We study clones on a four-element set related to the clone $${\mathsf {DMA}}$$ of all term functions subdirectly irreducible De Morgan algebra $${\mathbf {DM}}_{{{\mathbf {4}}}}$$ . find generating sets for preserving subalgebras , automorphisms truth order and information as well defined by conjunctions these conditions. identify covers in lattice four-valued describe above which contain discr...

We generalize the notion of a monadic algebra to that of a pseudomonadic algebra. In the same way as monadic algebras serve as algebraic models of epistemic modal system S5, pseudomonadic algebras serve as algebraic models of doxastic modal system KD45. The main results of the paper are: (1) Characterization of subdirectly irreducible and simple pseudomonadic algebras, as well as Tokarz’s prope...

In this paper we initiate an investigation into the class of meet semilattices endowed with endomorphism. A consideration subdirectly irreducible algebras leads to a description subclass those (S;∧,k)(S;∧,k) in which (S;∧)(S;∧) is semilattice and kk endomorphism on SS characterised by property k⩾idSk⩾idS. We particularly show that such algebra if only it chain one following forms ⋯<aj&am...

In this paper we give suitable notions of congruences and subdirectly irreducible algebras for the class of quasi-modal algebras introduced in [1]. We also prove some characterizations of subdirectly irreducible algebras following the similar results given by G. Sambin [5] for modal algebras.