Algebraic Semantics of Substructural Logics: Constructions of residuated lattices

MANUELA BUSANICHE

Concepción

Simposio; XVIII Simposio Latinoamericano de Lógica Matemática; 2019

Association for Symbolic Logic

Substructural logics encompass many interesting logics: intuitionistic logic, fuzzy logic, relevance logic, linear logic, many-valued logics. They are logics that, when formulated as Gentzen-Style systems, lack some of the three basic structural rules: contraction, weakening or exchange. Their algebraic semantics are based on residuated lattices, therefore the analysis of these mathematical structures constitute an important tool to understand and study those logical systems uniformly.The study of substructural logics from the semantical point of view, as systems whose algebraic models are residuated structures settles a new perspective, where mathematics becomes the main tool of research. But the multitude of different structures makes the study complicated, thus the investigation of interesting subvarieties of residuated lattices is an appealing problem to address. In this talk, we will present some mathematical constructions of residuated lattices from simpler or better-known structures. We will define the subvarieties of residuated lattices whose members are built using these constructions, and we will explain the logical applications of our study.