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The paper proposes and studies temporal logics for attributed words, that is,data words with a (finite) set of (attribute,value)-pairs at each position. Itconsiders a basic logic which is a semantical fragment of the logic$LTL^\downarrow_1$ of Demri and Lazic with operators for navigation into thefuture and the past. By reduction to the emptiness problem for data automata itis shown that this basic logic is decidable. Whereas the basic logic onlyallows navigation to positions where a fixed data value occurs, extensions arestudied that also allow navigation to positions with different data values.Besides some undecidable results it is shown that the extension by a certainUNTIL-operator with an inequality target condition remains decidable.

Temporal Logics on Words with Multiple Data Values