Pseudo-valuations on pre-logics

Based on the Buşneag’s model 1,2,3], the notion of pseudo-valuations (valuations) on a pre-logic is introduced, and a pseudo-metric is induced by a pseudo-valuation on pre-logics. Related properties are investigated, and conditions for a real-valued function on a pre-logic to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation ∗ in pre-logics is uniformly continuous.