Contextualism, supervaluation, and fuzzy logic
Vienna Group, Project Leader (PL) The Project Leader (PL) of a CRP is the main representative of the CRP. She/he is a Principal Investigator of an Individual Project in the CRP she/he represents. She/he is normally the representative of the CRP to the ESF and in the Scientific Committee of the EUROCORES Programme. She/he is responsible for communication with the other Principal Investigators of her/his CRP. An Associated Partner can not act as a PL. PL / Principal Investigator (PI) A scientist who leads an Individual Project (IP) is a Principal Investigator (PI). He/she applies via the EUROCORES CRP for funding from a national funding organisation which is participating in a EUROCORES Programme (EUROCORES Funding Organisation -EFO). He/she must be based in a country or associated with an organisation participating in the EUROCORES programme and eligible to apply to that organisation. There can be maximum 2 PIs per IP (One PI and one Co-PI). PI Christian Fermüller, funding:
People: Matthias Baaz, Agata Ciabattoni, Christian Fermüller, Christoph Roschger
Phenomena and concepts of vagueness have been the subject of intense debates and investigations in two very different fields. On the one hand, there is a prolific and lively discourse on vagueness in analytic philosophy, that is well documented: Various competing 'theories of vagueness' seek to explain correct reasoning with vague propositions and predicates. On the other hand, fuzzy logics, i.e., degree based truth functional logics are often explicitly motivated as 'logics of vagueness'. For the most part, these two fields proceed without much interaction. At times rather polemic debates between philosophers, logicians, and engineers about adequate concepts of reasoning with vague information, witness severe differences in aims, methods, and standards between the relevant fields.
The main aim of this project is to show how these seemingly incompatible and competing approaches to reasoning under vagueness may usefully complement each other, if viewed, not so much as different theories about the same phenomena, but rather as conceptual models of different aspects of vagueness at different levels of idealization and abstraction. In building corresponding bridges between deductive fuzzy logic and relevant philosophical accounts, we will focus on two theories of vagueness - supervaluationism and contextualism - that are not only topical and popular among many experts, but for which also corresponding formal logical frameworks have already been worked out to some degree.
Building on previous work on connections between supervaluation and fuzzy logic, we aim at a formal framework that integrates contexts, admissible precisifications, truth functional connectives and relevant modal operators. Different intended applications that require the processing of vague information will thus receive a flexible basis for analysis, formalization, and implementation of corresponding proof systems.
LoCoMoTion - Logics for combining models of reasoning under imperfect information
Barcelona Group, Principal Investigator (PI) A scientist who leads an Individual Project (IP) is a Principal Investigator (PI). He/she applies via the EUROCORES CRP for funding from a national funding organisation which is participating in a EUROCORES Programme (EUROCORES Funding Organisation -EFO). He/she must be based in a country or associated with an organisation participating in the EUROCORES programme and eligible to apply to that organisation. There can be maximum 2 PIs per IP (One PI and one Co-PI). PI Lluís Godo, funding: MECPeople: Teresa Alsinet Felix Bou, Pilar Dellunde, Francesc Esteva, Lluis Godo, Enrico Marchioni, Carles Noguera
Most relevant models of reasoning with imperfect information try to address and formalize three notions: uncertainty, truthlikeness and vagueness. These three notions appear as the basic axes of information-based reasoning models which respectively correspond to complete vs. incomplete information, exact vs. approximate information and sharp vs gradual information.
Uncertainty models and measures are meant to deal with incomplete information states and usually refer to the notion of belief regarding the truth of a proposition (usually crisp but not necessarily so) and is typically graded. From a logical point of view, uncertainty formalisms (e.g. probabilistic, possibilistic) 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, this last concept being often associated with reasoning by analogy which is an important form of non-demostrative inference. According to Niiniluoto, the truthlike value of a sentence is considered as its degree of proximity to the truth, even though it may not be true. This degree, also of an intensional nature, is given by the (semantical) distance that separates (or dually, by the similarity between) the models of a sentence and the models of the reality. On the other hand, information may contain expressions which refer to gradual properties. For this kind of inherently vague properties there are no suitable characterizations of their meaning in terms of two-valued (true/false) interpretations, since graduality calls for intermediate truth states. So far, most successful and in-depth studied information based models to represent and reason with vague propositions are those systems of mathematical fuzzy logic known as t-norm based fuzzy logics.
In this project we want to put the emphasis in developing formal systems combining fuzziness with both uncertainty and truthlikeness. We think that defining modal many- valued logical systems is the right way to attack this combination problem, and it will fill an existing gap in the literature. We will pay special attention to semantics 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 subprojects to some modal extensions of t-norm based fuzzy logics relevant to the above mentioned combinations.
Fuzzy logic as a basis for a common framework of vague reasoning
Prague Group, Principal Investigator (PI) A scientist who leads an Individual Project (IP) is a Principal Investigator (PI). He/she applies via the EUROCORES CRP for funding from a national funding organisation which is participating in a EUROCORES Programme (EUROCORES Funding Organisation -EFO). He/she must be based in a country or associated with an organisation participating in the EUROCORES programme and eligible to apply to that organisation. There can be maximum 2 PIs per IP (One PI and one Co-PI). PI Petr Hájek, funding: GACRPeople: Libor Behounek, Marta Bilkova, Petr Cintula, Petr Hajek, Zuzana Hanikova, Martin Holena, Rostislav Horcik, Petra Ivaničová, Ivan Kramosil, Ondrej Majer, Michal Pelis
The four aims of the Prague group refer to the general clusters of research tasks listed at the overview page:
- To lead and coordinate the project's objective (B) to further develop tnorm based fuzzy logics. We concentrate on broadening of our knowledge of the subject and establishing novel parts of the field in order to make the theory sufficiently rich and flexible to serve as a background for the connections/translations from/to other formalisms (objective (A)) and to establishing relation to other forms of imperfect information (objective (D), and aim (4) of this sub-project).
- As a part of the objective (C) to concentrate on evaluation and comparison games associated with fuzzy logics and related substructural logics and their relation to other parts of the project.
- As a part of the objective (D) to concentrate on relations with probability and possibility theory. In particular, analysis of the notions of conditional possibility and similar notions in a very abstract setting and their use in fuzzy logic.
- To lead and coordinate LoMoReVI in its objective (E) of applying the results achieved during the project in the area of knowledge extraction from data.
