Abstract. The practice of first-order logic is replete with meta-level concepts. Most notably there are meta-variables ranging over formulae, variables, and terms, and properties of syntax such as alpha-equivalence, capture-avoiding substitution and assumptions about freshness of variables with respect to metavariables. We present one-and-a-halfth-order logic, in which these concepts are made explicit. We exhibit both sequent and algebraic specifications of one-and-a-halfth-order logic derivability, show them equivalent, show that the derivations satisfy cut-elimination, and prove correctness of an interpretation of first-order logic within it. We discuss the technicalities in a wider context as a case-study for nominal algebra, as a logic in its own right, as an algebraisation of logic, as an example of how other systems might be treated, and also as a theoretical foundation

In this paper we outline a general approach to the study of metareasoning, not in the sense of explicating the semantics of explicitly specified meta-level control policies, but in the sense of providing a basis for selecting and justifying computational actions. This research contributes to a developing attack on the problem of resource-bounded rationality, by providing a means for analysing and generating optimal computational strategies. Because reasoning about a computation without doing it necessarily involves uncertainty as to its outcome, probability and decision theory will be our main tools. We develop a general formula for the utility of computations, this utility being derived directly from the ability of computations to affect an agent's external actions. We address some philosophical difficulties that arise in specifying this formula, given our assumption of limited rationality. We also describe a methodology for applying the theory to particular problem-solving systems, a...

Human reasoning in hypothesis-testing tasks like Wason's (1966, 1968) selection task has been depicted as prone to systematic biases. However, performance on this task has been assessed against a now outmoded falsificationist philosophy of science. Therefore, the experimental data is reassessed in the light of a Bayesian model of optimal data selection in inductive hypothesis testing. The model provides a rational analysis (Anderson, 1990) of the selection task that fits well with people's performance on both abstract and thematic versions of the task. The model suggests that reasoning in these tasks may be rational rather than subject to systematic bias. Over the past 30 years, results in the psychology of reasoning have raised doubts about human rationality. The assumption of human rationality has a long history. Aristotle took the capacity for rational thought to be the defining characteristic of human beings, the capacity that separated us from the animals. Descartes regarded the ability to use language and to reason as the hallmarks of the mental that separated it from the merely physical. Many contemporary philosophers of mind also appeal to a basic principle of rationality in accounting for everyday, folk psychological explanation whereby we explain each other's behavior in terms of our beliefs and desires (Cherniak, 1986; Cohen, 1981; Davidson, 1984; Dennett, 1987; but see Stich, 1990). These philosophers, both ancient and modern, share a common view of rationality: To be rational is to reason according to rules (Brown, 1989). Logic and mathematics provide the normative rules that tell us how we should reason. Rationality therefore seems to demand that the human cognitive system embodies the rules of logic and mathematics. However, results in the psychology of reasoning appear to show that people do not reason according to these rules. In both deductive (Evans, 1982, 1989;

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Since its inception, artificial intelligence has relied upon a theoretical foundation centred around perfect rationality as the desired property of intelligent systems. We argue, as others have done, that this foundation is inadequate because it imposes fundamentally unsatisfiable requirements. As a result, there has arisen a wide gap between theory and practice in AI, hindering progress in the field. We propose instead a property called bounded optimality. Roughly speaking, an agent is bounded-optimal if its program is a solution to the constrained optimization problem presented by its architecture and the task environment. We show how to construct agents with this property for a simple class of machine architectures in a broad class of real-time environments. We illustrate these results using a simple model of an automated mail sorting facility. We also define a weaker property, asymptotic bounded optimality (ABO), that generalizes the notion of optimality in classical complexity th...

The long-term goal of our field is the creation and understanding of intelligence. Productive research in AI, both practical and theoretical, benefits from a notion of intelligence that is precise enough to allow the cumulative development of robust systems and general results. This paper outlines a gradual evolution in our formal conception of intelligence that brings it closer to our informal conception and simultaneously reduces the gap between theory and practice. 1 Artificial Intelligence AI is a field in which the ultimate goal has often been somewhat ill-defined and subject to dispute. Some researchers aim to emulate human cognition, others aim at the creation of

Confirmation bias, as the term is typically used in the psychological literature, connotes the seeking or interpreting of evidence in ways that are partial to existing beliefs, expectations, or a hypothesis in hand. The author reviews evidence of such a bias in a variety of guises and gives examples of its operation in several practical contexts. Possible explanations are considered, and the question of its utility or disutility is discussed. When men wish to construct or support a theory, how they torture facts into their service! (Mackay, 1852/ 1932, p. 552) Confirmation bias is perhaps the best known and most widely accepted notion of inferential error to come out of the literature on human reasoning. (Evans, 1989, p. 41) If one were to attempt to identify a single problematic aspect of human reasoning that deserves attention above all others, the confirmation bias would have to be among the candidates for consideration. Many have written about this bias, and it appears to be sufficiently strong and pervasive that one is led to wonder whether the bias, by itself, might account for a significant fraction of the disputes, altercations, and misunderstandings that occur among individuals, groups, and nations. Confirmation bias has been used in the psychological literature to refer to a variety of phenomena. Here I take the term to represent a generic concept that subsumes several more specific ideas that connote the inappropriate bolstering of hypotheses or beliefs whose truth is in question.

A program is bounded optimal for a given computational device for a given environment, if the expected utility of the program running on the device in the environment is at least as high as that of all other programs for the device. Bounded optimality differs from the decision-theoretic notion of rationality in that it explicitly allows for the finite computational resources of real agents. It is thus a central issue in the foundations of artificial intelligence. In this paper we consider a restricted class of agent architectures, in which a program consists of a sequence of decision procedures generated by a learning program or given a priori. For this class of agents, we give an efficient construction algorithm that generates a bounded optimal program for any episodic environment, given a set of training examples. The algorithm includes solutions to a new class of optimization problems, namely scheduling computational processes for real-time environments. This class appears to conta...

A new cognitive architecture for artificial vision is proposed. The architecture, aimed at an autonomous intelligent system, is cognitive in the sense that several cognitive hypotheses have been postulated as guidelines for its design. The first one is the existence of a conceptual representation level between the subsymbolic level, that processes sensory data, and the linguistic level, that describes scenes by means of a high-level language. The conceptual level plays the role of the interpretation domain for the symbols at the linguistic levels. A second cognitive hypothesis concerns the active role of a focus of attention mechanism in the link between the conceptual and the linguistic level: the exploration process of the perceived scene is driven by linguistic and associative expectations. This link is modeled as a timedelay attractor neural network. Results are reported obtained by an experimental implementation of the architecture.

The rational choice framework assumes that individuals know what is in their self interest and make choices accordingly. Do they? When they go to the supermarket (in a developed country with a market economy) arguably they do act accordingly. In such settings, the individual knows, almost certainly, whether the choice would be beneficial, ex post. Indeed financial markets in the developed market economies (usually) possess the essential characteristics consistent with substantive rationality. However, it is simply not possible to make sense out of the diverse performance of economies and polities both historically and contemporaneously if individuals really knew their self interest and acted accordingly. Instead people act in part upon the basis of myths, dogmas, ideologies and "half-baked " theories. We argue here both that ideas matter, and that the way that ideas are communicated among people is crucial to building useful theories that will enable us to deal with strong uncertainty problems at the individual level.2 For most of the interesting issues in political and economic markets uncertainty, not risk, characterizes choice-making. Under conditions of uncertainty, individuals ' interpretation of their environment will reflect the