SYSMICS is a European project funded under the 2015 Marie Sklodowska-Curie Action RISE. It gathers 25 universities in all 5 continents and 55 researchers have taken part in the action. The project spans across the period 1 March 2016 – 28 February 2019.
The acronym SYSMICS stands for: Syntax meets Semantics – Methods, Interactions, and Connections in Substructural logics.Substructural logics are formal reasoning systems that refine classical logic by weakening the structural rules in Gentzen sequent calculus. While classical logic generally formalises the notion of truth, substructural logics allow to handle more precisely resources, vagueness, meaning, and language syntax; these systems are motivated by studies in computer science, epistemology, economy, and linguistics. In addition, from a theoretical point of view, substructural logics provide a refined perspective of classical logic, since the former often exhibit features which are either absent or trivialised in the classical case.
Traditionally, substructural logics have been investigated following three main approaches: proof theoretic, algebraic and abstract study. Although some connections among these approaches were observed long ago, in large part these practices developed in independence. As a result, the research directions, tools and motivations for each approach developed in relative isolation.
The main objective of this project is to establish a network of collaborations between the experts of these diverse methods to investigate substructural logics in a cohesive fashion, taking into account these three distinct yet complementary points of view. This combined perspective on substructural logics might have a deep impact on the field and this project will provide a stable basis of cooperation for a large, international community of algebraists, logicians and theoretical computer scientists. To reach this goal, the workloadhas been organized in work packages as follows:
WP1 – Managements tasks and practicalities.
WP2 – Organisation of the two conferences. Press conferences. Organisation of four workshops. Preparation of two broad audience-oriented papers.
WP3 – Organisationof two schools.
WP4 – Developing a theory of translations between logics, establishing connections between deductive theorems and algebraic filters, study finite and infinite Beth’s definability for abstract logics, and to develop a resource-conscious Abstract Algebraic Logic
WP5 – Developinganalytic calculi for substructural logics, and deploy them toprove meta-logical theorems.
WP6 – Developing the algebraic machinery needed for a deeper understanding ofsubstructural logics.
WP7 – Export the method of canonical formulas to substructural logics. Providealgebraic methods for verifying the robustness of proof systems.
WP8 – Dual semantics for substructural logics and canonical extensions. Comprehensivestudy of completions and their applications to decidability problems.
WP9 – Algebraic semantics of modal extensions of substructural logics. Investigationof relations between truth preserving consequence relations andparaconsistency.
