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sav08:first-order_logic_is_undecidable [2008/04/03 12:58] vkuncak |
sav08:first-order_logic_is_undecidable [2008/04/03 12:59] vkuncak |
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| (($\lnot F$) is true in some Herbrand model) iff ($M$ does not accept $w$) | (($\lnot F$) is true in some Herbrand model) iff ($M$ does not accept $w$) | ||
| - | So, we work with formula $G$ denoting $\lnot F$, interpreted over Herbrand model, and we express the condition that all Turing machine computation histories are non-accepting. | + | So, we work with formula $G$ denoting $\lnot F$, interpreted over Herbrand model, and we express the condition that all Turing machine computation histories are non-accepting. In other words, $F$, when interpreted over Herbrand interpretations, says that there exists an accepting Turing computation history. |
| The fact that we work over Herbrand models helps us talk about computation histories, because we can encode strings and reachability. | The fact that we work over Herbrand models helps us talk about computation histories, because we can encode strings and reachability. | ||