formulas. | + | We next introduce sets of formulas as a way of talking about potentially infinite conjunctions of formulas. We will need this when reducing reasoning in first-order logic to reasoning in propositional logic. |
| We say that interpretation $I$ is a model for a set of formulas $S$, written $I \models S$, iff for each $F \in S$, $I \models F$. In other words, we view a set of formulas as a (potentially infinite) conjunction; when $S$ is finite then $I \models S$ is the same condition as $I \models \bigwedge_{F \in S} F$. | We say that interpretation $I$ is a model for a set of formulas $S$, written $I \models S$, iff for each $F \in S$, $I \models F$. In other words, we view a set of formulas as a (potentially infinite) conjunction; when $S$ is finite then $I \models S$ is the same condition as $I \models \bigwedge_{F \in S} F$. | ||