For a given language $L$, the problem of partial $\vee$-algebras asks whether there is a universal algorithm which for any finite partial $\vee$-algebra $\mathcal A$, and any identity $p\approx q\in\mathrm Eq(\mathcal L\cup\mathcal A)$ with no variables, decides whether or not $F\vee(A)\models p\approx q$. First, it is shown that the solution of the word problem implies the solution of the problem of partial algebras for any variety $\vee$. Second, if the problem of partial $\vee$-algebras is solvable, then, a class of finite presentations can be given for which the word problem is solvable.