EUROCORES_LogiCCC: LoMoReVI_Contextualism, supervaluation, and fuzzy logic

Vagueness is a ubiquitous phenomenon pervading almost all forms of human interaction. It is a topic with many facets that receives attention from many disciplines ranging from the humanities (philosophy, linguistics, cognitive science, psychology) to sciences (logic, mathematics, computer science) and engineering applications (data extraction, control theory, etc.). By focusing on logical issues and corresponding formal models of reasoning with vague information this project seeks to integrate different strands of relevant research in a new and useful manner. These models will refer to a common formal framework, allowing to clarify the relation between different theories of vagueness, but also to other forms of imperfect information and to potential application scenarios. The main method consists in providing connections and translations between different accounts of reasoning under vagueness, using various logical formalisms as flexible descriptive tools. This is expected to lead to extensions and novel applications of logical games, t-norm based fuzzy logics, modal logics and corresponding analytic deduction systems.

Vagueness is a ubiquitous phenomenon pervading almost all forms of human interaction. It is a topic with many facets that receives attention from many disciplines ranging from the humanities (philosophy, linguistics, cognitive science, psychology) to sciences (logic, mathematics, computer science) and engineering applications (data extraction, control theory, etc.). In answer to a call by the European Science Foundation ESF, a consortium of logicians and computer scientists in Barcelona, in Prague, and in Vienna devised the collaborative research project Logical Models of Reasoning with Vague Information (LoMoReVI) that explored an approach to vagueness based on the idea that a formal logic of vagueness suggests a graded notion of truth and thus brings into play so-called fuzzy logics as a mathematical basis for corresponding models. These models have been extended in various ways that take up insights from other research areas concerned with the phenomenon of vagueness, in particular analytic philosophy and semantics of natural language. The Austrian part of the project has been motivated by the fact that linguists and philosophers often point out that fuzzy logics are too narrow a basis for modeling vagueness: Only a systematic consideration of contexts of utterances leads to models that reflect relevant features of human communication. Consequently the research team at TU Vienna investigated formal bridges between fuzzy logics and contextual models. For example, it has been shown that, starting with a mathematical frame for a context based evaluation of vague statements, one may extract implicit degrees of truth from such frames in a systematic manner. This leads to functions over degrees of truth that match the formal counterparts of logical connectives like and, or, not, and implies as they are used in various fuzzy logics. It turned out that semantic games are a particular useful and flexible formal tool for this endeavor. Moreover, the game based approach opens a route to another concern of the project. Namely, to describe analytic deduction systems that support the automated search for formal proofs of validity or, more generally, of logical consequence claims in the relevant logics. On the other hand, considering extensions of existing semantic games leads to results on fuzzy quantifiers that are intended as models of vague quantifier expressions like many, few, or about half. Given the indicated fruitfulness of the game based approach, it will be explored in a more systematic manner in follow-up projects.