Stable model semantics: Difference between revisions

Revision as of 00:31, 4 July 2014

Revision as of 09:48, 7 July 2014

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The definition of a stable model below, reproduced from [Gelfond and Lifschitz, 1988], uses two conventions. First, a truth assignment is identified with the set of atoms that get the value '''T'''. For instance, the truth assignment

<table COLS=$ WIDTH="20%">

{| cols=$ width="20%"

<td valign="top">

|<math>p</math>

|<math>q</math>

<br>

|<math>r</math>

'''T'''

|<math>s</math>

</td>

|-

<td valign="top">

|'''T'''

<math>q</math>

|'''F'''

<br>

|'''F'''

|'''T'''.

</td>

|}

<td valign="top">

<math>r</math>

<br>

'''F'''

</td>

<td valign="top">

<math>s</math>

<br>

'''T'''

</td>

</table>

is identified with the set <math>\{p,s\}</math>. This convention allows us to use the set inclusion relation to compare truth assignments with each other. The smallest of all truth assignments <math>\emptyset</math> is the one that makes every atom false; the largest truth assignment makes every atom true.