Spanish AC project corresponding to the EUROCORES FP006 project "Logical Models for Reasoning under Vague Information (LoMoReVI)
The main goal is to develop "formal systems combining fuzziness with both uncertainty and truthlikeness". Fuzziness refers to gradual and vague properties, and most successful information based models to reason with vague propositions are those systems of mathematical fuzzy logic called t-norm based fuzzy logics. On the other hand, uncertainty models deal with incomplete information, and from a logical point of view, uncertainty formalisms are captured by intensional, modal-like logics, ... which are non-truth functional. Truthlikeness, probably the less known of the above three notions, can be regarded as a special case of the more general concept of similarity and its logical counterpart as some form of similarity-based reasoning, where the truthlike value of a sentence is considered as its degree of proximity to the truth (even though it may not be true).
We think that defining modal many-valued logical systems is the right way to attack this combination problem, and this will fill an existing gap in the literature. Our efforts will be devoted to semantic issues. In particular we will study the adaptation of the dialogue game semantics for fuzzy logics, which is also a common focus of interest of the other two partners of the full Eurocores project (Prague and Vienna), to some modal expansions of t-norm based fuzzy logics relevant to the above mentioned combinations. Additional issues over the above t-norm based logical systems that we will develop are fuzzy description logics, temporal and dynamic extensions of modal many-valued logics, as well as flexible inconsistency handling mechanisms such as (i) revision/merging operators which have been scarcely considered in the literature in the many-valued context, or (ii) argumentation models in the presence of vagueness/uncertainty.