Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

Hidden Markov models (HMMs) have been successful for modelling the dynamics of carefully dictated speech, but their performance degrades severely when used to model conversational speech. Since speech is produced by a system of loosely coupled articulators, stochastic models explicitly representing this parallelism may have advantages for automatic speech recognition (ASR), particularly when trying to model the phonological effects inherent in casual spontaneous speech. This paper presents a preliminary feasibility study of one such model class: loosely coupled HMMs. Exact model (...) estimation and decoding is potentially expensive, so possible approximate algorithms are also discussed. Comparison of one particular loosely coupled model on an isolated word task suggests loosely coupled HMMs merit further investigation. An approximate algorithm giving performance which is almost always statistically indistinguishable from the exact algorithm is also identified, making more extensive research computationally feasible. (shrink)

The paper shows why and how an empirical study of fast-and-frugal heuristics can provide norms of good reasoning, and thus how (and how far) rationality can be naturalized. We explain the heuristics that humans often rely on in solving problems, for example, choosing investment strategies or apartments, placing bets in sports, or making library searches. We then show that heuristics can lead to judgments that are as accurate as or even more accurate than strategies that use more information and computation, (...) including optimization methods. A standard way to defend the use of heuristics is by reference to accuracy-effort trade-offs. We take a different route, emphasizing ecological rationality (the relationship between cognitive heuristics and environment), and argue that in uncertain environments, more information and computation are not always better (the “less-can-be-more” doctrine). The resulting naturalism about rationality is thus normative because it not only describes what heuristics people use, but also in which specific environments one should rely on a heuristic in order to make better inferences. While we desist from claiming that the scope of ecological rationality is unlimited, we think it is of wide practical use. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

In practice, scoring rules elicit good probability estimates from individuals, while betting markets elicit good consensus estimates from groups. Market scoring rules combine these features, eliciting estimates from individuals or groups, with groups costing no more than individuals. Regarding a bet on one event given another event, only logarithmic versions preserve the probability of the given event. Logarithmic versions also preserve the conditional probabilities of other events, and so preserve conditional independence relations. Given logarithmic rules that elicit relative probabilities of (...) base event pairs, it costs no more to elicit estimates on all combinations of these base events. (shrink)

Imitation, deliberation, and mindreading are characteristically human sociocognitive skills. Research on imitation and its role in social cognition is flourishing across various disciplines; it is here surveyed under headings of behavior, subpersonal mechanisms, and functions of imitation. A model is then advanced within which many of the developments surveyed can be located and explained. The shared circuits model explains how imitation, deliberation, and mindreading can be enabled by subpersonal mechanisms of control, mirroring and simulation. It is cast at a middle, (...) functional level of description, between the level of neural implementation and the level of conscious perceptions and intentional actions. The shared circuits model connects shared informational dynamics for perception and action with shared informational dynamics for self and other, while also showing how the action/perception, self/other and actual/possible distinctions can be overlaid on these shared informational dynamics. It avoids the common conception of perception and action as separate and peripheral to central cognition. Rather, it contributes to the situated cognition movement by showing how mechanisms for perceiving action can be built on those for active perception. (shrink)

Why should moral philosophers, moral psychologists, and machine ethicists care about computational complexity? Debates on whether artificial intelligence (AI) can or should be used to solve problems in ethical domains have mainly been driven by what AI can or cannot do in terms of human capacities. In this paper, we tackle the problem from the other end by exploring what kind of moral machines are possible based on what computational systems can or cannot do. To do so, we analyze normative (...) ethics through the lens of computational complexity. First, we introduce computational complexity for the uninitiated reader and discuss how the complexity of ethical problems can be framed within Marr’s three levels of analysis. We then study a range of ethical problems based on consequentialism, deontology, and virtue ethics, with the aim of elucidating the complexity associated with the problems themselves (e.g., due to combinatorics, uncertainty, strategic dynamics), the computational methods employed (e.g., probability, logic, learning), and the available resources (e.g., time, knowledge, learning). The results indicate that most problems the normative frameworks pose lead to tractability issues in every category analyzed. Our investigation also provides several insights about the computational nature of normative ethics, including the differences between rule- and outcome-based moral strategies, and the implementation-variance with regard to moral resources. We then discuss the consequences complexity results have for the prospect of moral machines in virtue of the trade-off between optimality and efficiency. Finally, we elucidate how computational complexity can be used to inform both philosophical and cognitive-psychological research on human morality by advancing the moral tractability thesis. (shrink)

Bayesian epistemologists support the norms of probabilism and conditionalization using Dutch book and accuracy arguments. These arguments assume that rationality requires agents to maximize practical or epistemic value in every doxastic state, which is evaluated from a subjective point of view (e.g., the agent’s expectancy of value). The accuracy arguments also presuppose that agents are opinionated. The goal of this paper is to discuss the assumptions of these arguments, including the measure of epistemic value. I have designed AI agents based (...) on the Bayesian model and a nonmonotonic framework and tested how they achieve practical and epistemic value in conditions in which an alternative set of assumptions holds. In one of the tested conditions, the nonmonotonic agent, which is not opinionated and fulfills neither probabilism nor conditionalization, outperforms the Bayesian in the measure of epistemic value that I argue for in the paper (α-value). I discuss the consequences of these results for the epistemology of rationality. (shrink)

Axiomatic rationality is defined in terms of conformity to abstract axioms. Savage limited axiomatic rationality to small worlds, that is, situations in which the exhaustive and mutually exclusive set of future states S and their consequences C are known. Others have interpreted axiomatic rationality as a categorical norm for how human beings should reason, arguing in addition that violations would lead to real costs such as money pumps. Yet a review of the literature shows little evidence that violations are actually (...) associated with any measurable costs. Limiting axiomatic rationality to small worlds, I propose a naturalized version of rationality for situations of intractability and uncertainty, all of which are not in. In these situations, humans can achieve their goals by relying on heuristics that may violate axiomatic rationality. The study of ecological rationality requires formal models of heuristics and an analysis of the structures of environments these can exploit. It lays the foundation of a moderate naturalism in epistemology, providing statements about heuristics we should use in a given situation. Unlike axiomatic rationality, ecological rationality can explain less-is-more effects, formalize when one should move from ‘is’ to ‘ought,’ and be evaluated by goals beyond coherence, such as predictive accuracy, frugality, and efficiency. Ecological rationality can be seen as a formalization of means–end instrumentalist rationality, based on Herbert Simon’s insight that rational behavior is a function of the mind and its environment. (shrink)

The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance theTractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational‐level theories of cognition. To utilize this constraint, a precise and workable definition of “computational tractability” is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomial‐time computability, leading to theP‐Cognition thesis. This article (...) explains how and why the P‐Cognition thesis may be overly restrictive, risking the exclusion of veridical computational‐level theories from scientific investigation. An argument is made to replace the P‐Cognition thesis by theFPT‐Cognition thesisas an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixed‐parameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified. (shrink)

Despite their success in describing and predicting cognitive behavior, the plausibility of so-called ‘rational explanations’ is often contested on the grounds of computational intractability. Several cognitive scientists have argued that such intractability is an orthogonal pseudoproblem, however, since rational explanations account for the ‘why’ of cognition but are agnostic about the ‘how’. Their central premise is that humans do not actually perform the rational calculations posited by their models, but only act as if they do. Whether or not the problem (...) of intractability is solved by recourse to ‘as if’ explanations critically depends, inter alia, on the semantics of the ‘as if’ connective. We examine the five most sensible explications in the literature, and conclude that none of them circumvents the problem. As a result, rational ‘as if’ explanations must obey the minimal computational constraint of tractability. (shrink)

Department of Economics, George Mason University, MSN 1D3, Carow Hall, Fairfax VA 22030, USA E-mail: [email protected] (http://hanson.gmu.edu).

The case for the superiority of Conviction Narrative Theory (CNT) over probabilistic approaches rests on selective employment of a double standard. The authors judge probabilistic approaches inadequate for failing to apply to “grand-world” decision problems, while they praise CNT for its treatment of “small-world” decision problems. When both approaches are held to the same standard, the comparative question is murkier.

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...) the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...) of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers. (shrink)

We report two experiments which tested whether cognitive capacities are limited to those functions that are computationally tractable (PTIME-Cognition Hypothesis). In particular, we investigated the semantic processing of reciprocal sentences with generalized quantifiers, i.e., sentences of the form Q dots are directly connected to each other, where Q stands for a generalized quantifier, e.g. all or most. Sentences of this type are notoriously ambiguous and it has been claimed in the semantic literature that the logically strongest reading is preferred (Strongest (...) Meaning Hypothesis). Depending on the quantifier, the verification of their strongest interpretations is computationally intractable whereas the verification of the weaker readings is tractable. We conducted a picture completion experiment and a picture verification experiment to investigate whether comprehenders shift from an intractable reading to a tractable reading which should be dispreferred according to the Strongest Meaning Hypothesis. The results from the picture completion experiment suggest that intractable readings occur in language comprehension. Their verification, however, rapidly exceeds cognitive capacities in case the verification problem cannot be solved using simple heuristics. In particular, we argue that during verification, guessing strategies are used to reduce computational complexity. (shrink)

Susan Hurley's shared circuits model (SCM) rightly begins in action and progresses through a series of layers; but it fails to reach action understanding because it relies on mirroring as a driving force, draws on heavily criticized theories, and neglects the need for shared experience in our grasp of social understanding.

According to Church’s thesis, we can identify the intuitive concept of effective computability with such well-defined mathematical concepts as Turing computability and partial recursiveness. The almost universal acceptance of Church’s thesis among logicians and computer scientists is puzzling from some epistemological perspectives, since no formal proof is possible of a thesis that involves an informal concept such as effectiveness. Elliott Mendelson has recently argued, however, that equivalencies between intuitive notions and precise notions need not always be considered unprovable theses, and (...) that Church’s thesis should be accepted as true.I want to discuss a thesis that is nearly as important in current research in computer science as Church’s thesis. I call the newer thesis the tractability thesis, since it identifies the intuitive class of computationally tractable problems with a precise class of problems whose solutions can be computed in polynomial time. After briefly reviewing the theory of intractability, I compare the grounds for accepting the tractability thesis with the grounds for accepting Church's thesis. Intimately connected with the tractability thesis is the mathematical conjecture, whose meaning I shall shortly explain, that P≠NP. Unlike Church's thesis, this conjecture is precise enough to be capable of mathematical proof, but most computer scientists believe it even though no proof has been found. As we shall see below, understanding the grounds for acceptance of the conjecture that P≠NP has implications for general questions in the philosophy of mathematics and science, especially concerning the epistemological importance of explanatory and conceptual coherence. (shrink)