D. Hume (1739/1987) argued that causality is not observable. P. W. Cheng (1997) claimed to present "a theoretical solution to the problem of causal induction first posed by Hume more than two and a half centuries ago" (p. 398) in the form of the power PC theory (L. R. Novick & P. W. Cheng, 2004). This theory claims that people's goal in causal induction is to estimate causal powers from observa...

Let F be a field and F[x, y] the ring of polynomials in two variables over F. Let f ∈ F[x, y] and consider the residue class ring R := F[x, y]/fF[x, y]. Our first aim is to study digit representations in R, i.e., we ask for which f each element r ∈ R admits a digit representation of the form d0 + d1x + · · · + d`x with digits di ∈ F[y] satisfying degy di < degy f . These digit systems are motiv...