Descriptive knowledge about an Information System can be expressed in declarative form by means of a binary Boolean based language. This paper presents a contribution to the study of an arbitrary multivalued Information System structure by introducing an algebra (not binary) that allows the treatment of multiple valued data tables with systematic algebraic techniques. Elements |ti| and ||tp||, called arrays and co-arrays, are defined, operations ~, ‡ and ∘ are described. The proposed methodology allows multivalued algebraic expressions describing a multivalued Information System (multivalued Object Attribute Table). Furthermore, the same Information System can be described by several distinct, but equivalent, algebraic expressions. Among these, the prime-ar expression is singled out. The usefulness of the described algebra to represent an Information System is shown.

An algebra for the treatment of multivalued Information systems

Theory and techniques allowing the inference of precise declarations from a multivalued table are developed. The concepts of cartesian subuniverse and cartesian cosubuniverse are presented, together with a symbolic notation that allows the expression of definitions and theorems in compact array and coarray form. This symbolic notation also provides straight forward computational techniques to deal efficiently with the involved inductive or deductive calculi.

A Numerical Computation for Declarative Expressions

Descriptive knowledge about a multivalued data table or Object Attribute Table can be expressed by means of a binary Boolean based language. Efforts to design computer programs that determine declarations have been made. This endeavor is mainly directed to binary declarations.

The Zero Array: A Twilight Zone

Scientific and engineering disciplines are developing daily. This progress is strongly connected to complex techniques and methods. Over the years countless efforts have been made to process data. However it is surprising to observe that the majority of methods and techniques used are binary based. In recent years, due to the development of Knowledge Discovery in Databases, many techniques and tools that discover useful information and knowledge in databases have been designed. Knowledge Discovery in Databases is the nontrivial process of identifying valid, novel, potentially useful, and understandable patterns in data [1].

A framework for combining multivalued data: a practical approach

A reality, supposedly described by an Object Attrribute Table, and an unspecified language capable to describe subsets of objects are assumed. The requirements for an statement to be true are investigated, using set theoretical concepts only. The results lead to a sufficient condition for a statement to be deduced from a set of other statements (premises), by means of some algorithmic approach.

A Formulation for Language Independent Prelogical Deductive Inference

This paper deals with the systematical checking of the possible equality of two functions or what is the same, of two expressions. The nature of the problem is first considered. The concept of Universe is reexamined. The concepts of Object Attribute Power Table, Prime Universe, Prime Table and Canonical Expression, unique for each class of equivalent functions, are introduced. A procedure to determine the Canonical Expression is presented.

Josep Miró

Papers

Equality of Functions in CAST

A Numerical Computation for Declarative Expressions

A Formulation for Language Independent Prelogical Deductive Inference