Logical Models of Reasoning with Vague Information

Collaborative Research Project within the EUROCORES programme LogICCC of the European Science Foundation (ESF)

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.). Given this wide range of different aspects and approaches, no comprehensive, uniform theory of vagueness can be expected to emerge without methodological difficulties. However, we think that focusing on logical issues and corresponding formal models of reasoning with vague information allows to integrate different strands of relevant research in a new and useful manner. These models should 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. Our main method will consist 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.

We envisage a comprehensive foundational framework that integrates relevant aspects of reasoning with vague information, mainly consisting in extensions of and translations between logical formalisms. Five clusters of research tasks circumscribe our aims:

  1. Explore and formalize connections between degree based, supervaluational, epistemic and contextualist theories of vagueness and the respective role of formal logic in these approaches.
  2. Develop t-norm based fuzzy logics as an information based model of reasoning under vagueness, in particular including higher order formalisms and modal extensions.
  3. Explore the role of game theory in modeling vagueness and define various logical games (dialogue, evaluation and comparison games) associated with fuzzy logics and related logics.
  4. Investigate relations to other forms of imperfect information, with special attention to communication of agents in contexts of vague information.
  5. Explore applications to knowledge extraction from data in different frameworks (GUHA method, Lixto web tool).