The project MATOMUVI is a European project funded under the 2009 IRSES call. It gathers 15 universities in 5 countries (Argentina, Brazil, Czech Republic, Italy, and Spain) and has involved so far circa 30 researchers within these countries. The project spans across the period 15 March 2011 – 15 March 2015.
The scientific objectives of the project aim at exploring some of the most promising new directions outlined by the recent results in many-valued logic. The overall expected benefits include the expansion and reinforcement of the applicability of many-valued logic to real life problems, a systematisation of the existing knowledge on the subject and extensions of the current tools to cope with more complex problems, where vagueness and uncertainty are entangled.
Objective 1: Systematisation of the study of many-valued logics related to residuated lattices
The study of many-valued logics has seen in the last decades a vast amount of interest among researchers worldwide. Those studies gave rise to a multitude of logical systems. One of the objectives of our research is to systematise their study. Our plan of studies includes a unified algebraic study of prominent many-valued logics; the abstract study of translations and interpretations among logical systems, and applications of the tools offered by the formal combinations of logics.
Objective 2: Formal systems for vagueness and uncertainty
The second objective of our research is the development of unified formal systems in which vagueness and uncertainty can be handled together. Contrary to classical probability theory, which deals with yes-no events, continuously valued events are denoted by sentences in many-valued logic. The challenge is to extend classical results to many-valued logics, aiming at a general theory of probabilities over continuously valued events. These objectives call for a deeper comprehension of duality theory for the algebras of many-valued logics, advanced in the representation theory for the algebraic semantics of many-valued logic and an implementation of theoretical studies into formal systems geared to applications.
Objective 3: Stable foundations to our collaborations and coordinated further research
Based on our joint research enterprise, we will endeavour to create a solid partnership out of our existing network of collaborations. To this end, we will set the bases for a consortium whose activities will be the study, promotion and development of the topic of vague and uncertain reasoning.
The consortium will facilitate the flow of information through the community and stimulate an environment favourable to the development of projects of mutual interest.
The main research topics touched by the project are organised in work packages (WPs).