Abstract

We propose a binary resolution system over Boolean lattices. We shall assume that truth values form a complete Boolean lattice L where its supremum operator is infinitely distributive over the infimum one. Binary L -resolution will operate on graded clauses. A graded clause is a pair of the form ( l 1 ∨ ⋯ ∨ l n , c ) where l i are literals and c is a truth degree in L . The refutational soundness and completeness of the proposed resolution proof method will be proved.

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