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Landes, Jürgen; Paris, Jeff B.; Vencovská, Alena (2007): Language Invariance and Spectrum Exchangeability in Inductive Logic. In: Mellouli, Khaled (ed.) : Symbolic and Quantitative Approaches to Reasoning with Uncertainty : 9th European Conference, ECSQARU 2007, Hammamet, Tunisia, October 31 - November 2, 2007 ; proceedings. Lecture Notes in Computer Science, Vol. 4724. Berlin, Heidelberg: Springer Berlin Heidelberg pp. 151-160
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A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) t-heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.