Qualitative Reasoning

The need for a formal language in which to express and reason about spatial concepts is of crucial importance in many areas of AI and visual systems. For the last five years, spatial reasoning research by the Qualitative Spatial Reasoning Group, University of Leeds, has centred on the development and application of such a language -the RCC spatial logic. Below, we briefly describe the work of the group in this area.

One of the original motivations for research in qualitative physics was the development of intelligent tutoring systems and learning environments for physical domains and complex systems. This article demonstrates how a synergistic combination of qualitative reasoning and other AI techniques can be used to create an intelligent learning environment for students learning to analyze and design thermodynamic cycles. Pedagogically this problem is important because thermodynamic cycles express the key properties of systems which interconvert work and heat, such as power plants, propulsion systems, refrigerators, and heat pumps, and the study of thermodynamic cycles occupies a major portion of an engineering student's training in thermodynamics. This article describes CyclePad, a fully implemented articulate virtual laboratory that captures a substantial fraction of the knowledge in an introductory thermodynamics textbook and provides explanations of calculations and coaching support for students who are learning the principles of such cycles. CyclePad employs a distributed coaching model, where a combination of on-board facilities and a server-based coach accessed via email provide help for students, using a combination of teleological and case-based reasoning. CyclePad is a fielded system, in routine use in classrooms scattered all over the world. We analyze the combination of ideas that made CyclePad possible and comment on some lessons learned about the utility of various AI techniques based on our experience in fielding CyclePad.

We introduce a novel approach to the creation of Virtual Reality Art installations, which supports the design of alternative worlds, in which laws of Physics can be redefined to induce new user experiences. To implement this concept of "Alternative Reality", we have used Artificial Intelligence techniques to support the definition of the virtual environment behaviour, an approach inspired by Qualitative Reasoning systems. Besides the redefinition of physical laws, we have developed mechanisms for eliciting causal relations between events, as causality plays an important part in users' perception of virtual worlds. Our pilot installation is a CAVE TM -like system incorporating a state-of-theart computer game engine as visualisation software, which hasbeen ported to this immersive display. The event-based system underlying the game engine is used to bypass the native Physics engine and replace it with our Alternative Reality software. A first prototype has been fully implemented, the Alternative Reality modules totaling over 100,000 lines of C++ code. We present early results obtained with this approach, illustrated with examples taken from two artistic briefs, developed by digital artists associated to this research.

The paradox of the preface and the lottery paradox are paradoxes of practical certainty sharing certain features. The paradox of the lottery argues that rational agents are at once practically certain that each ticket in a lottery will lose but also practically certain some ticket will win. The paradox of the preface argues that rational agents are at once practically certain that all facts in a written volume are true, yet are also practically certain that some fact is wrong. A difference between real lotteries and prefaces is that a winning lottery ticket is generally an intended feature of the lottery, whereas incorrect facts are generally unintended.

The European Union regulatory framework on organic farming gave a new impulse to the institutionalisation of the Portuguese organic farming movement. This paper offers an analytical account based on interviews with key market and institutional actors within the organic food sector in Portugal. The qualitative analysis undertaken is underpinned by the premises of convention theory and aims at showing that this particular market is becoming polarised. This polarisation is featured by the official/pro-certification claims (where industrial and opinion conventions hold sway) and the unofficial/beyond certification claims (underpinned by green, inspirational and domestic conventions). A trend towards the 'conventionalisation' of the organic market is gradually emerging, whilst a tendency for 'movement resistance' still persists. This paper reflects upon the polarisation and polarised claims that are enmeshed in a market of disputes of contested meanings and competing conventions around organic food.

Consultation is an important feature of research and, increasingly, researchers are required to work in partnership with stakeholders to increase the impact of their work. Our aim is to demonstrate what can be learned from the scholarship on, and practice of, member checking to facilitate productive knowledge exchange. Using dialogical analysis we explore three member check interactions from three different qualitative psychology projects focusing our analysis on difficult moments between researchers and participants conceptualised here as ‘sore spots’. We identify two major genres in these sequences: participant ambivalence and participant challenge. We then consider passages that allow us to explore a more theoretical understanding of these two genres in terms of the metaphor of portraits and mirrors. Overall, we outline how implicit epistemologies and theories of subjectivity (uncomplicated, blank, and complex) may be linked to the way in which stakeholders approach research. We also provide a map with regard to the theories within which member checks can be undertaken, associated research practices in terms of a range of researcher responses to stakeholder ambivalence and challenge, and implications of these moments for knowledge exchange for qualitative research but also for psychological science as a whole. We conclude that sore spots in knowledge exchange process can be productive opportunities of transformational validity.

Keywords: member check; knowledge exchange; research impact; dialogical analysis; participant validation

The Spatial Semantic Hierarchy is a model of knowledge of large-scale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and as a method for robot exploration and map-building. The multiple levels of the SSH express states of partial knowledge, and thus enable the human or robotic agent to deal robustly with uncertainty during both learning and problem-solving.

This paper addresses some particular issues related to the difficult task of automatic mapping of Web information to help the user to find interesting and unexpected information on the Web. The approach puts together qualitative and quantitative reasoning. The qualitative reasoning is done through a spatial mereotopological calculus since we metaphorically see Web sites as space regions. As a result, documents/sites are grouped together into classes according to the spatial relation they satisfy. Quantitative reasoning is done through Information Retrieval techniques allowing users to choose a document based on a similarity measure between documents/sites. Experiments have been undertaken in two directions: to find an intuitive model to display the Web map through the development of a system called HyperMap and to discover interesting and unexpected information from the spatial Web maps metaphor.

This work is part of a larger attempt to explore the nature of symbolic understanding involving graphic technology. This study describes learning advanced mathematics that occurs through constructing qualitative reasoning methods using graphic technology. Data was gathered from a precalculus class who, for a few weeks, investigated and explored asymptotic behavior of rational functions. The analysis is based on observations of group discussions and written works. Learning about asymptotes using software which serves as tool box for numerical evaluation and graphic representation amplifies epistemological complexities related to the infinity concept. Using the software to watch examples of rational functions, generated by symbolic and graphic operations between polynomial functions, enabled students to leave their own traces on the formalization of asymptoteson its definition, its symbolic structure, and its computational procedures. The discrepancy between technology as a support for visual perception but a tool that cannot support the conception of approaching infinities, makes the study of asymptotes an intriguing domain for investigating what is being manipulated with software and how.

We present a methodology to perform Financial Analysis with as much information as available. The problem we solve is the assessment of investment projects; we are to determine whether or not an investment project is profitable. We perform that task at the qualitative, semiquantitative, and quantitative levels, depending on how much information there is at hand. The main advantage of the method presented here is that it can deal with very little information about quantities, still yielding some results. The least piece of information the system can work with is a set of Order of Magnitude Relations (omrs) among the model variables. If those omrs are sufficient to disambiguate the results of our model, we can tell whether an investment project is worthwhile or not. Our system remembers what has been said, and takes any additional information to refine its results. If all we have is a few omrs it may or may not determine the outcome of our investment project analysis. Later on, we provide the system with some more information (perhaps imprecise), and the results will be refined. The more precise the provided information is, the more accurate the results will be. If at the end, all provided variables are precise, the results are the same as performed via traditional analysis. This methodology takes ideas from the field of Qualitative Reasoning, some algorithms from graph theory and information structures, and the traditional interval computation arithmetic to perform operations under uncertainty.

This paper investigates the challenging problem of encoding the common sense knowledge involved in the manipulation of spatial objects from a reasoning about actions and change perspective. In particular, we propose a formal solution to a puzzle composed of non-trivial objects (such as holes and strings) assuming a version of the Situation Calculus written over first-order Equilibrium Logic, whose models

Qualitative modeling and reasoning is a most interesting area for applying and experimenting with machine learning techniques. Qualitative reasoning tasks of interest where machine learning can be applied include modeling, diagnosis, control, discovery, design, and knowledge compilation. This paper reviews examples of recent research into some of these applications areas. In particular, the examples given illustrate how Inductive Logic Programming (ILP; Muggleton 1990, 1992) applies naturally to these tasks when qualitative representations are used.

Foundational ontologies are axiomatic accounts of high-level domain-independent categories about the real world. They constitute toolboxes of reusable information modeling primitives for building ap- plication ontologies in specific domains. As such, they enhance seman- tic interoperability between agents by specifying descriptively adequate shared conceptualisations. The design of foundational ontologies gives rise to completely new challenges in respect of their content

This paper demonstrates that qualitative reasoning plays a crucial role for both an efficient and physi- cally correct approach to the automated formulation of an accurate quantitative model which explains a set of observations. The model which "best" repro- duces the measured data is selected within a model space whose elements are constructed by exploiting specific knowledge and techniques of

We present a methodology to perform Financial Analysis with as much information as available. The problem we solve is the assessment of investment projects; we are to determine whether or not an investment project is profitable. We perform that task at the qualitative, semiquantitative, and quantitative levels, depending on how much information there is at hand. The main advantage of the method presented here is that it can deal with very little information about quantities, still yielding some results. The least piece of information the system can work with is a set of Order of Magnitude Relations (omrs) among the model variables. If those omrs are sufficient to disambiguate the results of our model, we can tell whether an investment project is worthwhile or not. If all we have is a few omrs it may or may not determine the outcome of our investment project analysis. Later on, we provide the system with additional information (perhaps imprecise), and the results will be refined. The more precise the provided information is, the more accurate the results will be. If at the end, all provided variables are precise, the results are the same as performed via traditional analysis.

The crisis in science education and the need for innovative computer-based learning environments has prompted us to develop a multi-agent system, Betty's Brain that implements the learning by teaching paradigm. The design and implementation of the system based on cognitive science and education research in constructivist, inquiry-based learning, involves an intelligent software agent, Betty, that students teach using concept map representations with a visual interface. Betty is intelligent not because she learns on her ...

This paper presents and discusses work on the automated generation of qualitative (diagnostic) models from simulation models that have been developed for (control) engineering purposes. This work is motivated by an attempt to build model-based tools that support a closer integration of diagnostic considerations in early design phases of on-board systems for vehicles and based on the insight that such an attempt has to limit the required modeling efforts. We present the mathematical foundations and the implementation of the abstraction process and discuss the various difficulties and problems encountered when we applied the software to real automotive subsystems. These difficulties include complexity and methodological issues, and what should be, but has not been, a major concern of research on qualitative reasoning: How to obtain adequate qualitative domains.

This paper describes the use of qualitative reasoning mechanisms in designing computer-based teachable agents that users explicitly teach to solve problems using concept maps. Users can construct the required problem-solving knowledge structures without becoming involved in sophisticated programming activities. Once taught, the agent attempts to answer questions using qualitative reasoning schemes that are intuitive and easy to apply. Students can reflect on the agent’s responses, and then revise and refine this knowledge through visual interfaces. Preliminary studies have demonstrated the effectiveness of this approach.

This paper gives a isomorphic representation of the subtheories RT − , RT − EC, and RT of Asher and Vieu’s first-order ontology of mereotopology RT0. It corrects and extends previous work on the representation of these mereotopologies. We develop the theory of p-ortholattices – lattices that are both orthocomplemented and pseudocomplemented – and show that the identity (x·y) ∗ = x ∗ +y ∗ defines the natural class of Stonian p-ortholattices. Equivalent conditions for a p-ortholattice to be Stonian are given. The main contribution of the paper consists of a representation theorem for RT − as Stonian p-ortholattices. Moreover, it is shown that the class of models of RT − EC is isomorphic to the non-distributive Stonian p-ortholattices and a representation of RT is given by a set of four algebras of which one need to be a subalgebra of the present model. As corollary we obtain that Axiom (A11) – existence of two externally connected regions – is in fact a theorem of the remaining axioms...

The main approaches to qualitative reasoning are surveyed, compared and contrasted. These are the constraint based, component centred and processed based approaches. Later sections consider the efficiency of the reasoning techniques and possible applications (for instance in diagnosis and measurement interpretation). The paper concludes with a number of sections which consider representation of space and time, order of magnitude reasoning, hierarchical and multiple models and the method by which qualitative models might be generated.

This paper proposes fuzzy qualitative representation of trigonometry (FQT) in order to bridge the gap between qualitative and quantitative representation of physical systems using Trigonometry. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; the Cartesian translation and orientation are replaced by their fuzzy membership functions. Trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. We developed a MATLAB toolbox XTrig in terms of 4-tuple fuzzy numbers to demonstrate the characteristics of the FQT. This approach addresses a representation transformation interface to connect qualitative and quantitative descriptions of trigonometry-related systems (e.g., robotic systems).

Qualitative probabilistic networks were designed to overcome, to at least some extent, the quantification problem known to probabilistic networks. Qualitative networks abstract from the numerical probabilities of their quantitative counterparts by using signs to summarise the probabilistic influences between their variables. One of the major drawbacks of these qualitative abstractions, however, is the coarse level of representation detail that does not provide for indicating strengths of influences. As a result, the trade-offs modelled in a network remain unresolved upon inference. We present an enhanced formalism of qualitative probabilistic networks to provide for a finer level of representation detail. An enhanced qualitative probabilistic network differs from a basic qualitative network in that it distinguishes between strong and weak influences. Now, if a strong influence is combined, upon inference, with a conflicting weak influence, the sign of the net influence may be readily determined. Enhanced qualitative networks are purely qualitative in nature, as basic qualitative networks are, yet allow for resolving some trade-offs upon inference.

Qualitative probabilistic networks are qualitative abstractions of probabilistic networks, summarising probabilistic influences by qualitative signs. As qualitative networks model influences at the level of variables, knowledge about probabilistic influences that hold only for specific values cannot be expressed. The results computed from a qualitative network, as a consequence, can be weaker than strictly necessary and may in fact be rather uninformative. We extend the basic formalism of qualitative probabilistic networks by providing for the inclusion of context-specific information about influences and show that exploiting this information upon reasoning has the ability to forestall unnecessarily weak results.

Making inferences is crucial for understanding the world. The school may develop such skills but there are few formal opportunities for that. This paper describes an experiment designed to investigate the use of qualitative reasoning models to support deaf students in making inferences about the behaviour of populations in interactions such as commensalism, amensalism, and predation. The experiment was done in two sessions. In both, the teacher presented the concepts, which were translated to the signed language, and at the end the students answer to a test, consisting of objective questions and a written essay. In the second session qualitative models about the interactions were used to show the structure of the two populations system and the dynamics of the system over time. Statistical analysis showed that the use of qualitative models had a significant positive effect on the performance of the students. They gave more correct answers to objective questions and produced less trivial conclusions in their essays. We are confident that qualitative models have an important role to play in their scientific education and in the acquisition of Portuguese as a second language.

If we allow the magnitude and angle of a complex number (expressed in polar form) to range over an interval, it describes a semicircular region, similar to a fan; these regions are what we call complex fans. Complex numbers are a special case of complex fans, where the magnitude and angle are point intervals. Operations (especially addition) with complex numbers in polar form are complicated. What most applications do is to convert them to rectangular form, perform operations, and return the result to polar form. However, if the complex number is a Complex Fan, that transformation increases ambiguity in the result. That is, the resulting Fan is not the smallest Fan that contains all possible results. The need for minimal results took us to develop algorithms to perform the basic arithmetic operations with complex fans, ensuring the result will always be the smallest possible complex fan. We have developed the arithmetic operations of addition, negation, subtraction, product, and div...

In this report, inspired by non-constructive simulation developed in the qualitative reasoning field, we present a non-constructive interval simulation algorithm for the simulation of dynamic systems. To perform this kind of simulation, we first recast two integration methods, which were originally used in traditional numerical simulation, and made them suitable for performing interval simulation in a non-constructive manner. Then we proposed an iterative interval narrowing algorithm to control the growth of intervals during simulation. To achieve better accuracy and efficiency of the simulation, we designed several simulation modes to meet different requirements of various problems. The proposed simulation algorithm was theoretically studied in terms of its completeness, soundness, convergence, and stability. Finally two classical dynamic systems, as well as an electrical circuit model containing an algebraic loop, were used as test examples to demonstrate the validity of the proposed simulation approach.

In this paper, we describe an application of Q2Q2 learning, a recently developed approach to machine learning in numerical domains, to the automated modelling of an aquatic ecosystem from measured data. We modelled the time behaviour of phytoplankton and zooplankton in Danish Lake Glumsø using data collected by S.E. Jørgensen. The novelty of Q2Q2 learning is in its paying attention to the qualitative correctness of induced numerical models. We assessed the results by, first, performing a comparison of numerical accuracy between our approach and some state-of-the-art numerical machine learning algorithms applied to the Glumsø data, and second, we obtained expert evaluation of the induced models. The results show that Q2Q2 approach is at least comparable to competing methods in terms of numerical accuracy and gives good insight into domain phenomena.

The field of Qualitative Spatial Reasoning is now an active research area in its own right within AI (and also in Geographical Information Systems) having grown out of earlier work in philosophical logic and more general Qualitative Reasoning in AI. In this paper (which is an updated version of [25]) I will survey the state of the art in Qualitative Spatial Reasoning, covering representation and reasoning issues as well as pointing to some application areas.

La gestione della sicurezza delle dighe è compito importante a causa della rilevanza delle possibili conseguenze di malfunzionamenti o cedimenti delle strutture gestite e difficile per la complessità dei problemi che si devono affrontare.
L'intelligenza artificiale può contribuire alla gestione della sicurezza strutturale fornendo nuovi metodi e approcci di modellazione dei sistemi fisici.
In questa nota si presenta un progetto - DAMSAFE - che ha condotto allo sviluppo e al rilascio di sistemi di supporto alle decisioni nel campo della gestione della sicurezza delle dighe. Nell'ambito del progetto DAMSAFE si è fatto uso di modelli causali qualitativi, strutture di rappresentazione gerarchiche orientate agli oggetti e altre forme di rappresentazione integrate in un ambiente per la valutazione dei dati provenienti dal monitoraggio e dalle ispezioni di grandi dighe.

Incomplete information is present in many engineering domains, hindering traditional and non—traditional simulation techniques. This paper describes SQPC (semi—quantitative physics compiler), an implemented approach to modelling and simulation that can predict the behavior ofincompletely specified systems, such as those that arise in the water control domain. SQPC is the first system that unifies compositional modeling techniques with semi—quantitative representations. We describe SQPC's foundations, ...

This special volume of Decision Support Systems includes six papers on Qualitative Reasoning in Business, Finance, and Econo~aics. These papers represent a growing interest in using the techniques of Qualitative Reasoning-an approach to formulating and solving physics and engineering problems which has undergone much recent development within the field of Artificial Intelligence-in intelligent decision support systems. Readers of this journal need no introduction to the issues in decision support systems in general, but a short introduction to the field of Qualitative Reasoning (QR) from the perspective of Artificial Intelligence is a useful prologue to the papers themselves. This intioduction is necessarily the personal view of the editors, an addition to the many views of QR that have been published and debated elsewhere [2,

We formally construct the extended set of qualitative labels L over a well-ordered set. The qualitative descriptions of a given set are defined as L-fuzzy sets. In the case where the well-ordered set is finite, a distance between L-fuzzy sets is introduced based on the properties of the lattice L. The concept of the information contained in a qualitative label is introduced, leading to a formal definition of the entropy of an L-fuzzy set as a Lebesgue integral. In the discrete case, this integral becomes a weighted average of the information of the labels, corresponding to the Shannon entropy in information theory.

This paper presents a proposal for the development of laboratory assignments about the design and implementation of advanced interfaces for mobile robots using speech recognition. In these assignments, the main objective is the analysis of the possibilities for using speech interfaces as a complementary system for other interaction components with a mobile robot, such as artificial vision. The paper also