Simplification of many-valued logic formulas using anti-links

We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called "removal of anti-links". Possible applications of anti-links include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. Anti-links do not compute any normal form of a given formula themselves, rather, they remove certain forms of redundancy from formulas in negation normal form (NNF). Their main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we define an anti-link operation on a generic language for expressing many-valued logic formulas called "signed NNF" and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way

On Binary Max-Sum and Tractable HOPs

The Max-Sum message-passing algorithm has been used to approximately solve several unconstrained optimization problems, specially in the distributed context. In general, the complexity of computing messages is exponential. However, if the problem is modeled using the so called Tractable HOPs (THOPs), binary MaxSum's messages can be computed in polynomial time. In this paper we review existing THOPs, and present new ones, aiming at providing an updated view of efficient message computation.Peer Reviewe

Optimisation d'algorithmes d'inference monotone en logique des propositions et du premier ordre

SIGLECNRS T 66465 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc