Representation theorems for probability functions satisfying spectrum exchangeability in inductive logic
De Finetti's representation theorem [see \textit{H. Gaifman}, ``Applications of de Finetti's theorem to inductive logic'', in: \textit{R. Carnap} and \textit{R. C. Jeffrey} (eds.), Studies in inductive logic and probability. Vol. I. Berkeley--Los Angeles--London: University of California Press, 235--251 (1971; Zbl 0246.02024)] plays a central role in the study of conventional, unary, inductive logic, because it gives a transparent access to examples of probability functions satisfying some basic conditions, and it makes it possible to restyle problems from inductive logic into elementary differential and integral calculus, where intuitions and techniques are already well developed. In this paper, a de Finetti-style representation theorem is proved, covering the class of all probability functions satisfying spectrum exchangeability in polyadic inductive logic and giving an application by characterizing those probability functions satisfying spectrum exchangeability, which can be extended to a language with equality whilst still satisfying this property.
scientific article; zbMATH DE number 5777528
scientific article