ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 65,   1   (1996)
pp.   111-123

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 $L$.

AMS subject classification.  06C15; Secondary 03G12, 81P10
Keywords.  Ortholattice, logic, state, Bell-type inequality