Logics for Qualitative Reasoning

The project is concerned with the logical foundations of qualitative representation and reasoning applied in artificial intelligence. Qualitative Reasoning (QR) has emerged as a subfield of Artificial Intelligence to deal with representation and reasoning about continuous aspects of entities and systems in a symbolic, but human-like manner. The main issue in the QR approach is to develop an adequate tool for modeling situations in which information is not sufficiently precise or cannot be described by numerical values.

The project aims to develop logical theories and tools for qualitative representation and reasoning, with applications to many domains for which qualitative inference methods are significant.

The research at the first stage of the project is concerned with a systematic study and further development of qualitative logics, such as qualitative logics of time and space, logics for order-of-magnitude qualitative reasoning, and qualitative logics for dynamic (fuzzy) systems, among others. The primary objective, however, is to establish new qualitative logics for dealing with those problems which so far do not have logical representation in a qualitative style. In the construction of the logics we will concentrate on the relational logics which allow to represent within a uniform formalism the three basic components of formal systems: syntax, semantics, and deduction apparatus. In this way the relational approach provides a general framework for representation, investigation, and implementation of various theories with different languages and/or semantics. The relational methods are powerful and have already been applied in the representation of qualitative reasoning. The ultimate objective is to develop a unified logical framework in the relational style that captures significant types of qualitative representation and reasoning methods used in different areas of science.

The project is also aimed at analysis of model-theoretic properties of qualitative logics, such as definability and expressive power, finite model property, and decidability, among others. The third research objective is the construction and implementation of deduction systems for the logics developed in the project. We focus on decidable logics and their automated decision procedures in the style of relational dual tableaux.

The project is based at the Institute of Philosophy at the University of Warsaw. In total, the project team will consist of five researchers, three PhD students, and one graduate student.

Project details:

Project title: Logics for Qualitative Reasoning
Principal Investigator: Joanna Golińska-Pilarek
Funding Organization: National Science Centre (NCN) in Poland
Project type: MAESTRO 1 (advanced grants)
Project Volume: 1 013 320 PLN
Project Duration: June 2012 – May 2017
Host Institution: University of Warsaw, Institute of Philosophy

Project Team:

Domenico Cantone, University of Catania, Italy (since 2013)
Son Thanh Cao, University of Warsaw, Poland (since October 2013)
Joanna Golińska-Pilarek, University of Warsaw, Poland
Tomasz Lechowski, University of Warsaw, Poland (since October 2013)
Marianna Nicolosi Asmundo, University of Catania, Italy (since 2013)
Ewa Orłowska, National Institute of Telecommunications, Poland
Przemysław Wałęga, University of Warsaw, Poland (since October 2012)
Michał Zawidzki, University of Lodz and University of Warsaw, Poland (since October 2013)