By a near

-lattice is meant an upper

-semilattice where is defined a parti binary operation

with respect to the induced order whenever

,

has a common lower bound. Alternatively, a near

-lattice can be described as an algebra with one ternary operation satisfying nine simple conditions. Hence, the class of near

-lattices is a quasivariety. A

-semilattice

is said to have sectional (antitone) involutions if for each

there exists an (antitone) involution on [

, 1], where 1 is the greatest element of

. If this antitone involution is a complementation,

is called an ortho

-semilattice. We characterize these near

-lattices by certain identities.