Technical ReportPDF Available

Concept-oriented model and nested partially ordered sets

Authors:

Abstract

Concept-oriented model of data (COM) has been recently defined syntactically by means of the concept-oriented query language (COQL). In this paper we propose a formal embodiment of this model, called nested partially ordered sets (nested posets), and demonstrate how it is connected with its syntactic counterpart. Nested poset is a novel formal construct that can be viewed either as a nested set with partial order relation established on its elements or as a conventional poset where elements can themselves be posets. An element of a nested poset is defined as a couple consisting of one identity tuple and one entity tuple. We formally define main operations on nested posets and demonstrate their usefulness in solving typical data management and analysis tasks such as logic navigation, constraint propagation, inference and multidimensional analysis.
A preview of the PDF is not available
... COM has been described at conceptual level as well as syntactically using the concept-oriented query language (COQL) [30,29,25] with limited formalization. COM has also been implemented in two systems: a self-service tool for analytical data integration, ConceptMix [24] and a framework for data wrangling and agile data transformations, DataCommandr [22]. ...
... An independent but very important mechanism is that this structure allows for labels with duplicate names but it restricts its use according to the type constraint (structural analogue of the function extension principle). Another way to visualize nested partially ordered sets is to show it is a nested Euler diagram with both sets and elements partially ordered or a tree representing inclusion relation with nodes partially ordered [25]. ...
Preprint
Full-text available
The plethora of existing data models and specific data modeling techniques is not only confusing but leads to complex, eclectic and inefficient designs of systems for data management and analytics. The main goal of this paper is to describe a unified approach to data modeling, called the concept-oriented model (COM), by using functions as a basis for its formalization. COM tries to answer the question what is data and to rethink basic assumptions underlying this and related notions. Its main goal is to unify major existing views on data (generality), using only a few main notions (simplicity) which are very close to how data is used in real life (naturalness).
... The solution is based on a new general-purpose model, called the concept-oriented model (COM) (Savinov, 2014b(Savinov, , 2014c(Savinov, , 2012c(Savinov, , 2011a(Savinov, , 2009a. It provides a unified view on data by combining many existing views and patterns of thoughts currently used in data modeling. ...
... It is also tightly integrated with a novel approach to programming, called concept-oriented programming (COP) (Savinov, 2005c(Savinov, , 2008(Savinov, , 2009b(Savinov, , 2012a. A distinguishing property of this model is that it relies on order-theoretic basis (Savinov, 2014c) but its use of partial order is different from the approaches described in (Raymond, 1996) and (Buneman et al., 1991;Zaniolo, 1984). COM is inherently multidimensional and analytical but at the same time it works directly with transactional data without the need to define such elements as cubes, measures and dimensions for each analysis scenario like it is done in standard OLAP models (Pedersen & Jensen, 2001;Pedersen, 2009). ...
Preprint
Full-text available
In spite of its fundamental importance, inference has not been an inherent function of multidimensional models and analytical applications. These models are mainly aimed at numeric (quantitative) analysis where the notions of inference and semantics are not well defined. In this paper we argue that inference can be and should be integral part of multidimensional data models and analytical applications. It is demonstrated how inference can be defined using only multidimensional terms like axes and coordinates as opposed to using logic-based approaches. We propose a novel approach to inference in multidimensional space based on the concept-oriented model of data and introduce elementary operations which are then used to define constraint propagation and inference procedures. We describe a query language with inference operator and demonstrate its usefulness in solving complex analytical tasks.
Conference Paper
Full-text available
The main goal of concept-oriented programming (COP) is describing how objects are represented and accessed. References (object locations) in COP are made first-class elements responsible for many important functions which are difficult to model via objects. COP rethinks and generalizes such primary notions of object-orientation as class and inheritance by introducing a novel construct, concept, and a new relation, inclusion. They make it possible to describe many mechanisms and patterns of thoughts currently belonging to different programming paradigms: modeling object hierarchies (prototype-based programming), precedence of parent methods over child methods (inner methods in Beta), modularizing cross-cutting concerns (aspect-oriented programming), value-orientation (functional programming).
Chapter
Full-text available
Book
By ‘model’ we mean a mathematical description of a world aspect. With the proliferation of computers a variety of modeling paradigms emerged under computational intelligence and soft computing. An advancing technology is currently fragmented due, as well, to the need to cope with different types of data in different application domains. This research monograph proposes a unified, cross-fertilizing approach for knowledge-representation and modeling based on lattice theory. The emphasis is on clustering, classification, and regression applications. It is shown how rigorous analysis and design can be pursued in soft computing using conventional (hard computing) methods. Moreover, non-Turing computation can be pursued. The material here is multi-disciplinary based on our on-going research published in major scientific journals and conferences. Experimental results by various algorithms are demonstrated extensively. Relevant work by other authors is also presented both extensively and comparatively.
Article
We demonstrate the power of object identities (oid's) as a database query language primitive. We develop an object-based data model, whose structural part generalizes most of the known complex-object data models: cyclicity is allowed in both its schemas and instances. Our main contribution is the operational part of the data model, the query language IQL, which uses oid's for three critical purposes: (1) to represent data-structures with sharing and cycles, (2) to manipulate sets and (3) to express any computable database query. IQL can be statically type checked, can be evaluated bottom-up and naturally generalizes most popular rule-based database languages. The model can also be extended to incorporate type inheritance, without changes to IQL. Finally, we investigate an analogous value-based data model, whose structural part is founded on regular infinite trees and whose operational part is IQL.
Article
Identity is that property of an object which distinguishes each object from all others. Identity has been investigated almost independently in general-purpose programming languages and database languages. Its importance is growing as these two environments evolve and merge. We describe a continuum between weak and strong support of identity, and argue for the incorporation of the strong notion of identity at the conceptual level in languages for general purpose programming, database systems and their hybrids. We define a data model that can directly describe complex objects, and show that identity can easily be incorporated in it. Finally, we compare different implementation schemes for identity and argue that a surrogate-based implementation scheme is needed to support the strong notion of identity.