Two new results on STP-based algebraic structures

In this paper we consider two semi-tensor product (STP) based algebraic structures. First, the set of matrices of arbitrary dimensions (including scalars as 1 × 1 dimensional matrices) is considered. It is shown that under STP they form a monoid. Some useful submonoids are also investigated. Second. the set of static logical systems (SLSs) is investigated. Using the antecedence and consequence solutions, a lattice structure is posed to the set of SLSs. Certain properties are investigated.