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sav08:graphs_as_interpretations [2008/03/19 15:38] vkuncak |
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| Note: there is no formula $F$ in this language ${\cal L} = \{edge\}$ that characterizes property "graph has no cycles". All properties expressed in first-order logic on graphs are "local". | Note: there is no formula $F$ in this language ${\cal L} = \{edge\}$ that characterizes property "graph has no cycles". All properties expressed in first-order logic on graphs are "local". | ||
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| + | Many more properties become expressible if we take as domain $D$ the set of all subsets of $V$ and allow set operations in our language. | ||
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| + | * [[http://citeseer.ist.psu.edu/benedikt95relational.html|Relational Expressive Power of Constraint Query Language]] | ||
| + | * [[http://citeseer.ist.psu.edu/context/64580/0|H. Gaifman, On local and non-local properties, in Logic Colloquium '81, North Holland, 1982]] | ||