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Horn Formulas as Linear Inequalities and Nonlocality Paradoxes

Tobias Fritz ( ICFO, Barcelona )

Abstract: A Horn formula can be interpreted as a system of linear
inequalities over the Boolean semiring. Similarly, a union-closed set
system is the Boolean version of a polytope. I will show how a
resolution-like Fourier-Motzkin algorithm can be used to compute a Horn
formula determining a union-closed set system from its generating sets and
describe the output of some sample computations. In particular, one can
use the software to calculate all Hardy-type nonlocality paradoxes as Bell
inequalities over the Boolean semiring. Everything is work in progress,
and I will mention the problem of redundancy elimination as a major
obstacle towards further progress.



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