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Jun 1, 2013 · Let A = 〈 A, ≤ t, ≤ f, ≤ i, − t 〉 be an interlaced trilattice with t-involution. Using De Morgan laws, it is not difficult to prove the following: Proposition 3.5. The relations ∼ 1 and ∼ 2 defined in the previous section are congruences of any interlaced trilattice with t-involution. Proof
- Umberto Rivieccio
- 2013
Jun 1, 2013 · In [31], Rivieccio presented product representations for the varieties of interlaced trilattices and interlaced trilattices with one involution´t. A trilattice is said to be interlaced if the six ...
- Umberto Rivieccio
This paper presents the new algebra of trilattices, which are understood as the triadic generalization of lattices. As with lattices, there is an order-theoretic and an algebraic approach to trilattices. Order-theoretically, a trilattice is defined as a triordered set in which six triadic operations of some small arity exist. The Reduction Theorem guarantees that then also all finitary ...
- Klaus Biedermann
- 1999
1) is an interlaced pre-bilattice. 2) ∗There are two bounded lattices and , such that the bilattice is isomorphic to ⊙ ∗. Theorem 2.2 [14] Let us have a bilattice , which is bounded. The following are equivalent 1) is an interlaced bilattice.
Basis and Crystal. Now one could go ahead and replace the lattice points by more complex objects (called basis), e.g. a group of atoms, a molecule, ... . This generates a structure that is referred to as a crystal: [11][12][13][14] A crystal is defined as a lattice with a basis added to each lattice site. Usually the basis consists of an atom ...
The main results are that every interlaced bilattice is isomorphic to the Ginsberg-Fitting product of two bounded lattices and that the variety of interlaces bilattices is equivalent to the varieties of bounded lattice with two distinguishable distributive elements, which are complements of each other.
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trilattice logics as well. The sequent calculi G B and G L can be obtained in a completely analogous way. Therefore, we will concentrate on G B. Cut-free sequent calculi for the logic ‘ base underlying both ‘ B and ‘ L have not been obtained so far. Constructing a cut-free sequent calculus for ‘ base might turn out to be difficult.
