this is for holding javascript data
Simon McGill edited untitled.tex
over 8 years ago
Commit id: 8dd131191b26a03177eac2256a61641b0d18417e
deletions | additions
diff --git a/untitled.tex b/untitled.tex
index 2d62dae..4ab1d72 100644
--- a/untitled.tex
+++ b/untitled.tex
...
We will say that one theory of rationality $R_1: (B_1 \times D_1 \times \Phi_1 \times S) \to (2^{B_1} \times 2^{D_1} \times 2^A)$ is \emph{subsumed} by another $R_2: (B_2 \times D_2 \times \Phi_2 \times S) \to (2^{B_2} \times 2^{D_2} \times 2^A)$ if and only if $R_2$ can compute $R_1$ under a transformation of individual variables, and we write this $R_1 \preceq R_2$:
\[ R_1 \preceq R_2 \textrm{ iff } \\
\exists f_B: B_1 \to B_2, \ f_D: D_1 \to D_2, \ f_\Phi: \Phi_1 \to \Phi_2 . \\
\forall b \in B_1, \ d \in D_1, \ \phi \in \Phi_2, \ s \in S : R_1(b, d, \phi, s) =
R_2\bigg(f_B(b), R_2\left(f_B(b), f_D(d), f_\phi(\phi),
s\bigg) s\left)
\]
...