Abstract
Qualitative relations in biological systems were studied by means of lattices. The first main representations gave place to lattices being double pseudo-Boolean algebras. So, close to the poset which defined the lattices, two operations appeared: the Heyting arrow and the dual Heyting arrow. Both are important to relate noncomparable elements in terms of processes concerned with increasing and decreasing energies in the system, as results from the order defining the poset which considers the lattice elements as relational energetic states. The present developments find out mathematical properties of lattice structures satisfying dual Heyting arrow operations between noncomparable elements.
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