MINIMAL AND MAXIMAL SETS OF BELL-TYPE INEQUALITIES HOLDING IN A LOGIC
H. LANGER and M. MACZYNSKI
Abstract.
It is shown that for every integer $n>1$ the poset $(\\f\:2^\1,\ldots,n \to Z\,| \sum_I\subseteq\1,\ldots,n\f(I)p(\bigwedge_i\in Ia_i)\in [0,1]$ for all states $p$ on $L$ and all $a_1,\ldots,a_n\in L \,|\,L\;:$ ortholattice$\\,,\,\subseteq)$ possesses a smallest and a greatest element. The functions in this poset are interpreted as Bell-type inequalities holding in $L$.
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