Showing papers on "Abductive reasoning published in 2002"

Logic and human reasoning: an assessment of the deduction paradigm.

Abstract: The study of deductive reasoning has been a major paradigm in psychology for approximately the past 40 years. Research has shown that people make many logical errors on such tasks and are strongly influenced by problem content and context. It is argued that this paradigm was developed in a context of logicist thinking that is now outmoded. Few reasoning researchers still believe that logic is an appropriate normative system for most human reasoning, let alone a model for describing the process of human reasoning, and many use the paradigm principally to study pragmatic and probabilistic processes. It is suggested that the methods used for studying reasoning be reviewed, especially the instructional context, which necessarily defines pragmatic influences as biases.

Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction

Abstract: In this paper, we propose a reconstruction of logic-based approaches to abductive reasoning in terms of ampliative adaptive logics. A main advantage of this reconstruction is that the resulting logics have a proof theory. As abductive reasoning is non-monotonic, the latter is necessarily dynamic (conclusions derived at some stage may at a later stage be rejected). The proof theory warrants, however, that the conclusions derived at a given stage are justified in view of the insight in the premises at that stage. Thus, it even leads to justified conclusions for undecidable fragments. Another advantage of the proposed logics is that they are much closer to natural reasoning than the existing systems. Usually, abduction is viewed as a form of “backward reasoning”. The search procedure by which this is realized (for instance, some form of linear linear resolution) is very different from the search procedures of human reasoners. The proposed logics treat abduction as a form of “forward reasoning” (Modus Ponens in the “wrong direction”). As a result, abductive steps are very natural, and are moreover nicely integrated with deductive steps. We present two new adaptive logics for abduction, and illustrate both with some examples from the history of the sciences (the discovery of Uranus and of Neptune). We also present some alternative systems that are better suited for non-creative forms of abductive reasoning.

An Abductive Approach for Analysing Event-Based Requirements Specifications

Abstract: We present a logic and logic programming based approach for analysing event-based requirements specifications given in terms of a system's reaction to events and safety properties. The approach uses a variant of Kowalski and Sergot's Event Calculus to represent such specifications declaratively and an abductive reasoning mechanism for analysing safety properties. Given a system description and a safety property, the abductive mechanism is able to identify a complete set of counterexamples (if any exist) of the property in terms of symbolic "current" states and associated event-based transitions. A case study of an automobile cruise control system specified in the SCR framework is used to illustrate our approach. The technique described is implemented using existing tools for abductive logic programming.

Epistemic Mediators and Model-Based Discovery in Science

Abstract: What I call theoretical abduction (sentential and model-based) certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanations occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action and of external representations in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. I will present some aspects of this kind of reasoning derived from the “cognitive” history of the discovery of the non-Euclidean geometries. Geometrical diagrams are considered external representations which play both a mirror role (to externalize rough mental models), and an unveiling role (as gateways to imaginary entities). I describe them as epistemic mediators able to perform various abductive tasks (discovery of new properties or new propositions/hypotheses, provision of suitable sequences of models as able to convincingly verifying theorems, etc.).

Internal critique: A logic is not a theory of reasoning and a theory of reasoning is not a logic

Abstract: Publisher Summary This chapter discusses relations between the study of reasoning and the theory of implication. The chapter illustrates that, in order to understand the relations between reasoning and logic, it is crucial not to confuse issues of implication with issues of inference. Inference and implication are very different things and the relation between them is rather obscure. Logic as a theory of implication is a very different sort of theory from logic as a theory of reasoning or methodology. Historically the term "logic" has been used in both ways. Current usage favors restriction of the term "logic" to the theory of implication. The theory of reasoning is best called "the theory of reasoning" or "methodology". There are many technical studies of implication and of logic understood as the theory of implication. Inference and reasoning are not well understood. This is because a theory of inference or reasoning must be part of a theory of rationality and rationality is not well understood.

On the Proof Dynamics of Inference to the Best Explanation

Abstract: “Inference to the best explanation” — here called “abduction” — is a distinctive and recognizable pattern of evidential reasoning. It is ubiquitous at or near the surface of typical arguments offered in judicial and scientific contexts, and in ordinary life. It is part of “commonsense logic.” An abductive argument is open to attack in characteristic ways, and may be defended in characteristic ways by supporting arguments. Abductive arguments are fallible, but there are only a small number of ways in which they can go wrong. This analysis provides a framework for justification, criticism, and dialogue concerning the evaluation of evidence. It should be helpful in the law of evidence and in the training of investigators.

Partial abductive inference in Bayesian belief networks - an evolutionary computation approach by using problem-specific genetic operators

Abstract: Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the K most probable configurations given observed evidence. When we are interested only in a subset of the network's variables, this problem is called partial abductive inference. Both problems are NP-hard, and so exact computation is not always possible. In this paper, a genetic algorithm is used to perform partial abductive inference in BBNs. The main contribution is the introduction of new genetic operators designed specifically for this problem. By using these genetic operators, we try to take advantage of the calculations previously carried out, when a new individual is evaluated. The algorithm is tested using a widely-used Bayesian network and a randomly generated one, and then compared with a previous genetic algorithm based on classical genetic operators. From the experimental results, we conclude that the new genetic operators preserve the accuracy of the previous algorithm and also reduce the number of operations performed during the evaluation of individuals. The performance of the genetic algorithm is thus improved.

Species of Abductive Reasoning in Fact Investigation in Law

Abstract: Imaginative reasoning is as vital in law as it is in any other discipline. During fact investigation, hypotheses, in the form of possible charges or complaints, must be generated or discovered, as well as evidence bearing on these hypotheses. During the later process of proof, arguments in defense of the relevance, credibility, and probative force of offered evidence on hypotheses must also be generated. In no context known to me are hypotheses, evidence, and arguments linking them supplied at the outset for investigators and attorneys. These ingredients must be generated by imaginative or creative thinking. How we are able to generate new ideas has been an object of study for millennia. In spite of this, our imaginative and creative reasoning abilities are not well understood. There is considerable debate about the forms of reasoning that take place as we generate new ideas and evidential tests of them. This Article concerns a form of reasoning called “abduction,” which was suggested over a century ago by the American philosopher Charles S. Peirce as a reasoning mechanism underlying imaginative and creative thought. Most of us hear about two forms of reasoning: (1) deduction, showing that something is necessarily true, and (2) induction,showing that something is probably true. There is reason to believe that new ideas, in the form of hypotheses, may not be generated by induction or deduction. In this Article I will suggest that there are several species of abductive reasoning by which we show that something is possibly or plausibly true. I relate these species of abduction to intellectual tasks performed by investigators during fact investigation and to those performed by advocates during the process of proof. Consideration of these species of abductive reasoning exposes the richness of this important discovery-related activity.

Probabilistic Argumentation Systems and Abduction

Abstract: Probabilistic argumentation systems are based on assumption-based reasoning for obtaining arguments supporting hypotheses and on probability theory to compute probabilities of supports. Assumption-based reasoning is closely related to hypothetical reasoning or inference through theory formation. The latter approach has well known relations to abduction and default reasoning. In this paper assumption-based reasoning, as an alternative to theory formation aiming at a different goal, will be presented and its use for abduction and model-based diagnostics will be explained. Assumption-based reasoning is well suited for defining a probability structure on top of it. On the base of the relationships between assumption-based reasoning on the one hand and abduction on the other hand, the added value introduced by probability into model based diagnostics will be discussed. Furthermore, the concepts of complete and partial models are introduced with the goal to study the quality of inference procedures. In particular this will be used to compare abductive to possible explanations.

Spatial reasoning : theory and practice

Abstract: formal languages can also serve as document encoding languages, for instance, first-order logic. The syntax and semantics are the usual ones for firstorder logic, taking special care in giving adequate semantics to spatial relations and predicates. A final example of a general document encoding rule stated informally in natural language is the following: “in the Western culture, documents are usually read top-bottom and left-right.” (7.1) A problem of stating rules in natural language is ambiguity. In fact, we do not know if one should interpret the “and” as commutative or not. Should one first go top-bottom and then left-right? Or, should one apply any of the two interchangeably? It is not possible to say from the rule merely stated in natural language. In the next section, we define an abstract propositional formal language to express qualitative spatial relations among document objects to formally express document encoding rules. 7.3.2 Relations adequate for documents Considering relations adequate for documents and their components, requires a preliminary formalization step. This consists of regarding a document as a formal model. At this level of abstraction a document is a tuple 〈D,R, l〉 of document objectsD, a binary relationR, and a labeling functionl. Each document object d ∈ D consists of the coordinates of its bounding box (defined as the smallest rectangle containing all elements of that object) D = {d | d = 〈id, x1, y1, x2, y2〉} where id is an identifier of the document object and (x1, y1) (x2, y2) represent the upper-left corner and the lower-right corner of the bounding box of the document object. In addition, we consider the logical labeling information. Given a set of labels L, logical labeling is a functionl, typically injective, from document objects to labels: l : D → L In the following, we consider an instance of such a model where the set of relations R is the set of bidimensional Allen relations and where the set of labels L is {title, body of text, figure, caption, footer, header, page number, graphics }. We shall refer to this model as a spatial [bidimensional Allen] model.Bidimensional Allen relations consist of 13 ×13 relations: the product of Allen’s 13 interval relations [Allen, 1983, van Benthem, 1983b] on two orthogonal axes. (Consider an inverted coordinate system for each document with origin (0,0) in the left-upper corner. The x axis spans horizontally increasing to the right, while the y axis spans vertically towards the bottom.) Each relation r ∈ A is a tuple of Allen interval relations of the 134 • Chapter 7. THICK 2D RELATIONS FOR DOCUMENT UNDERSTANDING form: precedes,meets, overlaps, starts, during, finishes, equals, andprecedes i, meets i, overlaps i, starts i, during i, finishes i. We shall refer to the set of Allen bidimensional relations simply as A and to the propositional language over bidimensional Allen relations asL the remainder of the chapter. Since Allen relations are jointly exhaustive and pairwise disjoint, so is A. This implies that given any two document objects there is one and only one A relation holding among them.

Standard logic as a model of reasoning: The empirical critique

Abstract: Publisher Summary This chapter describes standard logic as a model of reasoning. The notion of formal logic has figured centrally in conceptions of human reasoning, rationality, and adaptiveness. The chapter reviews the evidence, appraises its weight, and offers a summative judgment of the place of logic in human thinking. "Standard logic," includes the canons of formal deduction, the special case of disconfirming hypotheses by finding counterevidence for their implications, and also the principles of probabilistic and statistical inference developed by mathematicians over the past couple of hundred years. It also examines deliberate or reflexive reasoning. The chapter argues that standard logic or subsets of it can be implemented in quite different ways and that human cognition incorporates more than one implementation. In addition, almost all the research on the role of standard logic in human thinking concerns deliberate rather than reflexive reasoning. Accordingly, the present analysis focuses on deliberate reasoning and the place of standard logic in it.

Abductive Reasoning Network-Based Diagnosis System for Fault Section Estimation in Power Systems

Abstract: This paper presents an abductive reasoning network (ARN) for real-time fault section estimation in power systems. The proposed ARN handles complicated and knowledge-embedded relationships between the circuit breaker status (input) and the corresponding candidate fault section (output) using a hierarchical network with several layers of function nodes of simple low-order polynomials. The relay status is then further used to validate the final fault section. Test results confirm that the proposed diagnosis system can obtain rapid and accurate diagnosis results with flexibility and portability for diverse power system fault diagnosis. In addition, the proposed method performs better than the artificial neural networks (ANN) classification method both in developing the diagnosis system and in estimating the practical fault section. Moreover, this study demonstrates the feasibility of applying the proposed method to real power system fault diagnosis.

A Query-Driven Anytime Algorithm for Argumentative and Abductive Reasoning

Abstract: This paper presents a new approximation methodfor computing arguments or explanations in the context of logic-based argumentative or abductive reasoning. The algorithm can be interrupted at any time returning the solution foundso far. The quality of the approximation increases monotonically when more computational resources are available. The methodis basedon cost functions andreturns lower and upper bounds.

On the problem of performing exact partial abductive inference in Bayesian belief networks using junction trees

Abstract: Partial abductive inference in Bayesian belief networks has been usually expressed as an extension of total abductive inference (abduction over all the variables in the network). In this paper we study the transformation of the partial problem in a total one, analyzing and trying to improve the method previously appeared in the literature. We also outline an alternative approach, and compare both methods by means of experimentation. The experimental results reveal that the problem of partial abductive inference is difficult to solve by exact computation.

Analogical and Case-Based Reasoning: Their Implications for Education

Abstract: (2002). Analogical and Case-Based Reasoning: Their Implications for Education. Journal of the Learning Sciences: Vol. 11, No. 1, pp. 123-126.

A Peircean View of Teacher Beliefs and Genuine Doubt

Abstract: In this paper we outline C. S. Peirce’s four ideas about how beliefs become fixed, or stabilized, as well as his concept of genuine doubt with respect to teacher beliefs. We then describe an abductive reasoning process that illustrates how a person resolves doubt. We use a case example of a teacher experiencing doubt and resolving it through the abductive reasoning process to illustrate both our thinking and the utility of the process. The data for the case example were captured in an online learning community based on active teacher inquiry into personal beliefs and practices. We argue that, as such, the community serves to irritate teacher beliefs and support teachers as they experience and work to resolve genuine doubt. We conclude with a discussion of the importance of genuine doubt and abductive reasoning in teacher education.

Local reasoning and knowledge compilation for efficient temporal abduction

Abstract: Generating abductive explanations is the basis of several problem solving activities such as diagnosis, planning, and interpretation. Temporal abduction means generating explanations that do not only account for the presence of observations, but also for temporal information on them, based on temporal knowledge in the domain theory. We focus on the case where such a theory contains temporal constraints that are required to be consistent with temporal information on observations. Our aim is to propose efficient algorithms for computing temporal abductive explanations. Temporal constraints in the theory and in the observations can be used actively by an abductive reasoner in order to prune inconsistent candidate explanations at an early stage during their generation. However, checking temporal constraint satisfaction frequently generates some overhead. We analyze two incremental ways of making this process efficient. First we show how, using a specific class of temporal constraints (which is expressive enough for many applications), such an overhead can be reduced significantly, yet preserving a full pruning power. In general, the approach does not affect the asymptotic complexity of the problem, but it provides significant advantages in practical cases. We also show that, for some special classes of theories, the asymptotic complexity is also reduced. We then show how, compiled knowledge based on temporal information, can be used to further improve the computation, thus, extending to the temporal framework previous results in the case of atemporal abduction. The paper provides both analytic and experimental evaluations of the computational advantages provided by our approaches.

When Is Genetic Reasoning Not Fallacious

Abstract: Attempts to evaluate a belief or argument on the basis of its cause or origin are usually condemned as committing the genetic fallacy. However, I sketch a number of cases in which causal or historical factors are logically relevant to evaluating a belief, including an interesting abductive form that reasons from the best explanation for the existence of a belief to its likely truth. Such arguments are also susceptible to refutation by genetic reasoning that may come very close to the standard examples given of supposedly fallacious genetic reasoning.

Semantic resolution for e-commerce

Abstract: We describe a research project on resolving semantic differences for multi-agent systems (MAS) in electronic commerce. The approach can be characterized as follows: (1) agents in a MAS may have their own specific ontologies defined on top of a shared base ontology; (2) concepts in these ontologies are represented as frame-like structures based on DAML+OIL language; (3) the semantic differences between agents are resolved at runtime through inter-agent communication; and (4) the resolution is viewed as an abductive inference process, and thus necessarily involves approximate reasoning.

Abductive Reasoning in Law: Taxonomy and Inference to the Best Explanation

Abstract: Following the positivistic philosophy of Karl Popper and Hans Reichenbach,1 many traditionalist thinkers on rational proof in law still assume a sharp distinction between “the context of discovery” and “the context of justification.” These traditionalists regard the context of justification as the proper province of legal reasoning. Justification deals with the analysis and appraisal of decisions, judgments, arguments, and verdicts once they are already “on the table.” Thus, questions about the rational adequacy of a judge’s verdict, or about a police decision to charge a suspect, or about the viability of a case that the District Attorney chooses to prosecute are all important to traditional theories. However, questions about discovery2 play little or no role in many accounts of evidential reasoning in law. The traditionalist does not claim that discovery and imagination are unimportant. Rather, her claim is that a theory of legal reasoning should concern itself only with the logic of rational arguments. Imagination and discovery should be left to the psychologist. The legal theorist Neil MacCormick states this traditional stance very succinctly: “[I]n relation to legal reasoning, the process which is worth studying is the process of argumentation as a process of justification.”3

Epistemic Mediators and Chance Morphodynamics

Abstract: The recent epistemological and cognitive studies concentrate on the concept of abduction, as a means to originate and refine new ideas. Traditional cognitive science and computational accounts concerning abduction aim to illustrate discovery and creativity processes in terms of theoretical and “internal” aspects, by means of computational simulations and/or abstract cognitive models. We will illustrate in this papercognitive models. We will illustrate in this paper that some typical internal abductive processes are involved in chance discovery and production (for example through radical innovations). Nevertheless, especially concrete manipulations of the external world constitute a fundamental passage in chance discovery: by a process of manipulative abduction it is possible to build prostheses (epistemic mediators) for human minds, by interacting with external objects and representations in a constructive way. In this manner it is possible to create implicit knowledge through doing and to produce various opportunity to find, for example, anomalies and fruitful new risky perspectives. This kind of embodied and unexpressed knowledge holds a key role in the subsequent processes of scientific comprehension and discovery. The paper describes some of the “templates” of manipulative behavior which account for the most common cognitive and epistemic acting related to chance discovery and chance production. The last part of the paper is devoted to illustrate chance discovery from the perspective of dynamical systems. Chance discovery and production can be viewed as a kind of event related to the transformations of the attractors responsible of the cognitive system performances. Theoretical and Manipulative Reasoning Science is one of the most explicitly constructed, abstract, and creative forms of human knowledge. In the twentieth century Kuhnian ideas about irrationality of conceptual change and paradigm shift (Kuhn 1962) brought philosophers of science to distinguish between a logic of discovery and a logic of justification, and to the direct conclusion that a logic of discovery, and then a rational model of discovery, cannot exist. Today researchers have by and large abandoned this attitude by concentrating on the concept of abduction pointed out by C.S. Peirce as a fundamental mechanism by which it Copyright c 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. is possible to account for the introduction of new explanatory hypotheses in science. Abduction is the process of inferring certain facts and/or laws and hypotheses that render some sentences plausible, that explain or discover some (eventually new) phenomenon or observation; it is the process of reasoning in which explanatory hypotheses are formed and evaluated. There are two main epistemological meanings of the word abduction (Magnani 2001): 1) abduction that only generates “plausible” hypotheses (“selective” or “creative”) and 2) abduction considered as inference “to the best explanation”, which also evaluates hypotheses. To illustrate from the field of medical knowledge, the discovery of a new disease and the manifestations it causes can be considered as the result of a creative abductive inference. Therefore, “creative” abduction deals with the whole field of the growth of scientific knowledge. This is irrelevant in medical diagnosis where instead the task is to “select” from an encyclopedia of pre-stored diagnostic entities. Theoretical abduction1 certainly illustrates much of what is important in creative abductive reasoning, in humans and in computational programs, but fails to account for many cases of explanations occurring in science when the exploitation of environment is crucial. It fails to account for those cases in which there is a kind of “discovering through doing”, cases in which new and still unexpressed information is codified by means of manipulations of some external objects (epistemic mediators). The concept of manipulative abduction2 captures a large part of scientists thinking where the role of action is central, and where the features of this action are implicit and hard to be elicited: action can provide otherwise unavailable information that enables the agent to solve problems by starting and by performing a suitable abductive process of generation or selection of hypotheses. Many attempts have been made to model abduction by developing some formal tools in order to illustrate its comMagnani (Magnani 2001; 2002a) introduces the concept of theoretical abduction. He maintains that there are two kinds of theoretical abduction, “sentential”, related to logic and to verbal/symbolic inferences, and “model-based”, related to the exploitation of internalized models of diagrams, pictures, etc., cf. below in this paper. Manipulative abduction and epistemic mediators are introduced and illustrated in (Magnani 2001). putational properties and the relationships with the different forms of deductive reasoning (Bylander et al. 1991). Some of the formal models of abductive reasoning are based on the theory of the epistemic state of an agent (Boutilier & Becher 1995), where the epistemic state of an individual is modeled as a consistent set of beliefs that can change by expansion and contraction (belief revision framework). These kinds of logical models are called sentential (Magnani 2001). They exclusively deal with selective abduction (diagnostic reasoning)3 and relate to the idea of preserving consistency. Exclusively considering the sentential view of abduction does not enable us to say much about creative processes in science, and, therefore, about the nomological and most interesting creative aspects of abduction. It mainly refers to the selective (diagnostic) and merely explanatory aspects of reasoning and to the idea that abduction is mainly an inference to the best explanation (Magnani 2001).

The Methodological Status of Agent-Based Simulations

Abstract: In this paper I give a tentative assessment of the methodological status of agent based simulations. I first show under which conditions ABS can be a complement to traditional modelling. I then consider whether they can be held as a sound methodology of their own. Various topics relevant to the argument are briefly discussed, such as the forecasting role of theories, the realism of assumptions, Hayek's insights on economics methodology. I cast the arguments given into some results of modern theory of abductive inference, providing a framework that helps clarify the logical status of simulations, and gives some hints on how to foster their role as a self sustained tool for economic reasoning.

Partial Abductive Inference in Bayesian Networks: An Empirical Comparison Between GAs and EDAs

Abstract: Partial abductive inference in Bayesian networks is intended as the pro-cess of generating the K most probable configurations for a distinguished subset of the network variables (explanation set), given some observations (evidence). This problem, also known as the Maximum a Posteriori Problem, is known to be NP-hard, so exact computation is not always possible. As partial abductive inference in Bayesian networks can be viewed as a combinatorial optimization problem, Genetic Algorithms have been successfully applied to give an approximate algorithm for it (de Campos et al., 1999). In this work we approach the problem by means of Estimation of Distribution Algorithms, and an empirical comparison between the results obtained by Genetic Algorithms and Estimation of Distribution Algorithms is carried out.

Repairing inconsistent databases: a model-theoretic approach and abductive reasoning

Abstract: In this paper we consider two points of views to the problem of coherent integration of distributed data. First we give a pure model- theoretic analysis of the possible ways to 'repair' a database. We do so by characterizing the possibilities to 'recover' consistent data from an in- consistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. Then we in- troduce an abductive application to restore the consistency of a given database. This application is based on an abductive solver (A-system) that implements an SLDNFA-resolution procedure, and computes a list of data-facts that should be inserted to the database or retracted from it in order to keep the database consistent. The two approaches for coherent data integration are related by soundness and completeness results.

Describing Young Children's Deductive Reasoning.

Abstract: This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. Ways of reasoning deductively are highlighted, using examples drawn from observations of young students. One-step deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple premises, are used to distinguish different ways of reasoning. (Author) Reproductions supplied by EDRS are the best that can be made from the original document. PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY TO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) U.S. DEPARTMENT OF EDUCATION Office of Educational Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as received from the person or organization originating it. Minor changes have been made to improve reproduction quality. Points of view or opinions stated in this document do not necessarily represent official OERI position or policy. DESCRIBING YOUNG CHILDREN'S DEDUCTIVE REASONING David A Reid Acadia University This paper reports results related to the development Of a consistent descriptive language for research on mathematical reasoning Ways of reasoning deductively are highlighted using examples drawn from observations of young students. Onestep deductions versus multi-step deductions, known versus hypothetical premises, and single versus multiple premises, are used to distinguish different ways of reasoning. This paper reports results related to the development of a consistent descriptive language for research on mathematical reasoning. These results arose out of a long term research project (the PRISM project [1]) aimed at elaborating and clarifying previous models and terminology for describing reasoning. The model now in use for this research project describes reasoning across five dimensions: need, target, kind of reasoning, formulation and formality; and has been used to describe reasoning of students of all ages (Reid 1995a,b, 1997, 1998, in press). In this paper one dimension, ways of reasoning, will be highlighted, using results drawn from observations of students aged about seven years. THE MODEL The PRISM project took as its beginning point a model for reasoning outlined by Reid (1995a, 1996b). It includes four dimensions for describing reasoning. Need includes the needs to explain and to verify mathematical statements and to explore to discover. new statements. This dimension of the model was inspired by the work of Bell (1976) and de Villiers (1990). Kind of reasoning includes reasoning deductively, inductively and by analogy, and was inspired by the work of Polya (1954/1990). Formulation refers to the degree of awareness the reasoner has of their own reasoning. Formality refers to the degree to which the expression of the reasoning conforms to the requirements of mathematical style. The work of Lakatos (1978) and Blum & Kirsch (1991) inspired this dimension. One of the refinements of this model that has resulted from the PRISM project is the addition of a fifth dimension, target, that describe who the reasoning is for: a teacher, a peer or oneself This model of reasoning is compatible with those being developed by others. For example, Sowder and Hard (1998) have outlined a model describing what they call "proof schemes". In terms of the PRISM model it offers additional detail concerning kinds of reasoning but is limited to those kinds of reasoning related specifically to the need to verify.

Formal approaches to practical reasoning: A survey

Abstract: Publisher Summary The purpose of this chapter is to indicate what kind of formal logical systems are suitable for the modeling of actual practical reasoning behavior. The approach is to start from the familiar traditional notion of logic and indicate how more and more features need to be added to it. The chapter illustrates that the urgent need of models comes mainly from computer science and artificial intelligence. As there is pressure to build devices which help and replace the human in some of his daily activities, logic is called upon to provide realistic models of such activities and logic is therefore forced to evolve to accommodate human practice. The chapter highlights traditional notion of a logic as a consequence relation to the more complex notion of what known as a practical reasoning system. These are the kinds of logical systems needed for a better modeling of practical reasoning.

Semantic resolution for E-Commerce

Abstract: We describe a research project on resolving semantic differences for multi-agent systems (MAS) in electronic commerce. The approach can be characterized as follows: (1) agents in a MAS may have their own specific ontologies defined on top of a shared base ontology; (2) concepts in these ontologies are represented as frame-like structures based on DAML+OIL language; (3) the semantic differences between agents are resolved at runtime through inter-agent communication; and (4) the resolution is viewed as an abductive inference process, and thus necessarily involves approximate reasoning.