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

Andrew Schumann

DOI: http://dx.doi.org/10.12775/LLP.2006.002


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 Vasiľév’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 Vasiľév’s syllogistic is called a vectorial lattice on closure \cap-semilattice. These constructions are introduced for the first time.


Aristotle’s syllogistic; Vasiľév’s syllogistic; vectorial lattice on ?-semilattice; vectorial lattice on closure \cap-semilattice; quartum non datur

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