ACKNOWLEDGMENTS This thesis wouldn't have been possible without the help and support of certain people. I could not possibly itemize my gratitude in detail, but I would like to mention some of the most important names. First and foremost, I would like to thank my advisor, Constantine Tsinakis, for introducing me to the subject of residuated lattices, and for his guidance and advice. Despite his...

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a non-associative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logics of lattice-ordered residuated unital groupoids. This paper is based on an alternative...

The primary goal of this paper is to extend the notion derivation studied in lattices, residuated lattices and multilattices by introducing two-parameter derivations multilattices. After defining notion, we illustrate it with several examples study properties some related notions. Finally, use set complemented elements fixed points characterize those derivations.

We introduce a new product bilattice construction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize ...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

Right-residuated binars and right-divisible residuated binars are defined as precursors of generalized hoops, followed by some results and open problems about these partially ordered algebras. Next we show that all complete homomorphic images of a complete residuated lattice A can be constructed easily on certain definable subsets of A. Applying these observations to the algebras of Hajek’s Bas...

This paper reveals some relations between fuzzy logic and quantum on partial residuated implications (PRIs) induced by t-norms as well proposes monoids (PRMs) lattices (PRLs) defining adjoint pairs. First of all, we introduce the connection lattice effect algebra according to concept given Borzooei, together with proof that operation in any commutative quasiresiduated is t-norm. Then, offer gen...