In Busneag (Math. Japonica 44(2) (1996) 285) I defined a
pseudo-valuation on a Hilbert
algebra (A,→,1) (cf. (J. Math. 2 (1985) 29; Collection de Logique Math. 21 (1966)) as a real-valued function
v on
A satisfying
v(1)=0 and
v(x→y)≥v(y)−v(x) for every
x,yA (
v is called a
valuation if
x=1 whenever
v(x)=0). In Busneag (Math. Japonica 44(2) (1996) 285) it is proved that every pseudo-valuation (valuation)
v induces a pseudo-metric (metric) on
A defined by
dv(x,y)=v(x→y)+v(y→x) for every
x,yA, under which
→ is uniformly continuous in both variables. The aim of this paper is to provide several theorems on extensions of pseudo-valuations (valuations).