Residuated (lattices) Multilattices and Applications
Organizer
Speaker
Lele Celestin
Time
Monday, March 9, 2026 3:30 PM - 4:30 PM
Venue
A6-101
Online
Zoom 204 323 0165
(BIMSA)
Abstract
A lattice is a partially ordered set in which every pair of elements has both a greatest lower bound and a least upper bound. Lattice theory finds applications in various domains, including fuzzy logic programming and coding theory, information retrieval and access control. However, many real-world reasoning systems involve ambiguity, partiality, or incomparability; features that standard lattice structures are not well equipped to model. Multilattices extend the notion of lattices by permitting elements to have multiple, possibly incomparable, joins or meets. In this way, they provide a more exible framework by allowing multiple, potentially incomparable, upper or lower bounds. Residuated lattices are algebraic structures that naturally emerge in the study of ordered systems, logic, and theoretical computer science. They provide a unifying framework for analyzing a wide range of logical systems; particularly substructural logics, and offer deep insights into order-theoretic properties and algebraic reasoning. Over the years, various subclasses of residuated lattices have been investigated, including MV-algebras, which correspond to Lukasiewicz logic; BL-algebras, associated with Basic Logic; and MTL-algebras, which represent the algebraic semantics of monoidal t-norm based logic. Each class is characterized by additional axioms or structural properties that capture specific behaviors within logical and algebraic frameworks. Other notable classes of residuated lattices include Boolean algebras, idempotent residuated lattices, pseudo-complemented residuated lattices, and R`-monoids (i.e., divisible residuated lattices), among others. In 2008, the concept of semi-Boolean algebras was introduced as a generalization of Boolean algebras by relaxing certain structural constraints. Building on these developments, this talk proposes to define and explore new classes of residuated (residuated) multilattices, investigate their structural properties, and examine their potential applications in logic, computation, coding theory, knowledge representation and Formal Concept Analysis.