Logical approach to solving problems
The principle of truth functionality is a basic principle in many-valued logic in general, and in classical logic in particular. According to this principle, the truth-value of a complex formula is uniquely determined by the truth-values of its sub-formulas. However, real-world information is inescapably incomplete, uncertain or inconsistent, which is in conflict with this principle. One solution is to extend the usual algebraic deterministic semantics of logical systems by importing the idea of non-deterministic computations from computer science. Such an approach has led to the introduction of non-deterministic multi-valued matrices (Nmatrices). Studying and extending this idea was the aim of the 'Non-deterministic matrices and their applications for non-classical logics' (NDMANCL) project, funded by the EU. The project has been successful in helping with the development of the semantic framework of a new logical formalism, based on Nmatrices and their applications. Furthermore, its theoretical results have included refining and enlarging the framework by introducing new useful modifications. These enable Nmatrices to capture much wider classes of logics. As a result of NDMANCL, a foundational methodology has been developed for providing modular non-deterministic semantics for non-classical logics. In addition, the project has explored the application of Nmatrices in proof theory, automated deduction and fuzzy logic, which is reasoning under uncertainty. Nmatrices have proved to be a powerful tool, the use of which maintains all the advantages of ordinary propositional many-valued matrices but is applicable to a much wider range of logics. Now complete, the project has contributed to the recognition and adoption of the non-deterministic semantic paradigm by the scientific community.
