Symbolic Reasoning Research Articles

Think!: A unified numerical–symbolic knowledge representation scheme and reasoning system

More and more applications of artificial intelligence technologies are made in biomedical software and equipment. These applications are multiple: intelligent alarms, intelligent monitoring, diagnosis support, …. Several different knowledge representation schemes are already in use: decision trees, first-order logic expert systems, calculations (mathematical modeling), trained neural network simulations, …. All these techniques have their own preferred field of application, and they do not overlap. Building a complete diagnosis support tool would require the use of several of these techniques. The problem is therefore communication between these very different systems and the complexity of the composite result. This paper describes the Think! formalism: a unified symbolic-connectionist representation scheme which tries to subsume some of the precited formalisms. Being able to integrate these knowledge representation schemes in a single model enables us to use existing knowledge bases and existing knowledge extraction techniques to make them communicate and work together.

Descartes's Regulae, mathematics, and modern psychology: "the Noblest example of all" in Light of Turing's (1936) On computable Numbers.

There are surprisingly strong connections between the philosophy of mind and the philosophy of mathematics. One particular important example can be seen in the Regulae (1628) of Descartes. In "the noblest example of all," he used his new abstract understanding of numbers to demonstrate how the brain can be considered as a symbol machine and how the intellect's algebraic reasoning can be mirrored as operations on this machine. Even though his attempt failed, it is illuminating to explore it because Descartes launched 2 traditions--mechanistic philosophy of mind and abstract mathematics--that would diverge until A. Turing (1936) approached symbolic reasoning in a similar "symbol machine-existence proof" way. Descrates's and Turing's thought experiments, which mark the beginning of modern psychology and cognitive science, respectively, indicate how important the development of mathematics has been for the constitution of the science of mind.

Symbols, Impossible Numbers, and Geometric Entanglements: British Algebra through the Commentaries on Newton's Universal Arithmetick

Symbols, Impossible Numbers, and Geometric Entanglements is the first history of the development and reception of algebra in early modern England and Scotland. Not primarily a technical history, this book analyses the struggles of a dozen British thinkers to come to terms with early modern algebra, its symbolic style, and negative and imaginary numbers. Professor Pycior uncovers these thinkers as a 'test-group' for the symbolic reasoning that would radically change not only mathematics but also logic, philosophy and language studies. The book furthermore shows how pedagogical and religious concerns shaped the British debate over the relative merits of algebra and geometry. Positioning algebra firmly in the Scientific Revolution and pursue Newton the algebraist, it highlights Newton's role in completing the evolution of algebra from an esoteric subject into a major focus of British mathematics. Other thinkers covered include Oughtred, Harriot, Wallis, Hobbes, Barrow, Berkeley and MacLaurin.

Visual and Symbolic Reasoning in Mathematics: Making Connections With Computers?

In this article, we analyze the visual and symbolic strategies developed by students to express generalizations of number patterns and the connections they make between them. By analysis of a series of case studies, we compare the approaches adopted by students working through parallel task sequences, which integrate different computer tools in different ways. Finally, we make suggestions as to how students might be encouraged to exploit visual reasoning alongside the symbolic and draw out implications for curriculum design.

Q2 Symbolic Reasoning about Noisy Dynamic Systems

Symbolic reasoning about continuous dynamic systems requires consistent qualitative abstraction functions and a consistent symbolic model. Classically, symbolic reasoning systems have utilized a box partition of the system space to achieve qualitative abstraction, but boxes can not provide a consistent abstraction. Our Q2 methodology abstracts a provably consistent symbolic representation of noise-free general dynamic systems. However, the Q2 symbolic representation has not been previously evaluated for efficacy in the presence of noise. We evaluate the effects of noise on Q2 symbolic reasoning in the domain of maneuver detection. We demonstrate how the Q2 methodology derives a symbolic abstraction of a general dynamic system model used in evaluating maneuver detectors. Simulation results represented by ROC curves show that the Q2 based maneuver detector is superior to a box-based detector. While no method is consistent in the presence of noise, the Q2 methodology is superior to the classic box’s approach for deriving qualitative decisions about noisy dynamic systems.

A Hybrid Architecture for Situated Learning of Reactive Sequential Decision Making

In developing autonomous agents, one usually emphasizes only (situated) procedural knowledge, ignoring more explicit declarative knowledge. On the other hand, in developing symbolic reasoning models, one usually emphasizes only declarative knowledge, ignoring procedural knowledge. In contrast, we have developed a learning model CLARION, which is a hybrid connectionist model consisting of both localist and distributed representations, based on the two-level approach proposed in [40]. CLARION learns and utilizes both procedural and declarative knowledge, tapping into the synergy of the two types of processes, and enables an agent to learn in situated contexts and generalize resulting knowledge to different scenarios. It unifies connectionist, reinforcement, and symbolic learning in a synergistic way, to perform on-line, bottom-up learning. This summary paper presents one version of the architecture and some results of the experiments.

Hybrid architecture for shape reconstruction and object recognition

The proposed architecture is aimed to recover 3-D- shape information from gray-level images of a scene; to build a geometric representation of the scene in terms of geometric primitives; and to reason about the scene. The novelty of the architecture is in fact the integration of different approaches: symbolic reasoning techniques typical of knowledge representation in artificial intelligence, algorithmic capabilities typical of artificial vision schemes, and analogue techniques typical of artificial neural networks. Experimental results obtained by means of an implemented version of the proposed architecture acting on real scene images are reported to illustrate the system capabilities.

A logic-based environment for reactive agents in intelligent CAD systems

This paper is an evolution of a previous article by the authors [1](Bento, J. P., Feijó, B., Lloyd-Smith, D., Computers and Structures, 1977, 63(5), 1015–1032) motivated by the need to provide computational support to an agent-based implementation of design processes. It presents a new programming environment to support the development of CAD systems based on a hybrid agent architecture in which the symbolic reasoning is carried out by first-order logic. The reactive behaviour of the agents can be achieved through a number of characteristics proposed for the object-oriented environment. This environment is also a general proposal for representing engineering design knowledge in which logic is integrated into an object-oriented paradigm. © 1998 Published by Elsevier Science Limited. All rights reserved.

In time and over time

Van Gelder's clear distinction between the quantitative nature of dynamical systems and the nonquantitative nature of computational processes provides a firm basis for distinguishing between processes that happen in time and processes that happen over time. Symbolic reasoning, the presumed basis of intelligent behavior in robots, happens over time. However, the movements and actions that robots must make to behave intelligently, happen in time. Attempting to connect the two, as classical artificial intelligence and robotics have presumed to be necessary, has produced a tension and an arbitrarily moving interface in the construction of robots. Adopting a robotic version of the dynamical hypothesis offers sound theoretical and scientific justification for those robotics researchers who continue to insist that getting the interaction dynamics of intelligent behavior right is a purely dynamical matter, and never a symbolic computational one.

Co‐management and self‐determination in Nunavut

This paper explores the question of power relations within co‐management institutions in Nunavut and, in particular, their role in the Inuit peoples’ efforts to achieve self‐determination. Following the presentation of an interpretive model outlining the three possible interactions within co‐management institutions—integration, transaction, and empowerment—a case study of the co‐management institutions pertaining to wildlife in Nunavut is conducted. The experience of the interim wildlife board, established in 1990, particularly the crisis surrounding the setting of a quota for beluga harvest in three southeast Baffin communities, can be interpreted as an attempt at co‐optation. Resistance from Inuit hunters allowed for an increase in the quotas, although the concept of quotas per se was not called into question. The Nunavut Wildlife Management Board, established in 1994, has more power than its predecessor. However, the initial experiences of the NWMB indicate that the Federal government is determined to maintain tight control over the management of sensitive wildlife species for economic or symbolic reasons. The co‐management experience in Nunavut must fit within the framework defined by Canadian society, thereby allowing for only limited self‐determination.

Clarifying and Teaching Bohm-Bawerk's “Marginal Pairs”

In history of economic thought courses, Eugen von Bohm-Bawerk (18511914) is usually introduced as one of the early Austrian economists who contributed to the theories of capital and interest. If time permits, however, key differences between the Austrian and neoclassical methods can easily be illustrated using Bohm-Bawerk's pairs theory of price.' Bohm-Bawerk begins a horse trade with one potential buyer and one potential seller. He adds traders on one side of the market, then on the other, and finally proposes a general rule for the determinants of price. Because the valuations of the last successful buyer and seller2 (one marginal pair) and of the first unsuccessful buyer and seller (another marginal pair) determine the range of feasible market-clearing prices, his analysis is commonly called marginal pairs. Students often find Bohm-Bawerk's 20-page discussion to be clear, if a bit wordy, and more intuitive than the curves of neoclassical microeconomic theory. It is a convenient way to illustrate the good and bad aspects of a number of attributes of the Austrian school: a preference for working with discrete units of indivisible goods, verbal rather than symbolic mathematical reasoning, cause-andeffect analysis rather than mutual determination, and imperfect markets with limited numbers of traders. For counterpoint, George Stigler's (1966, 313) comments are useful:

Automata based symbolic reasoning in hardware verification

Automata based symbolic reasoning in hardware verification

The Digital Anatomist distributed framework and its applications to knowledge-based medical imaging.

The domain of medical imaging is anatomy. Therefore, anatomic knowledge should be a rational basis for organizing and analyzing images. The goals of the Digital Anatomist Program at the University of Washington include the development of an anatomically based software framework for organizing, analyzing, visualizing and utilizing biomedical information. The framework is based on representations for both spatial and symbolic anatomic knowledge, and is being implemented in a distributed architecture in which multiple client programs on the Internet are used to update and access an expanding set of anatomical information resources. The development of this framework is driven by several practical applications, including symbolic anatomic reasoning, knowledge based image segmentation, anatomy information retrieval, and functional brain mapping. Since each of these areas involves many difficult image processing issues, our research strategy is an evolutionary one, in which applications are developed somewhat independently, and partial solutions are integrated in a piecemeal fashion, using the network as the substrate. This approach assumes that networks of interacting components can synergistically work together to solve problems larger than either could solve on its own. Each of the individual projects is described, along with evaluations that show that the individual components are solving the problems they were designed for, and are beginning to interact with each other in a synergistic manner. We argue that this synergy will increase, not only within our own group, but also among groups as the Internet matures, and that an anatomic knowledge base will be a useful means for fostering these interactions.

Formal Model for Road Traffic Collision Risk Avoidance

Abstract An on-board collision avoidance system contains a reasoning level which integrates numerical and symbolic information and returns accordingly the adequate deliberate response. The study focuses on the primitives that are required by both the analysis and the decision parts of the reasoning process. Some insight is gained in the symbolic reasoning process with the definition of a numerical expressive representation of the universe of discourse's dynamics. This study is based on the possibility theory and uses graph modelling.

Knowledge acquisition and representation for expert systems in the field of financial analysis

Knowledge acquisition and representation has been characterised as the major bottleneck in the development of expert systems (Barr & Geigenbaum, 1982), especially in problem domains of high complexity. Financial analysis is one of the most complicated practical problems, where the expert systems technology is highly applicable, mainly because of its symbolic reasoning and its explanation capabilities. The aim of this paper is to present a complete methodology for knowledge acquisition and representation for expert systems development in the field of financial analysis. This methodology has been implemented in the development of the FINEVA multicriteria knowledge-based decision support system for the assessment of corporate performance and viability. The application of this methodology in the development of the FINEVA system is presented.

Three Applications of a Familiar Formula

appears in many elementary mathematics courses. In this article I present three of my favorite applications of this formula, solutions to problems that at first glance might seem quite unrelated to it. The problems are simple enough that students with little mathematical background, possibly working in groups, can explore them on their own to discover and present solutions. The mixture of logical thinking and elementary algebra may help students see the power of symbolic reasoning in mathematics. Problem 1: Regions in the plane. Into how many regions is the plane partitioned by n lines, no two of which are parallel and no three of which are concurrent (i.e., have a common point)?

Distributed associative memories for high-speed symbolic reasoning

This paper briefly introduces a novel symbolic reasoning system based upon distributed associative memories which are constructed from correlation matrix memories (CMM). The system is aimed at high-speed rule-based symbolic operations. It has the advantage of very fast rule matching without the long training times normally associated with neural-network-based symbolic manipulation systems. In particular, the network is able to perform partial matching on symbolic information at high speed. As such, the system is aimed at the practical use of neural networks in high-speed reasoning systems. The paper describes the advantages and disadvantages of using CMM and shows how the approach overcomes those disadvantages. It then briefly describes a system incorporating CMM.

Rapid conceptual design evaluation using a virtual product model

This paper presents an architecture and test results for a computer-based system for assisting the conceptual phase of building design. The system uses 3D CAD to represent a graphic model of the design, and it uses AI symbolic models of the geometric forms, intended functions and computed and assigned behaviors of the design. The system uses A1 symbolic reasoning methods to analyze design behavior and compare predicted behavior with intended function. The Semantic Modeling Extension (SME) system incorporates a virtual product model: a small but extendible set of classes that define generic forms, functions and behaviors of facilities. After drawing a design using 3D CAD, a designer interactively creates interpretation objects as instances of the virtual product model. The interpretation objects express the meaning of the graphic representation with respect to a particular engineering issue, such as energy use or cost. The interpretation represents geometric and topological attributes of the features for use by automated design analysis tools. Interpretation objects unite support for graphically-oriented design thinking with support for automated symbolic reasoning. The paper includes an example building design scenario using the software prototype, illustrating how interpretation of the geometric model produces a symbolic model and supports multiple and changing analyses and evaluations during design. Students and practising engineers have tested the system in classes and workshops.

REDRAW — a diagrammatic reasoning system for qualitative structural analysis

For preliminary analysis of structures, human engineers often employ diagrams as a visual language to study and to gain intuitive understanding about the behavior of structures. This paper reports a preliminary study and the development of a prototype system for diagrammatic reasoning to better emulate the intuitive visual problem solving techniques of human engineers. Diagrammatic reasoning is a type of reasoning in which the primary means of inference is the direct manipulation and inspection of a diagram. Diagrammatic reasoning is prevalent in human problem-solving behavior, especially for problems involving spatial relationships among physical objects. Our research examines the relationship between diagrammatic reasoning and symbolic reasoning in a computational framework. We have built a system called REDRAW, that emulates the human capability for reasoning with pictures for qualitative analysis of simple frame structures. Diagrammatic representations provide an environment where inferences about the physical results of proposed structural configurations can take place in a more intuitive manner than that possible through purely symbolic representations.

Automatic construction of accurate models of physical systems

This paper describes an implemented computer program called PRET that automates the process of system identification: given hypotheses, observations, and specifications, it constructs an ordinary differential equation model of a target system with no other inputs or intervention from its user. The core of the program is a set of traditional system identification (SID) methods. A layer of artificial intelligence (AI) techniques built around this core automates the high-level stages of the identification process that are normally performed by a human expert. The AI layer accomplishes this by selecting and applying appropriate methods from the SID library and performing qualitative, symbolic, algebraic, and geometric reasoning on the user's inputs. For each supported domain (e.g., mechanics), the program uses a few powerful encoded rules (e.g., σF=0) to combine hypotheses into models. A custom logic engine checks models against observations, using a set of encoded domain-independent mathematical rules to infer facts about both, modulo the resolution inherent in the specifications, and then searching for contradictions. The design of the next generation of this program is also described in this paper. In it, discrepancies between sets of facts will be used to guide the removal of unnecessary terms from a model. Power-series techniques will be exploited to synthesize new terms from scratch if the user's hypotheses are inadequate, and sensors and actuators will allow the tool to take aninput-output approach to modeling real physical systems.