GETFUN · Generalizing Truth-Functionality

Generalizing Truth-Functionality

The scientific guideline of the GeTFun project was to study and relate various well-motivated ways in which the attractive properties and meta-properties of truth-functionality might be generalized to cover more extensive logical grounds. Besides the abstract, model- and proof-theoretical aspects, the project aimed to keep a strong focus in meaningful application areas where the complexity of the phenomena involved goes beyond the scope of standard approaches. The impact and relevance of the proposed line of work should accordingly be measured directly by its foundational character with respect to a better and deeper understanding of meaning in logics modeling complex phenomena and, of necessity, suitable general forms of compositional reasoning. The project had 10 Work Packages, each divided into 2 tasks. The investigations on the semantic perspective aimed to experiment with different ways of controlling the amount of non-determinism allowed by each non-standard variety of semantics, while retaining good computational behavior. The work on the proof-theoretical generalizations of the Principle of Compositionality fell into two main classes: work that generalizes Gentzen-type deductive systems by adding syntactical information to these systems in the form of generic labels, different levels of sequents, terms or a proof-search strategy, and work that constrains the deductive system via a strongly adequate semantics for it. Finally, the applications focused on complex and interacting systems that may be organized into the following broad areas: modal logics (with many uses, from security in computer science, specially of the reactive type, to modelling of quantum systems); logics for reasoning under uncertainty and inconsistency (such as paraconsistent and fuzzy logics, for instance, with applications to knowledge representation and databases, but also to probabilistic reasoning); and combinations of logical systems (e.g., fuzzy modal logics, where compositional aspects of complex systems will profit the most from results stemming from our investigations on the semantic and the proof-theoretical perspectives). The GeTFun project involved 16 partners from 9 different countries. Members of the project were involved in close to 100 secondments. As planned, the project held four successful international workshops (Rio de Janeiro, Brazil, in 2013; Vienna, Austria, in 2014; Natal, Brazil, in 2015; and Coimbra, Portugal in 2016). During its four year span, the scientific work encompassed by the GeTFun originated in more than 250 new research articles, published or submitted. Emphasis should be put on the fact that close to 50 of these papers are coauthored by project members coming from more than one GeTFun participant institution, which highlights the merits of the collaboration provided by the project. For the project logo, a summary, and further details on GeTFun see the website sqig.math.ist.utl.pt/GeTFun.

Data: CORDIS, © European Union