Formal Characterization Research Articles

Understanding Visualization: A Formal Approach Using Category Theory and Semiotics

This paper combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding visualization in practice, including: Relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualizations, and the use of those visualizations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how familiar information visualization concepts (such as literalness, sensitivity, redundancy, ambiguity, generalizability, and chart junk) arise naturally from it and can be defined formally and precisely. This paper generalizes previous work on the formal characterization of visualization by, inter alia, Ziemkiewicz and Kosara and allows us to formally distinguish properties of the visualization process that previous work does not.

Test-data generation for control coverage by proof

Abstract Many tools can check if a test set provides control coverage; they are, however, of little or no help when coverage is not achieved and the test set needs to be completed. In this paper, we describe how a formal characterisation of a coverage criterion can be used to generate test data; we present a procedure based on traditional programming techniques like normalisation, and weakest precondition calculation. It is a basis for automation using an algebraic theorem prover. In the worst situation, if automation fails to produce a specific test, we are left with a specification of the compliant test sets. Many approaches to model-based testing rely on formal models of a system under test. Our work, on the other hand, is not concerned with the use of abstract models for testing, but with coverage based on the text of programs.

Introduction to the special issue on spatial learning and reasoning processes

This issue presents the evolving understanding of spatial cognition. Considering individual differences in spatial problem solving has both expanded the domain of spatial thinking and led to new ways to measure spatial thinking. While there is general agreement in the field that spatial thinking is not one unitary process, there is less agreement about what cognitive processes might subserve spatial thinking. The SILC research center has found a typology used in semantic analysis helpful in guiding research. This typology postulates two dimensions of spatial representation— thinking about static versus moving objects, and thinking about spatial relations within versus between objects. There is evidence that these two dimensions are cognitively and neurologically distinct (Chatterjee 2008). Research in this issue expands what we know about these dimensions in understanding reasoning about spatial relations at small (object-level) scales and larger (navigation-level) scales. Understanding the mechanisms underlying spatial thinking requires programmatic research that crosses disciplinary boundaries in psychology (e.g., perception, cognition, linguistics) and between the social and natural sciences. This issue offers case studies to illustrate the value of this approach. Further, the issue provides examples of the interrelationship between basic science in this area and applications to education. A central goal of our work is to use our understanding of spatial thinking to support education, particularly science, technology, engineering and mathematics education. A number of papers in this issue approach complex spatial thinking by looking at how humans understand the complex spatial patterns found in nature (Atit et al., Harris et al., Hinze et al., Jee et al., and Resnick & Shipley). An interdisciplinary approach to spatial thinking has fostered collaborations between natural science experts and cognitive scientists. It also guides a developmental approach to visualizing spatial change that spans the range from novice (or young) spatial reasoner to expert. The successes reported in this issue in the fields of geology (Resnick et al. and Jee et al.), chemistry (Hinze et al.) and mathematics (Flanagan, Schultheis & Barkowsky and Taylor & Tenbrink) can serve as models for how to develop our understanding of how the mind works by understanding how it grasps formal scientific descriptions of the world and how to best educate novice spatial thinkers. Concretely, this issue offers formal characterization of how humans visualize non-rigid changes (Atit et al. and, Resnick & Shipley), reviews what we know about the development of this skill in children (Harris et al.), examines this skill in experts, and even how it enters into the language used when thinking about folding paper (Taylor & Tenbrink). This issue also explores new ways to promote spatial learning, by applying research on analogical processing. For example, Jee et al. show that students’ learning of the geoscience concept of a fault can be promoted by providing them with highly alignable contrasting pairs. The expansion of research has built on new ways of assessing spatial thinking. It has also suggested a natural learning path from action to abstraction, whereby spatial knowledge is initially grounded in embodied cognition and become more abstract through spatial processes such as gesture, sketching, analogical comparison and the use of T. F. Shipley (&) Department of Psychology and Spatial Intelligence and Learning Center, Temple University, Philadelphia, PA 19122, USA e-mail: tshipley@temple.edu

Interdependent Multi-Layer Networks: Modeling and Survivability Analysis with Applications to Space-Based Networks

This article develops a novel approach and algorithmic tools for the modeling and survivability analysis of networks with heterogeneous nodes, and examines their application to space-based networks. Space-based networks (SBNs) allow the sharing of spacecraft on-orbit resources, such as data storage, processing, and downlink. Each spacecraft in the network can have different subsystem composition and functionality, thus resulting in node heterogeneity. Most traditional survivability analyses of networks assume node homogeneity and as a result, are not suited for the analysis of SBNs. This work proposes that heterogeneous networks can be modeled as interdependent multi-layer networks, which enables their survivability analysis. The multi-layer aspect captures the breakdown of the network according to common functionalities across the different nodes, and it allows the emergence of homogeneous sub-networks, while the interdependency aspect constrains the network to capture the physical characteristics of each node. Definitions of primitives of failure propagation are devised. Formal characterization of interdependent multi-layer networks, as well as algorithmic tools for the analysis of failure propagation across the network are developed and illustrated with space applications. The SBN applications considered consist of several networked spacecraft that can tap into each other's Command and Data Handling subsystem, in case of failure of its own, including the Telemetry, Tracking and Command, the Control Processor, and the Data Handling sub-subsystems. Various design insights are derived and discussed, and the capability to perform trade-space analysis with the proposed approach for various network characteristics is indicated. The select results here shown quantify the incremental survivability gains (with respect to a particular class of threats) of the SBN over the traditional monolith spacecraft. Failure of the connectivity between nodes is also examined, and the results highlight the importance of the reliability of the wireless links between spacecraft (nodes) to enable any survivability improvements for space-based networks.

A General Framework for Rational Learning in Social Networks

This paper provides a formal characterization of the process of rational learning in social networks. Agents receive initial private information and select an option out of a choice set under uncertainty in each of infinitely many periods, observing the history of choices of their neighbors. Choices are made based on a common behavioral rule. Conditions under which rational learning leads to global consensus, local indifference and local disagreement are characterized. In the general setting considered rational learning can lead to pairs of neighbors selecting different actions once learning ends while not being indifferent among their choices. The effect of the network structure on the degree of information aggregation and speed of convergence is also considered and an answer to the question of optimal information aggregation in institutions provided. The results highlight distinguishing features between properties of Bayesian and non-Bayesian learning in social networks

A general framework for rational learning in social networks

This paper provides a formal characterization of the process of rational learning in social networks. Agents receive initial private information and select an action out of a choice set under uncertainty in each of infinitely many periods, observing the history of choices of their neighbors. Choices are made based on a common behavioral rule. Conditions under which rational learning leads to global consensus, local indifference, and local disagreement are characterized. In the general setting considered, rational learning can lead to pairs of neighbors selecting different actions once learning ends while not being indifferent among their choices. The effect of the network structure on the degree of information aggregation and speed of convergence is also considered, and an answer to the question of optimal information aggregation in networks is provided. The results highlight distinguishing features between properties of Bayesian and non-Bayesian learning in social networks.

The design of intelligent socio-technical systems

The design of intelligent socio-technical systems calls for careful examination of relevant social and organizational concepts. We present a method for supporting this design process, placing emphasis on different levels of formal characterization, with equal attention to both the analysis of concepts in a formal calculus independent of computational concerns, and the representation of concepts in a machine-processable form, fully cognizant of implementation issues—a step in the method we refer to as principled operationalization. There are many tools (i.e. formal languages) that can be used to support the design method; we define and discuss criteria for evaluating such tools. We believe that, were the method proposed to be adopted, it would enhance the state-of-the-art in the systematic design and engineering of socio-technical systems, respecting the fundamentally interdisciplinary nature of those tasks, in both their theoretical and practical dimensions.

Relational Formal Characterization of Rough Sets

Summary The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based models of rough sets [12] trying to formalize some parts of [19] following also [18] in some sense (Propositions 1-8, Corr. 1 and 2; the complete description is available in the Mizar script). Our main problem was that informally, there is a direct correspondence between relations and underlying properties, in our approach however [7], which uses relational structures rather than relations, we had to switch between classical (based on pure set theory) and abstract (using the notion of a structure) parts of the Mizar Mathematical Library. Our next step will be translation of these properties into the pure language of Mizar attributes.

Axiomatization of Socio-Economic Principles for Self-Organizing Institutions

We address the problem of engineering self-organizing electronic institutions for resource allocation in open, embedded, and resource-constrained systems. In such systems, there is decentralized control, competition for resources and an expectation of both intentional and unintentional errors. The “optimal” distribution of resources is then less important than the endurance of the distribution mechanism. Under these circumstances, we propose to model resource allocation as a common-pool resource management problem, and develop a formal characterization of Elinor Ostrom’s socio-economic principles for self-governing institutions. This article applies a method for sociologically inspired computing to give a complete axiomatization of six of Ostrom’s eight principles in the Event Calculus. A testbed is implemented for experimenting with the axiomatization. The experimental results show that these principles support enduring institutions, in terms of longevity and membership, and also provide insight into calibrating the transaction and running costs associated with implementing the principles against the behavioral profile of the institutional membership. We conclude that it is possible to express Ostrom’s principles in logical form and that they are necessary and sufficient conditions for enduring self-organizing electronic institutions to manage sustainable common-pool resources.

Insights into the function of RifI2: Structural and biochemical investigation of a new shikimate dehydrogenase family protein

The shikimate dehydrogenase (SDH) family consists of enzymes with diverse roles in secondary metabolism. The two most widespread members of the family, AroE and YdiB, function in amino acid biosynthesis and quinate catabolism, respectively. Here, we have determined the crystal structure of an SDH homolog belonging to the RifI class, a group of enzymes with proposed roles in antibiotic biosynthesis. The structure of RifI2 from Pseudomonas putida exhibits a number of distinctive features, including a substantial C-terminal truncation and an atypical mode of oligomerization. The active site of the enzyme contains substrate- and cofactor-binding motifs that are significantly different from those of any previously characterized member of the SDH family. These features are reflected in the novel kinetic properties of the enzyme. RifI2 exhibits much lower activity using shikimate as a substrate than AroE, and a strong preference for NAD+ instead of NADP+ as a cofactor. Moreover, the enzyme has only trace activity using quinate, unlike YdiB. Cocrystallization of RifI2 with NAD+ provided the opportunity to determine the mode of cofactor selectivity employed by the enzyme. We complemented this analysis by probing the role of a strictly conserved residue in the cofactor-binding domain, Asn193, by site directed mutagenesis. This study presents the first crystal structure and formal kinetic characterization of a new NAD+-dependent member of the SDH family.

A multi-level model for self-adaptive systems

This work introduces a general multi-level model for self-adaptive systems. A self-adaptive system is seen as composed by two levels: the lower level describing the actual behaviour of the system and the upper level accounting for the dynamically changing environmental constraints on the system. In order to keep our description as general as possible, the lower level is modelled as a state machine and the upper level as a second-order state machine whose states have associated formulas over observable variables of the lower level. Thus, each state of the second-order machine identifies the set of lower-level states satisfying the constraints. Adaptation is triggered when a second-order transition is performed; this means that the current system no longer can satisfy the current high-level constraints and, thus, it has to adapt its behaviour by reaching a state that meets the new constraints. The semantics of the multi-level system is given by a flattened transition system that can be statically checked in order to prove the correctness of the adaptation model. To this aim we formalize two concepts of weak and strong adaptability providing both a relational and a logical characterization. We report that this work gives a formal computational characterization of multi-level self-adaptive systems, evidencing the important role that (theoretical) computer science could play in the emerging science of complex systems.

Formally grounding spatio-temporal thinking

To navigate through daily life, humans use their ability to conceptualize spatio-temporal information, which ultimately leads to a system of categories. Likewise, the spatial sciences rely heavily on conceptualization and categorization as means to create knowledge when they process spatio-temporal data. In the spatial sciences and in related branches of artificial intelligence, an approach has been developed for processing spatio-temporal data on the level of coarse categories: qualitative spatio-temporal representation and reasoning (QSTR). Calculi developed in QSTR allow for the meaningful processing of and reasoning with spatio-temporal information. While qualitative calculi are widely acknowledged in the cognitive sciences, there is little behavioral assessment whether these calculi are indeed cognitively adequate. This is an astonishing conundrum given that these calculi are ubiquitous, are often intended to improve processes at the human-machine interface, and are on several occasions claimed to be cognitively adequate. We have systematically evaluated several approaches to formally characterize spatial relations from a cognitive-behavioral perspective for both static and dynamically changing spatial relations. This contribution will detail our framework, which is addressing the question how formal characterization of space can help us understand how people think with, in, and about space.

Towards a common agile software development model (ASDM)

In this paper we use a formal approach to describe Agile Software Development Methodologies. We extract common attributes and properties out of Agile Methodologies to establish a common Agile Software Development Model (ASDM). To build our model we take a look at the Agile Manifesto as well as eXtreme Programing (XP) and Scrum, and also a project-specific Agile Methodology called I2. We describe the Agile Software Development Methodologies in terms of Sets, Relations and Equations to make similarities and differences visible. With this formal characterization we can compare the Methodologies to each other and extract the common attributes and properties as parts of the common Agile Software Development Model (ASDM). After establishing our model we assess the explanatory power and aspects of completeness of the model to identify weakness and improvement potential. The explanatory power means the ability to characterize a Methodology and compare different Methodologies to each other. Completeness issues are related to the model itself, to the model's instantiations (e. g. describing XP with the ASDM) and the completeness of (relevant) Practices. Using this approach we try to achieve better theoretical understanding and comparability for Agile Methodologies.

Quantum Logic of the Unconscious and Schizophrenia

We introduce a quantum logic for quantum information, which we identify with the quantum logic of the psychodynamic unconscious, amenable to formal characterization through the theoretical framework of Quantum Mind. We claim that this sub rosa quantum logic of the normal mind’s unconscious domain is also the dominant, pathologically emerging logic of schizophrenia. We interpret Quantum Metalanguage as speaking as a quantum control about such a quantum logic. We then suggest that psychotherapists might learn this formal Quantum Metalanguage and apply it in practice in order to communicate more easily with schizophrenic patients. NeuroQuantology | September 2012 | Volume 10 | Issue 3 | Page 566-579

LEARNING HOW TO DESIGN A GRAPHICS PROCESSOR

This paper describes the design and implementation of a rudimentary graphics processor, called GRAFIX, intended for use in a simple handheld gaming console. The processor is a part of a laboratory in an undergraduate course on Digital Systems Design 2 (DSD2) [1-2]. The GRAFIX processor can perform two different operations: (a) drawing an individual pixel, and (b) drawing a line using the Bresenham line drawing algorithm.The DSD2 course provides foundational material on discrete mathematics and the theory of modern very-large switching circuits. It presents computer engineering students with a firm foundation in the modern theory of optimal logic design. It illustrates some applications through formal characterization of combiniational functions and sequential machines, using contemporary techniques for the automatic synthesis and diagnosis of digital systems. It discusses (i) the design of VLSI systems with problems and approaches; (ii) gound-up development of algebraic structures, lattices, Boolean algebras for a generalized switching theory; (iii) exact optimization of two-level switching functions; (iv) heuristic techniques for the optimization of two-level logic circuits; (v) analysis, synthesis and optimization of complemented binary decision diagrams (BDDs) [3]; and (vi) provides design examples throughout the course.This fairly high-level lab design of a graphics processor is possible because the students have acquired the necessary prerequisite knowledge from previous courses. None of the courses, however, has attempted to develop a complete processor of such scale. The machine specifications include: (a) interfacing of the host to the GRAFIX unit may be synchronous or asynchronous (one must be selected and the consequences of the choice must be discussed); (b) the frame buffer can be either a single port memory or a dual port memory (again, one must be selected, and the consequences of the choice must be discussed); (c) interfacing of the GRAFIX unit to the frame buffer may be synchronous or asynchronous. The GRAFIX lab is split into four sessions: (i) familiarization with tools and design of the arithmetic logic unit (ALU) for GRAFIX, (ii) design of its Data Path Unit (DPU), (iii) design of its Computing Control Unit (CCU), and (iv) integration and testing.The objectives of those sessions are to learn how to (a) formulate an architecture of a simple graphics processor, (b) formulate an appropriate ALU, (c) formulate a DPU and CCU, (d) formulate a Command Interpreter, (e) formulate an Controller/Sequencer, (f) formulate the CCU interfacing with the GRAFIX I/O and with the DPU, (g) construct test procedures for each unit and incremental testing, (h) construct a supervisory module to provide the completed GRAFIX processor with test input, (i) integrate the system, (j) test operation of the GRAFIX processor, and (k) describe the system. VERILOG is used as the hardware-description language of choice.The paper provides a detailed description of the architecture of the graphics processor, its design and implementation, as well as experience from running the laboratory many times.

Parameterized loop tiling

Loop tiling is a widely used program optimization that improves data locality and enables coarse-grained parallelism. Parameterized tiled loops, where the tile sizes remain symbolic parameters until runtime, are quite useful for iterative compilers and autotuners that produce highly optimized libraries and codes. Although it is easy to generate such loops for (hyper-) rectangular iteration spaces tiled with (hyper-) rectangular tiles, many important computations do not fall into this restricted domain. In the past, parameterized tiled code generation for the general case of convex iteration spaces being tiled by (hyper-) rectangular tiles has been solved with bounding box approaches or with sophisticated and expensive machinery. We present a novel formulation of the parameterized tiled loop generation problem using a polyhedral set called the outset . By reducing the problem of parameterized tiled code generation to that of generating standard loops and simple postprocessing of these loops, the outset method achieves a code generation efficiency that is comparable to existing code generation techniques, including those for fixed tile sizes. We compare the performance of our technique with several other tiled loop generation methods on kernels from BLAS3 and scientific computations. The simplicity of our solution makes it well suited for use in production compilers—in particular, the IBM XL compiler uses the inset-based technique introduced in this article for register tiling. We also provide a complete coverage of parameterized tiling of perfect loop nests by describing three related techniques: (i) a scheme for separating full and partial tiles; (ii) a scheme for generating tiled loops directly from the abstract syntax tree representation of loops; (iii) a formal characterization of parameterized loop tiling using bilinear forms and a Symbolic Fourier-Motzkin Elimination (SFME)-based parameterized tiled loop generation method.

2.4. Criteri d’identità e adeguatezza logica

Aim of the paper is to make some steps towards a formal characterization of identity criteria. First of all, we analyse some logical requirements identity criteria are supposed to satisfy and observe that some commonly used identity criteria fail to meet some of them. We focus in particular on the equivalence requirement. We consider then the proposals which have been given so far and aimed at providing logical adequacy to non-equivalent identity conditions. To this purpose, we analyse Williamson’s and De Clerq and Horsten’s treatment of identity criteria. We expand their formal framework, characterizing identity conditions in terms of contexts and levels of granularity too.

Exploring the conceptual universe.

Humans can learn to organize many kinds of domains into categories, including real-world domains such as kinsfolk and synthetic domains such as sets of geometric figures that vary along several dimensions. Psychologists have studied many individual domains in detail, but there have been few attempts to characterize or explore the full space of possibilities. This article provides a formal characterization that takes objects, features, and relations as primitives and specifies conceptual domains by combining these primitives in different ways. Explaining how humans are able to learn concepts within all of these domains is a challenge for computational models, but I argue that this challenge can be met by models that rely on a compositional representation language such as predicate logic. The article presents such a model and demonstrates that it accounts well for human concept learning across 11 different domains.

A core reference ontology for the customer relationship domain

Customer Relationship Management (CRM) has emerged as an important strategy that companies should implement in order to build profitable and stable relationships with their customer. The domain of CRM has peculiar characteristics: a CRM strategy is largely independent from the specific market sector, it requires multiple units cooperation, it implies the management of a huge amount of knowledge, it is fruitfully supported by software solutions, and finally it implies the integration of human and machine activities. These characteristics suggest that both companies aiming at implementing an efficient CRM strategy, and software houses offering ICT solutions supporting CRM would take great advantage from a common semantic model of CRM. The main contribution of this paper is thus the proposal of O-CREAM-v2, a core reference ontology lbr the CRM domain, specifically targeted to Small and Medium Sized Enterprises (SME). The design of O-CREAM-v2 has been based on requirements mainly elicited from a domain analysis, which considered the way the involved actors talk about CRM within their business, by analyzing documents and interviews with representatives of SME and ICT companies. Moreover, in order to guarantee accuracy in the definition of the basic concepts and to support interoperability within/between companies, O-CREAM-v2 has been developed within the framework provided by the well-known DOLCE foundational ontology, together with three DOLCE extensions, i.e. the ontology of Descriptions and Situations, the Ontology of Intbrmation Objects and the Ontology of Plans. O-CREAM-v2 is composed by two layers: an upper core, which models more general concepts and relations, and can be useful also in business domains other than CRM, and a lower core, representing concepts and relations specific to the CRM domain. The content requirements defined by the domain analysis pointed out that an ontology for the CRM domain has to account for both particulars (such as activities, otters, sales, etc.) and information about them (customer records, reports about sales, etc.). Moreover, since CRM is typically supported by software tools, O-CREAM-v2 includes the formal characterization of software applications. Thus, O-CREAM-v2 is structured into five modules: Relationships, Knowledge, Activities (all three spanning both the upper and the lower core), Software and Miscellaneous (both limited to the upper core). The five ()-CREAM modules arc described in details in the paper. The discussion is concluded by mentioning two possible exploitation perspectives for O-CREAM-v2, which could be the basis for building: (a) Web-based repositories supporting the mediation between supply and demand of CRM-related tools; (b) tools supporting users in building the formal representations of resources in ontology-based IR systems and in the semantic search engines application field.

Style Representation in Design Grammars

The concept of style is relevant for both the analysis and synthesis of designs. New styles are often formed by the adaptation of previous ones based on changes in design criteria and context. A formal characterization of style is given by shape grammars, which describe the compositional rules underlying a set of designs. Stylistic change can be modelled by grammar transformations, which allow the transformation of the structure and vocabulary of a grammar that is used to describe a particular style. In order for grammars to be useful beyond a single application, they should have the capability to be transformed according to changing design style needs. Issues of formalizing stylistic change necessitate a lucid and formal definition of style in the design language generated by a grammar. Furthermore, a significant aspect of the definition of style is the representation of aesthetic qualities attributed to the style. We focus on grammars for representing and generating styles of design and review the use of grammar transformations for modelling changes in style and design language. We identify a gap in knowledge in the representation of style in grammars and in driving strategic style change using grammar transformations.