The main objective of the project is the study and development of efficient systems that allow to extract information in the context of knowledge bases or sources that contain incomplete, vague or inconsistent information. From the theoretical point of view, we intend to advance in the study of appropriate logics to describe vague and uncertain information, mainly t-norm based fuzzy logics and modal extensions to reason about graded preferences and uncertainty, and fuzzy description logics as terminological knowledge representation languages involving fuzzy concepts and relations. On the other hand, we intend to advance the study of efficient systems for reasoning problems (e.g. consequence, subsumption) for these logics. these sources. In problems with inconsistent informa- tion, usual reasoning procedures can reach contradictory conclusions. So one of our goals is also to deepen in the application and development of logical argumentative models which present to the end user justified or warranted conclusions, and to extend these models to distributed environments, where knowledge is distributed between different agents. To limit the maximum response time of the reasoning systems we will also examine the application of efficient transformations based on the problems of satisfiability and maximum satisfiability, for which there are highly efficient algorithms. Finally, we will study the use of reasoning systems studied and developed in different application do- mains, such as effective reasoning in a graded BDI agent architecture, optimization with preferences, decision support in medical diagnosis and management of online political discussions.

MaToMUVI is a FP7-PEOPLE-2009-IRSES project (PIRSES-GA-2009- 247584)

This project pivots around the satisfiability problem for logical languages including propositional logic (SAT), constraint satisfaction problems (CSP), and the fuzzy extension of description logics (FDL). Our purpose is to advance in each of the three areas using the synergy between the four groups that was initiated by previous joint projects. The concrete goals of the proposal are the following.

In SAT we want to study the structure of instances arising in industry, and apply this knowledge to develop more efficient solvers, both for SAT and for MaxSAT. In CSP we want to contribute to the problem of classification of tractable constraint languages. We will also study algorithms for geometric instances of MaxCSP and random instances for SAT of interest in computational complexity theory. In FDL we will study the expressive power and the complexity of the fragments of first-order fuzzy logic that correspond to description logics, and algorithms for satisfiability with special attention to the case of finitely valued FDLs.

The main goal of the project is the study and development of efficient systems, able to cope with
information from knowledge sources consisting on incomplete information, hence, inconsistent and
vague information. On the one hand, we want to investigate the proper logics to describe such information types, mainly t-norm based logics and fuzzy extensions for description logics. On the other hand, we
will study efficient systems for automatic reasoning, able to infer valid information from the above
mentioned knowledge sources. As the obtained information may be inconsistent, the reasoning
procedures may conclude on wrong information, so, an objective will be to study the application
and development of argumentative models, able to justify the soundness of the obtained conclusions
in front of the final user. In order to bound the response time of the reasoning system we will explore
efficient transformations based on satisfiability and maximum satisfiability problems, that already
have highly efficient solving algorithms. Finally, through the worst-case and typical complexity
study, we will bound the solving hardness for some particular reasoning problems. For typical
case complexity, we will employ either generators of synthetic problems, or real problems obtained
from semantic web ontologies but including uncertainty and vagueness in the information encoded,
according to the studied fuzzy description logics of this project.

Funding: 81.554 €