A lattice for the language of Aristotle’s syllogistic and a lattice for the language of Vasiľév’s syllogistic

In this paper an algebraic system of the new type is proposed (namely, a vectorial lattice). This algebraic system is a lattice for the language of Aristotle’s syllogistic and as well as a lattice for the language of Vasiľev’s syllogistic. A lattice for the language of Aristotle’s syllogistic is called a vectorial lattice on \cap-semilattice and a lattice for the language of Vasiľev’s syllogistic is called a vectorial lattice on closure \cap-semilattice. These constructions are introduced for the first time.