In this paper we define a \textit{pseudo-valuation} on a BCK algebra (A,\rightarrow ,1) as a real-valued function v:A\rightarrow \mathbf{R} satisfying v(1)=0 and v(x\rightarrow y)\geq v(y)-v(x), for every x,y\in A ; v is called a \textit{valuation} if x=1 whenever v(x)=0. We prove that every pseudo-valuation (valuation) v induces a pseudo-metric (metric) on A defined by d_{v}(x,y)=v(x\rightarrow y)+v(y\rightarrow x) for every x,y\in A, where \rightarrow is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations) on BCK algebras.

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 Busneag, Dumitru, Istrata, Mihaela, Piciu, Dana