Polyhedral semantics and the tractable approximation of Łukasiewicz infinitely-valued logic

Marcelo Finger, Sandro Preto

Abstract:

In this work, we present polyhedral semantics as a means to tractably approximate Łukasiewicz infinitely-valued logic (Ł∞ ).
As Ł∞ is an expressive multivalued propositional logic whose decision problem is NP-complete, we show how to to obtain
an approximation for this problem providing a family of multivalued logics over the same language as Ł∞ . Each element of
the family is associated to a polynomial-time linear program, thus providing a tractable way of deciding each intermediate
step. We also investigate properties of the logic system derived from polyhedral semantics and the details of an algorithm for
the approximation process.