Ewa Orlowska

Incomplete Information: Rough Set Analysis

Introduction: What You Always Wanted to Know about Rough Sets.- Rough Sets and Decision Rules: Synthesis of Decision Rules for Object Classification On the Lower Boundaries in Learning Rules from Examples On the Best Search Method in the LEM1 and LEM2 Algorithms.- Algebraic Structure of Rough Set Systems: Rough Sets and Algebras of Relations Rough Set Theory and Logic-Algebraic Structures.- Dependence Spaces: Dependence Spaces of Information Systems Applications of Dependence Spaces.- Reasoning About Constraints: Indiscernibility-Based Formalization of Dependencies in Information Systems Dependencies between Many-Valued Attributes.- Indiscernibility-Based Reasoning: Logical Analysis of Indiscernibility Some Philosophical Aspects of Indiscernibility Rough Mereology and Anayltical Morphology.- Similarity-Based Reasoning: Similarity Versus Preference in Fuzzy-Based Logics A Logic for Reasoning about Similarity Information Systems, Similarity Relations and Modal Logics.- Extended Rough Set-Based Deduction Methods: Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations Rough Logics: A Survey with Further Directions On the Logic with Rough Quantifier.

Representation of nondeterministic information

Abstract In this paper we develop a method of dealing with nondeterministic information. We introduce the concept of knowledge representation system of nondeterministic information and we define a language providing a means for defining nondeterministic information. We also develop deduction methods for the language.

DAL—a logic for data analysis

Abstract In this paper we present some ideas how to analyse data using logic tools. We define a logic language for expressing data analysis problems and we develop a deductive system for the language to use proof procedures to obtain solutions to these problems.

Kripke semantics for knowledge representation logics

This article provides an overview of development of Kripke semantics for logics determined by information systems. The proposals are made to extend the standard Kripke structures to the structures based on information systems. The underlying logics are defined and problems of their axiomatization are discussed. Several open problems connected with the logics are formulated. Logical aspects of incompleteness of information provided by information systems are considered.

Expressive power of knowledge representation systems

In this article we attempt to clarify some aspects of expressive power of knowledge representation systems. We show that information about objects provided by a system is given up to an indiscernibility relation determined by the system and hence it is incomplete in a sense. We discuss the influence of this kind of incompleteness on definability of concepts in terms of knowledge given by a system. We consider indiscernibility relations as a tool for representing expressive power of systems, and develop a logic in which properties of knowledge representation systems related to definability can be expressed and proved. We present a complete set of axioms and inference rules for the logic.

Semantics of Vague Concepts

For many years vagueness understood as a deficiency of meaning has been the subject of investigations and many authors are engaged in this research. The present paper is an attempt to show that problems concerning semantics of vague concepts may find their proper foundation in the theory of rough sets originated by Pawlak (1982). We give a formal framework to what is considered to be different ways of making vague concepts precise and we describe semantics within this framework. Following the idea accepted by many logicians that reasoning in a language containing expressions representing vague concepts requires a special logic, we present a kind of modal logic suitable for deductions in the presence of vagueness.

Logic of nondeterministic information

In the paper we define a class of languages for representation o knowledge in those application areas when a complete information about a domain is not available. In the languages we introduce modal operators determined by accessibility relations depending on parameters.

Introduction: What You Always Wanted to Know about Rough Sets

In this chapter the major principles and the methodology of the rough set—style analysis of data are presented and discussed. A survey of various formalisms that provide the tools of this analysis is given. We discuss the aspects of incompleteness of information that can be handled in the presented formalisms. The formalisms are related to the methods and/or structures presented in this volume, in each case we point out a relevant link and we give the reference to the respective chapter.

Semantic analysis of inductive reasoning

Abstract Inductive learning is analysed from the semantic point of view. Processes of forming generalisations of concepts determined by examples of expert decisions are discussed. It is claimed that since concepts are relative to background knowledge, their inductive generalisations can be determined only approximately. Induction rules are defined providing a method of forming generalisations preserving positive and/or negative instances of concepts.

Relational Proof Systems for Modal Logics

The purpose of this paper is to give a survey of the relational formalization of modal logics. The paradigm ‘formulas are relations’ leads to the development of a relational logic based on algebras of relations. The logic can be viewed as a generic logic for the representation of nonclassical logics; in particular a broad class of multimodal logics can be specified within its framework. As a consequence, proof systems for the relational logic become a convenient tool for the development of a proof theory for nonclassical logics. The relational logic enables us to represent within a uniform formalism the three basic components of any propositional logical system: syntax, semantics and deduction apparatus. The essential observation, leading to a relational formalization of logical systems, is that a standard relational structure (a Boolean algebra with a monoid) constitutes a common core of a great variety of nonclassical logics. Exhibiting this common core on all the three levels of syntax, semantics and deduction, enables us to create a general framework for representation, investigation and implementation of nonclassical logics.