Modal Pseudocomplemented De Morgan Algebras

summary:Modal pseudocomplemented De Morgan algebras (or $mpM$-algebras for short) are investigated in this paper. This new equational class of algebras was introduced by A. V. Figallo and P. Landini ([Figallo, A. V., Landini, P.: Notes on $4$-valued modal algebras Preprints del Instituto de Ciencias Básicas, Univ. Nac. de San Juan 1 (1990), 28–37.]) and they constitute a proper subvariety of the variety of all pseudocomplemented De Morgan algebras satisfying $x\wedge (\sim x)^\ast = (\sim (x\wedge (\sim x)^\ast ))^\ast$. Firstly, a topological duality for these algebras is described and a characterization of $mpM$-congruences in terms of special subsets of the associated space is shown. As a consequence, the subdirectly irreducible algebras are determined. Furthermore, from the above results on the $mpM$-congruences, the principal ones are described. In addition, it is proved that the variety of $mpM$-algebras is a discriminator variety and finally, the ternary discriminator polynomial is described

Free Modal Pseudocomplemented De Morgan Algebras

Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. In particular, one of them is determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18]

A multi-scale hierarchical framework for developing understanding of river behaviour to support river management

The work leading to this paper was funded through the European Union’s FP7 programme under Grant Agreement No. 282656 (REFORM). The framework methodology was developed within the context of Deliverable D2.1 of the REFORM programme, and all partners who contributed to the development of the four parts of this deliverable are included in the author list of this paper. More details on the REFORM framework can be obtained from part 1 of Deliverable D2.1 (Gurnell et al. 2014), which is downloadable from http://​www.​reformrivers.​eu/​results/​deliverables

Monadic n×m\boldsymbol n\boldsymbol \times \boldsymbol m-valued Łukasiewicz-Moisil algebras

summary:Here we initiate an investigation into the class $\boldsymbol m\boldsymbol L\boldsymbol M_{\boldsymbol n\boldsymbol \times \boldsymbol m}$ of monadic $n\times m$-valued Łukasiewicz-Moisil algebras (or $mLM_{n \times m}$-algebras), namely $n\times m$-valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$-valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $\boldsymbol m\boldsymbol L\boldsymbol M_{\boldsymbol n\boldsymbol \times \boldsymbol m}$ is a discriminator variety and as a consequence, the principal congruences are characterized. Furthermore, the number of congruences of finite $mLM_{n \times m}$-algebras is computed. In addition, a topological duality for $mLM_{n \times m}$-algebras is described and a characterization of $mLM_{n \times m}$-congruences in terms of special subsets of the associated space is shown. Moreover, the subsets which correspond to principal congruences are determined. Finally, some functional representation theorems for these algebras are given and the relationship between them is pointed out