How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics

This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes exercises about it. The paper focuses on how Isaac developed an understanding of this concept, how he evaluated whether a mathematical assertion is true or false, how he generated counterexamples to disprove a statement, and the general role examples play for him in concept development and understanding.     

Experiences in Developing an Expert System for MBA Admissions

An expert system to assist in admitting students onto a part-time postgraduate course has been developed through three phases, using an expert systems shell. The first phase was an unstructured approach, which demonstrated the feasibility of the system but led to difficulties in development. The second phase followed a simplified systems analysis and resulted in a more comprehensive and structured system. However, its operation was cumbersome and unfriendly. The third phase involved developing a mathematical model of the decision-maker's judgement and led to a simpler, more effective and easier to use system.     

Expert Systems—Experiments with Rule Induction

There is currently much interest in the development of expert systems. Knowledge acquisition—developing the knowledge base from an expert—is one of the most time-consuming aspects of the process. Work is under way on methods of automating this procedure, one of which is rule induction from a set of examples. This paper introduces rule induction and evaluates some of the practical difficulties.     

Linking Discrete-Event Simulation Models with Expert Systems

This paper describes experiments designed to test the feasibility of linking discrete-event simulation models with expert systems. Two microcomputer systems are used: one contains the simulation model, while the other contains the expert system. The paper shows that by linking a simulation model with an expert system, it is possible to use the combination for simulation parameter learning, expert system development and expert system control of a simulation model.     

On the different ways that mathematicians use diagrams in proof construction

The processes by which individuals can construct proofs based on visual arguments are poorly understood. We investigated this issue by presenting eight mathematicians with a task that invited the construction of a diagram, and examined how they used this diagram to produce a formal proof. The main findings were that participants varied in the extent of their diagram usage, it was not trivial for participants to translate an intuitive argument into a formal proof, and participants’ reasons for using diagrams included noticing mathematical properties, verifying logical deductions, representing ideas or assertions, and suggesting proof approaches.     

Local computation in linear logic

This work deals with the exponential fragment of Girard's linear logic ([3]) without the contraction rule, a logical system which has a natural relation with the direct logic ([10], [7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism ([6]) with respect to the logical system in question. MSC: 03B40, 03F05.     

Compositional Meaning in Logic

The Fregean-inspired Principle of Compositionality of Meaning (PoC) for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of formal semantics and of the structure of logical derivations, the PoC is often directly reflected by metaproperties such as truth-functionality and analyticity, characteristic of computationally well-behaved logical systems.     

Physical model,theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular frequency and in the general spin-case

If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibrium turns out to be globally attractive, which can be proved by the construction of a suitable Ljapunov function. Then, the ball flight system can be transformed into a fourth-order scalar differential equation.     

Incremental Operator Assistance Knowledge System—an intelligent aid for a general class of problems

A new approach for knowledge representation and inference is introduced and discussed in this paper which is applicable to a wide range of daily problems—practically for all the problems, where some ‘strategy’ for fault search and rectification is provided by an expert. The system is efficient even if this ‘strategy’—that is, the general understanding of the actual problem—is weak. The theory finds its application in the ADAC project, corresponding to a problem raised by Circuit Foil, Luxembourg, a leader in the copper foil industry.     

Research into Expert Systems to Aid Simulation Model Formulation

The widespread availability of inexpensive computing power and recent developments in machine intelligence now makes it possible to consider computer assistance in the formulation phase of a discrete-event simulation model. The goal is to speed up this process. With this in mind, a series of prototype expert systems (written in LISP and run on an APPLE II) have been produced. The first prototype system was built using the ‘MYCIN’ approach. In the second prototype system a more informal approach was used, and the resulting computer-aided system is a natural-language understanding system. This paper outlines the need for such research and discusses the system development by describing the two main models and explaining why the natural-language approach was adopted.     

Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight

This paper focuses on the nonlinear vibration phenomenon caused by aircraft hovering flight in a rub-impact rotor system supported by two general supports with cubic stiffness. The effect of aircraft hovering flight on the rotor system is considered as a maneuver load to formulate the equations of motion, which might result in periodic response instability to the rotor system even the eccentricity is small. The dynamic responses of the system under maneuver load are presented by bifurcation diagrams and the corresponding Lyapunov exponent spectrums. Numerical analyses are carried out to detect the periodic, sub-harmonic and quasi-periodic motions of the system, which are presented by orbit diagrams, phase trajectories, Poincare maps and amplitude power spectrums. The results obtained in this paper will contribute an understanding of the nonlinear dynamic behaviors of aircraft rotor systems in maneuvering flight.     

Experiences with Using Expert Systems in O.R.

Increased awareness of expert systems technology, and the availability of relevant software, has tempted many O.R. groups to investigate the expert systems approach. This paper considers the strategies open to O.R. groups interested in employing expert systems, reviews some of the relevant software, and discusses what those O.R. groups who have already investigated the use of expert systems methods are actually doing.Some of the authors' experience of developing expert systems is discussed. The development of an expert system that helps bankers analyse company accounts is presented. The use of expert system methods as vehicles for decision analysis, and the possibilities for producing systems that act as O.R. consultants are also discussed.     

诊断和修理航空继电器故障的优化系统

为了减少目前航空继电器用于发现和修理故障的费用 ,本文建立了基于规则、事实以及其自身经验的一个专家系统——适应性诊断系统 ADS( A daptive Diagnostic System) .该系统利用推理对航空继电器检测和替换顺序进行了优化 ,使节省的费用大约为 50 % .     

A Problem-driven Approach to Expert System Development

Expert system technology can fairly be described as high profile at present. Yet its track record as a useful method for tackling problems is subject to widely differing views. This paper considers the domain of production planning and control, which has been described as a good application area for expert systems a domain where OR has had little success. The authors argue that mainstream expert system methodology is exploratory rather than problem-driven and thus is not suited to the domain. A problem-driven approach to expert system development is presented, an approach which makes use of soft systems methodology. The reasons for such an approach within production planning and control are discussed, and the use of soft systems methodology within the approach is reflected on.     

Supporting a complex audit judgment task: An expert network approach

An auditor considers a tremendous amount of data when assessing the risk that the internal control (IC) structure of an entity will fail to prevent or detect significant misstatements in financial statements. The myriad of relationships between IC variables that must be identified, selected, and analyzed often makes assessing control risk a difficult task. While some general procedures and guidelines are provided, audit standards dictate no specifically set procedures and rules for making a preliminary control risk assessment (CRA). Rather, the procedures and rules are left mostly to auditor judgment. This paper considers the appropriateness of applying artificial intelligence (AI) techniques to support this audit judgment task. It details the construction of a prototype expert network; an integration of an expert system (ES) and a neural network (NN). The rules contained in the ES model basic CRA heuristics, thus allowing for efficient use of well-known control variable relationships. The NN provides a way to recognize patterns in the large number of control variable inter-relationships that even experienced auditors cannot express as a logical set of specific rules. The NN was trained using actual case decisions of practicing auditors.     

Two Early Arabic Applications of Model-Theoretic Consequence

We trace two logical ideas further back than they have previously been traced. One is the idea of using diagrams to prove that certain logical premises do—or don’t—have certain logical consequences. This idea is usually credited to Venn, and before him Euler, and before him Leibniz. We find the idea correctly and vigorously used by Abū al-Barakāt in 12th century Baghdad. The second is the idea that in formal logic, P logically entails Q if and only if every model of P is a model of Q. This idea is usually credited to Tarski, and before him Bolzano. But again we find Abū al-Barakāt  already exploiting the idea for logical calculations. Abū al-Barakāt’s work follows on from related but inchoate research of Ibn Sīnā in eleventh century Persia. We briefly trace the notion of model-theoretical consequence back through Paul the Persian (sixth century) and in some form back to Aristotle himself.     

Expert systems in production scheduling

One area of computer-related studies that has recently been receiving considerable publicity is the development of expert systems. The more noteworthy applications of this approach to problem-solving are still in engineering and the natural sciences, but a growing number of applications to problems in business management are beginning to appear. This paper reviews recent research and discusses the applicability of an ‘expert system’ approach to problems in production scheduling.     

Logical testing for rule-base management

We present a procedure to logically reduce simple implications that comprise the rule-base of an expert system. Our method uses topological sorting on a digraph representation that detects logical inconsistency and circular reasoning in linear-time. Then, the sort order provides an efficient method to detect and eliminate forced values and redundant rules. We consider additional diagnostic aids for the rule-base manager, notably how to range the number of propositions that could be true and how to consolodate the rule-base. We than show how the simple case may be extended to logically test a general rule-base with a decomposition principle.     

Combinatorial optimization in the area of deductive derivability in expert production systems

We consider the problem of discrete optimization with 0–1 variables under the condition that the admissible solutions are logical production systems in the knowledge base of an expert system. A two-stage algorithm for solution of the problem is proposed. Translated fromDinamicheskie Sistemy, Vol. 12, pp. 108–113, 1993.     

Expert and novice facilitated modelling: A case of a Viable System Model workshop in a local food network

This paper provides an empirical study based on action research in which expert and novice facilitators in facilitated modelling workshops are compared. There is limited empirical research analysing the differences between expert and novice facilitators. Aiming to address this gap we study the behaviour of one expert and two novice facilitators during a Viable System Model workshop. The findings suggest common facilitation patterns in the behaviour of experts and novices. This contrasts literature claiming that experts and novices behave and use their available knowledge differently, and empirically supports the claim that facilitation skills can be taught to participants to enable them to self-facilitate workshops. Differences were also found, which led to the introduction of a new dimension—‘internal versus external’ facilitation. The implications of our findings for effective training and facilitation strategies in contexts in which external, expert facilitation is not always possible are also discussed, and limitations of this study are provided.