Instantial Relevance in Polyadic Inductive Logic

A survey of some recent results on Spectrum Exchangeability in Polyadic Inductive Logic

“…Through Theorem 7 this extension to L = is possible for any probability function w satisfying Sx and Li. Not only that but as shown in Landes et al (2009) for not purely unary languages the result goes the other way too:…”

“…As it stands however it will only be homogeneous if either p 0 > 0 or all the p i are non-zero for i > 0. Given this condition it turns out, see Landes et al (2009), that these simple u p L serve the required role in a de Finetti style representation theorem:…”

“…, b i+1 ) not uniform randomly as was the case for u p L but, roughly speaking, with a probability proportional to the number of ways of extending this state description to one of spectrum of length exactly t, again requiring that whenever c i = c j then b i , b j remain forever 13 The Ladder Theorem representation of u p L is given explicitly in Landes (2009, p. 71) and Paris and Vencovská (2009). [149] 36 Synthese (2011) 181:19-47 indistinguishable. For the precise details of this construction we refer the reader to Landes et al (2009) and Paris and Vencovská (2007).…”