# Anita WasilewskaStony Brook University | Stony Brook · Department of Computer Science

Anita Wasilewska

Ph.D.Mathematics, Warsaw Univ

## About

77

Publications

4,881

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

433

Citations

Introduction

**Skills and Expertise**

Additional affiliations

August 1986 - present

Education

September 1968 - May 1975

September 1961 - May 1967

**Warsaw University**

Field of study

- Mathematics, Computer Science

## Publications

Publications (77)

It is a great pleasure to write this tribute in honor of Scott A. Smolka on his 65th birthday. We revisit Goldin, Smolka hypothesis that persistent Turing machine (PTM) can capture the intuitive notion of sequential interaction computation. We propose a topological setting to model the abstract concept of environment. We use it to define a notion o...

It is a great pleasure to write this tribute in honor of Scott A. Smolka on his 65th birthday. We revisit Goldin, Smolka hypothesis that persistent Turing machine (PTM) can capture the intuitive notion of sequential interaction computation. We propose a topological setting to model the abstract concept of environment. We use it to define a notion o...

Hilbert style systems are easy to define and admit different proofs of the Completeness Theorem but they are difficult to use. By humans, not mentioning computers. Their emphasis is on logical axioms, keeping the rules of inference, with obligatory Modus Ponens, at a minimum.

We define and discuss here a Rasiowa and Sikorski Gentzen style proof system QRS for classical predicate logic. The propositional version of it, the RS proof system, was studied in detail in Chap. 6 These both proof systems admit a constructive proof of completeness theorem. We adopt Rasiowa, Sikorski (1961) technique of construction a counter mode...

Proof systems are built to prove, construct formal proofs of statements formulated in a given language formulated in a given language. First component of any proof system is hence its formal language \(\mathcal{L}\).

Intuitionistic logic has developed as a result of certain philosophical views on the foundation of mathematics, known as intuitionism. Intuitionism was originated by L. E. J. Brouwer in 1908. The first Hilbert style formalization of the intuitionistic logic, formulated as a proof system, is due to A. Heyting (1930). In this chapter we present a Hil...

Propositional languages are also called zero order languages, as opposed to predicate languages that are called first order languages. The same applies to the use of terms propositional and predicate logic; they are often called zero order and first order logics and we will use both terms equally.

The theory of computation is based on concepts defined by logicians and mathematicians. Logic plays a fundamental role in computer science, and this book explains the basic theorems, as well as different techniques of proving them in classical and some non-classical logics. Important applications derived from concepts of logic for computer technolo...

Until recently, till the end of the nineteenth century, mathematical theories used to be built in an intuitive or axiomatic way. In other words, they were based either intuitive ideas concerning basic notions of the theory – ideas taken from the reality – or on the properties of these notions expressed in systems of axioms. The historical developme...

We define here a general notion of a propositional language. We obtain, as specific cases, various languages for propositional classical logic as well as languages for many non-classical logics.

The Hilbert proof systems are systems based on a language with implication and contain a Modus Ponens rule as a rule of inference. They are usually called Hilbert style formalizations. We will call them here Hilbert style proof systems, or Hilbert systems, for short.

There are several quite distinct approaches to the Completeness Theorem, corresponding to the ways of thinking about proofs. Within each of the approaches there are endless variations in exact formulation, corresponding to the choice of methods we want to use to proof the Completeness Theorem. Different basic approaches are important, though, for t...

Logic builds symbolic models of our world. It builds them in such a way as to be able to describe formally the ways we reason in and about it. It also poses questions about correctness of such models and develops tools to answer them. Classical Logic was created to describe the reasoning principles of mathematics and hence reflects the “black” and...

Formal theories play crucial role in mathematics and were historically defined for classical predicate (first order logic) and consequently for other first and higher order logics, classical and non-classical.

The article explains why the author is so grateful to Professor Zdzisław Pawlak whom was possible to meet on her way from mathematics to computer science.

The incentive of the mobile applications presented in this paper is the extensive spread of the mobile phone culture during the past decade. The first application is CalorieMeter, a calorie intake monitoring application. Cheer Up, the second application is based on self-help scientific methodologies for diagnosing possibilities of different kinds o...

We present here a formal syntax and semantics for a notion of a descriptive granularity. We do so in terms of three abstract models: Descriptive, Semantic, and Granular. The descriptive model formalizes the syntactical concepts and properties of the data mining, or learning process. Semantic model formalizes its semantical properties. The Granular...

The pervasiveness of the mobile phone culture in informal economies in underdeveloped countries, as well as in immigrant communities in developed countries even in areas devoid of electricity and computers has been a motivation for the development of two mobile phone applications presented in our paper. The first is an account book application base...

There are over 3.5 billion mobile phones in the world and they are proliferating at astounding rates across socioeconomic and cultural boundaries. They also provide unprecedented opportunities for enabling social impact and technical activism. To most of the people in informal economies and immigrant communities, the mobile phone is the dominant co...

Africa is the fastest growing mobile phone market in the world. The portfolio of available mobile phone applications that impact the populations of the continent is however limited in number and scope. Future African graduates will be the main vectors for the development of mobile applications. In this paper we present a model of teaching mobile ap...

The proliferation of mobile phones across the world, to people of all statures, has provided platform to bring computing resources to the masses. In this paper we present three mobile phone applications designed to aid the businesses and people of informal economies in developing countries. The goal of the applications is to assist in the growth of...

We address the problem of specifying and detecting emergent behavior in networks of cardiac myocytes, spiral electric waves in particular, a precursor to atrial and ventricular fibrillation. To solve this problem we: (1) apply discrete mode abstraction to the cycle-linear hybrid automata (CLHA) we have recently developed for modeling the behavior o...

Glossary
Definition of the Subject
Introduction
Granular Model: Syntax and Semantics for Data Mining
Semantic Model
Descriptive Model
Granular Model Revisited: Satisfaction and Truth
Future Directions
Bibliography

We present here an abstract model in which data preprocessing and data mining proper stages of the Data Mining process are
are described as two different types of generalization. In the model the data mining and data preprocessing algorithms are
defined as certain generalization operators. We use our framework to show that only three Data Mining op...

We present here a formal syntax and semantics for descriptive data mining. We do so in terms of three abstract models: Descriptive, Semantic, and Granular. The Descriptive Model formalizes the syntactical concepts and properties of the data mining process. Semantic Model formalizes its semantical properties. The Granular Model establishes a relatio...

We present here a mathematical model for the Protein Secondary Structure Prediction (PSSP) problems and research. It also represents un effort to build a uniform foundations for PSSP research. The model, and hence the paper, is designed to facilitate and speed up understanding of the long standing PSSP research and its problems also for people who...

This book contains valuable studies in data mining from both foundational and practical perspectives. The foundational studies of data mining may help to lay a solid foundation for data mining as a scientific discipline, while the practical studies of data mining may lead to new data mining paradigms and algorithms. The foundational studies contain...

Data Mining, as defined in 1996 by Piatetsky-Shapiro ([1]) is a step (crucial, but a step nevertheless) in a KDD (Knowledge
Discovery in Data Bases) process. The Piatetsky-Shapiro’s definition states that the KDD process consists of the following
steps: developing an understanding of the application domain, creating a target data set, choosing the...

The model we present here formalizes the definition of Data Mining as the process of information generalization. In the model the Data Mining algorithms are defined as generalization operators. We show that only three generalizations operators: classification operator, clustering operator, and association operator are needed to express all Data Min...

We present here Semantic and Descriptive Models for Classification as components of our Classification Model (definition [17]).
We do so within a framework of a General Data Mining Model (definition [4]) which is a model for Data Mining viewed as a generalization
process and sets standards for defining syntax and semantics and its relationship for...

Successful secondary structure predictions provide a starting point for direct tertiary structure modelling, and also can significantly improve sequence analysis and sequence-structure threading for aiding in structure and function determination. Hence the improvement of predictive accuracy of the secondary structure prediction becomes essential fo...

The relational model provides simple methods for data analysis, such as query and reporting tools. Data mining systems also
provide data analysis capabilities. However, there is no uniform model which handles the representation and mining of data
in such a way as to provide a standardization of inputs, outputs, and processing. In this paper we pres...

Data mining techniques applied to decision support in real-life
problems require a multi-step process. Inputs and outputs of these steps
require some standard format to be followed in order to achieve a useful
platform for the execution of data mining algorithms. There is a need to
develop a uniform model where every operation can be expressed in a...

Today’s Data Base Management Systems do not provide functionality to extract potentially hidden knowledge in data. This problem gave rise in the 80’s to a new research area called Knowledge Discovery in Data Bases (KDD). In spite the great amount of research that has been done in the past 10 years, there is no uniform mathematical model to describe...

We use the notion of the rough set diagram introduced by A.
Wasilewska and L. Vigneron (1998) to present a general decision
procedure for validity of equations in rough Boolean algebra. First, we
establish equivalence of validity in rough Boolean algebra to validity
in so called simple rough Boolean algebra. Second, we propose a decision
method for...

We present here an approach we used for proving important
properties of clopen topological spaces. We combine powerful theorem
provers techniques (and implementations) with a graphical technique
based on a graphical representation of a rough set, called rough
diagrams. Rough diagrams are a generalization of a classical notion of
Venn Diagrams for a...

Today's Data Base Management Systems do not provide functionality to extract potentially hidden knowledge in data. This problem gave rise in the 80's to a new research area called Knowledge Discovery in Data Bases (KDD). In spite the great amount of research that has been done in the past 10 years, there is no uniform mathematical model to describe...

The rough R5 and R4 algebras investigated here are particular cases of topological rough algebras introduced by the first author [A. Wasilewska, “Topological rough algebras”, in: T. Y. Lin et al. (eds.), Rough sets and data mining: analysis of imprecise data, 411-425 (1997; Zbl 0860.03042)]. We examine and discuss here some of their most interestin...

Colloque sans acte à diffusion restreinte.

A concept of LT-fuzzy sets was introduced by Rasiowa and Cat Ho
(1992). LT-fuzzy sets are a modification of L-fuzzy sets introduced by
Goguen (1967). We introduce here a notion of a generalized rough set and
show that it can be considered as a particular case of a L-fuzzy set. We
also generalize the notion of a rough equality of sets, introduced by...

It is known [E. Orłowska, in: G. Dorn et al. (eds.), Foundations of logic and linguistics, Sel. Pap. 7th Int. Congr. Logic, Methodol. Philos. Sci., Salzburg/Austria 1983, 465-482 (1985; Zbl 0619.03020)] that the propositional aspect of rough set theory is adequately captured by the modal system S5. A Kripke model gives the approximation space (A,R)...

We present here an effective proof theory that allows one to reason within algebras of algebraic logic in a purely syntactic, algebraic fashion. We demonstrate the effectiveness of the method by discussing our automated proofs of problems and theorems taken from Professor Helena Rasiowa's book An Algebraic Approach to Non-Classical Logics, Studies...

We have used here a theorem prover DATAC (D#duction Automatique dans des Th#ories Associatives et Commutatives) to discover, study and compare properties of rough and corresponding modal algebras. The preliminary results were reported in [19]. The prover was developed at CRIN & INRIA Lorraine, Nancy (France), by the ørst author. The rough algebras...

We propose an interactive probabilistic inductive learning model which defines a feedback relationship between the user and the learning program. We extend previously described learning algorithms to a conditional model previously described by the authors, and formulate our Conditional Probabilistic Learning Algorithm (CPLA), applying conditions as...

We present here an application of Rough Set formalism to Machine Learning. The resulting Inductive Learning algorithm is described, and its application to a set of real data is examined. The data consists of a survey of voter preferences taken during the 1988 presidential election in the U.S.A. Results include an analysis of the predictive accuracy...

We present here an interactive probabilistic inductive learning system and its application to a set of real data. The data consists of a survey of voter preferences taken during the 1988 presidential election in the U.S.A. Results include an analysis of the predictive accuracy of the generated rules, and an analysis of the semantic content of the r...

We define a conditional probabilistic learning algorithm (CPLA). We use the condition suggestion algorithm (CSA) of M. Hadjimichael and A. Wasilewska [Rule reduction for knowledge representation systems, Bull. Pol. Ac.: Tech. 38, 113-120 (1990)] as a way to use the syntactic knowledge in the system to refine and reduce the number of decision rules...

This is an examination and extension of a knowledge system originally based on Pawlak’s theory of rough sets. The theory of the conditional knowledge representation system (CK) is applied to previously developed probabilistic models to develop the conditional probabilistic knowledge representation system (CPK). The conditional probabilistic rough s...

There are a number of algebraic models of information systems. They have been proposed by Codd (1972), Salton (1968), Scott (1970) and others. We deal here with a model which is the basis of a rough set investigations (Orlowska, 1984; Pawlak, 1982; Pawlak, 1984). This model was proved in (Marek, 1985) to be equivalent with the Codd's model of relat...

We define a notion of a conditional knowledge representation system, which extends the standard definition of knowledge representation systems [see Z. Pawlak, Int. J. Inf. Comput. Sci. 11, 344-356 (1982; Zbl 0501.68033), Z. Pawlak, S. K. M. Wong and W. Ziarko, Int. J. Man.Mach. Stud. 29(1), 81-95 (1988; Zbl 0663.68094)] and incorporates some ideas...

Reasoning about knowledge and knowledge representation has been an issue of concern in Artificial Intelligence for over two decades. More recently, researchers have realized that these issues also play a crucial role in other subfields of computer science, including cryptography, distributed computation, data base theory, and expert systems.
Any kn...

The concept of an information system, with manipulation based on the rough set theory, was introduced by Pawlak in 1982. The information system is defined by its set of objects, set of attributes, set of values of attributes, and a function, which maps the direct product of the first two sets onto the set of values of attributes. We introduce here,...

We use the algebraic theory of programs as in Blikle [2], Mazurkiewicz [5] in order to show that the difference between programs with and without recursion is of the same kind as that between cut free Gentzen type formalizations of predicate and prepositional logics.

We introduce here and investigate the notion of an alternative tree of decomposition. We show (Theorem 5) a general method of finding out all non-alternative trees of the alternative tree determined by a diagram of decomposition.

We introduce the notion of monadic second order definability (m.s.o definability) of automata, programs and logics and point out some classes of automata (theorem 7), programs (theorem 8) and logics (theorem 9) which are m.s.o definable.

We use here the notions and results from algebraic theory of programs in order to give a new proof of the decidability theorem for Suszko logic SCI (Theorem 3).
We generalize the method used in the proof of that theorem in order to prove a more general fact that any prepositional logic which admits a cut-free Gentzen type formalization is decidable...

This paper can be treated as a simplification of the Gentzen formalization of SCI-tautologies presented by A. Michaels in [1].

The model we present here formalizes the definition of Data Mining as the process of information generalization. In the model
the Data Mining algorithms are defined as generalization operators. We show that only three generalizations operators: classification
operator, clustering operator, and association operator are needed to express all Data Min...

We address the problem of specifying and detecting emergent behavior in networks of cardiac myocytes, spiral electric waves
in particular, a precursor to atrial and ventricular fibrillation. To solve this problem we: (1)Apply discrete mode-abstraction
to the cycle-linear hybrid automata (clha) we have recently developed for modeling the behavior of...

Cheer Up is a mobile based application that is based on tried and tested, "self-help" based, scientific methodologies for diagnosing depression and systematically healing it. This application is an attempt to make Cognitive Behavioral Therapy (referred as CBT hereafter) more accessible and make it more personalized compared to clinical visits and e...

## Projects

Project (1)

The NSF-CPS-Frontiers project CyberHeart is part of the NSF’s initiative to advance the state-of-the-art in Cyber-Physical Systems (CPS): engineered systems that are built from, and depend upon, the seamless integration of computation and physical components.