Lattice-theoretic properties of algebras of logic |
| |
Authors: | Antonio Ledda Francesco Paoli Constantine Tsinakis |
| |
Institution: | 1. Università di Cagliari, via Is Mirrionis 1, 09123 Cagliari, Italy;2. Vanderbilt University, 1323 Stevenson Center, Nashville, TN 37240, USA |
| |
Abstract: | In the theory of lattice-ordered groups, there are interesting examples of properties — such as projectability — that are defined in terms of the overall structure of the lattice-ordered group, but are entirely determined by the underlying lattice structure. In this paper, we explore the extent to which projectability is a lattice-theoretic property for more general classes of algebras of logic. For a class of integral residuated lattices that includes Heyting algebras and semi-linear residuated lattices, we prove that a member of such is projectable iff the order dual of each subinterval a,1] is a Stone lattice. We also show that an integral GMV algebra is projectable iff it can be endowed with a positive Gödel implication. In particular, a ΨMV or an MV algebra is projectable iff it can be endowed with a Gödel implication. Moreover, those projectable involutive residuated lattices that admit a Gödel implication are investigated as a variety in the expanded signature. We establish that this variety is generated by its totally ordered members and is a discriminator variety. |
| |
Keywords: | Primary 06F05 secondary 06D35 06F15 03G10 |
本文献已被 ScienceDirect 等数据库收录! |
|