Strategies of rule discovery in an inference task

It has long been known that subjects in certain inference tasks will seek evidence which can confirm their present hypotheses, even in situations where disconfirmatory evidence could be more informative. We sought to alter this tendency in a series of experiments which employed a rule discovery task, the 2-4-6 problem first described by Wason. The first experiment instructionally modified subjects confirmatory tendencies. While a disconfirmatory strategy was easily induced, it did not lead to greater efficiency in discovering the rule. The second experiment introduced subjects to the possibility of disconfirmation only after they had developed a strongly held hypothesis through the use of confirmatory evidence. This manipulation also failed to alter the efficiency of rule discovery. In the third experiment, subjects were taught to use multiple hypotheses at each step, in the manner of Platt's “Strong Inference”. This operation actually worsened performance. Finally, in the fourth experiment, the structure of the problem was altered slightly by asking subjects to seek two interrelated rules. A dramatic increase in performance resulted, perhaps because information which in previous tasks was seen as merely erroneous could now be related to an alternative rule. The four studies have broad implications for the psychological study of inference processes in general, and for the study of scientific inference in particular.     

Behavior identification as a mediator of dispositional inference.

According to Trope's (1986) 2-stage model, the use of situational information ("A was teased") to identify behavior ("A reacted aggressively") may result in subsequent dispositional inferences ("A is an aggressive person") that seem insensitive to situational information. Two determinants of the situational biasing effect on behavior identification were varied, namely, behavior ambiguity and order of situational and behavioral information. It was found that when behavior was ambiguous and preceded by situational information, the latter affected behavior identification but not dispositional inference; in contrast, when behavior was unambiguous or when it was followed by situational information, the latter affected dispositional inference but not behavior identification. Thus, the same conditions that allowed situational information to bias behavior identification also nullified the effect of situational information on dispositional inference.     

Exemplar models as a mechanism for performing Bayesian inference

Probabilistic models have recently received much attention as accounts of human cognition. However, most research in which probabilistic models have been used has been focused on formulating the abstract problems behind cognitive tasks and their optimal solutions, rather than on mechanisms that could implement these solutions. Exemplar models are a successful class of psychological process models in which an inventory of stored examples is used to solve problems such as identification, categorization, and function learning. We show that exemplar models can be used to perform a sophisticated form of Monte Carlo approximation known as importance sampling and thus provide a way to perform approximate Bayesian inference. Simulations of Bayesian inference in speech perception, generalization along a single dimension, making predictions about everyday events, concept learning, and reconstruction from memory show that exemplar models can often account for human performance with only a few exemplars, for both simple and relatively complex prior distributions. These results suggest that exemplar models provide a possible mechanism for implementing at least some forms of Bayesian inference.     

Word learning as Bayesian inference

The authors present a Bayesian framework for understanding how adults and children learn the meanings of words. The theory explains how learners can generalize meaningfully from just one or a few positive examples of a novel word's referents, by making rational inductive inferences that integrate prior knowledge about plausible word meanings with the statistical structure of the observed examples. The theory addresses shortcomings of the two best known approaches to modeling word learning, based on deductive hypothesis elimination and associative learning. Three experiments with adults and children test the Bayesian account's predictions in the context of learning words for object categories at multiple levels of a taxonomic hierarchy. Results provide strong support for the Bayesian account over competing accounts, in terms of both quantitative model fits and the ability to explain important qualitative phenomena. Several extensions of the basic theory are discussed, illustrating the broader potential for Bayesian models of word learning.     

An examination of the SEP candidate analogical inference rule within pure inductive logic

Within the framework of (Unary) Pure Inductive Logic we investigate four possible formulations of a probabilistic principle of analogy based on a template considered by Paul Bartha in the Stanford Encyclopedia of Philosophy [1] and give some characterizations of the probability functions which satisfy them. In addition we investigate an alternative interpretation of analogical support, also considered by Bartha, based not on the enhancement of probability but on the creation of possibility.     

Logic programming as classical inference

We propose a denotational semantics for logic programming based on a classical notion of logical consequence which is apt to capture the main proposed semantics of logic programs. In other words, we show that any of those semantics can be viewed as a relation of the form $T{\models }^{\star }X$ where T is a theory which naturally represents the logic program under consideration together with a set of formulas playing the role of “hypotheses”, in a way which is dictated by that semantics, ${\models }^{\star }$ is a notion of logical consequence which is classical because negation, disjunction and existential quantification receive their classical meaning, and X represents what can be inferred from the logic program, or an intended interpretation of that logic program (such as an answer-set, its well-founded model, etc.). The logical setting we propose extends the language of classical modal logic as it deals with modal operators indexed by ordinals. We make use of two kinds of basic modal formulas: ${\square }_{\alpha }\phi$ which intuitively means that the logical program can generate φ by stage α of the generation process, and ${◇}_{\alpha }{\square }_{\beta }\phi$ with $\alpha >\beta$, which intuitively means that φ can be used as a hypothesis from stage β of the generation process onwards, possibly expecting to confirm φ by stage α (so expecting ${\square }_{\alpha }\phi$ to be generated). This allows us to capture Rondogiannis and Wadge's version of the well-founded semantics [27] where a member of the well-founded model is a closed atom which receives an ordinal truth value of ${\mathtt{true}}_{\alpha }$ or ${\mathtt{false}}_{\alpha }$ for some ordinal α: in our framework, this corresponds to having $T{\models }^{\star }{\square }_{\alpha }\phi$ or $T{\models }^{\star }{\square }_{\alpha }\neg \phi$, respectively, with T being the natural representation of the logic program under consideration and the right set of “hypotheses” as dictated by the well-founded semantics. The framework we present goes much beyond the proposed traditional semantics for logic programming, as it can for instance let us investigate under which conditions a set of hypotheses can be minimal, with each hypothesis being activated as late as possible and confirmed as soon as possible, setting the theoretical foundation to sophisticated ways of making local use of hypotheses in knowledge-based systems, while still being theoretically grounded in a classical notion of logical consequence.     

The context as a moral rule in medical ethics

A purely deductive medical ethics cannot properly account for the varieties of circumstances which arise in medical practice. By contrast, a purely inductive medical ethics lacks sufficient guidance from ethical principles. In resolving ethical dilemmas in medicine, most often an appeal is made to middle-level axioms and methodological rules to mediate between theory and practice. I argue that this appeal must be augmented by considerations of context, such considerations, in effect, constituting a moral rule based on the social structure of medical practice. A contextual grid is proposed which assists the process of weighing values in resolving cases.     

Justifying inference to the best explanation as a practical meta-syllogism on dialectical structures

This article discusses how inference to the best explanation (IBE) can be justified as a practical meta-argument. It is, firstly, justified as a practical argument insofar as accepting the best explanation as true can be shown to further a specific aim. And because this aim is a discursive one which proponents can rationally pursue in—and relative to—a complex controversy, namely maximising the robustness of one’s position, IBE can be conceived, secondly, as a meta-argument. My analysis thus bears a certain analogy to Sellars’ well-known justification of inductive reasoning (Sellars, In: Essays in honour of Carl G. Hempel, 1969); it is based on recently developed theories of complex argumentation (Betz, In: Theorie dialektischer Strukturen, 2010a).     

Preliminaries to a psychology of inference

This paper presents a general pretheoretical framework for the study of inference. The framework is that of Social Judgment Theory which has been developed from Brunswik's probabilistic functionalism. The first section discusses the fundamental theoretical ideas and methodological principles. Important among these is the stress on the need to study the relation between the cognitive system and the inference task using parallel concepts for describing the cognitive system and the task, the theory of cognitive tasks, and the methodology of formal representative sampling. The second section describes a series of experimental paradigms developed from the basic ideas discussed in the first section. The third, and final section gives some examples of actual empirical research, mainly research concerned with the hypothesis testing process by means of which subjects learn inference tasks, studies on cognitive skills in using various rules for making inferences, new conceptions of feedback, research on the effects of feedforward, and interpersonal learning.     

Reasoning about a rule

Two experiments were carried out to investigate the difficulty of making the contra-positive inference from conditional sentences of the form, “if P then Q.” This inference, that not-P follows from not-Q, requires the transformation of the information presented in the conditional sentence. It is suggested that the difficulty is due to a mental set for expecting a relation of truth, correspondence, or match to hold between sentences and states of affairs. The elicitation of the inference was not facilitated by attempting to induce two kinds of therapy designed to break this set. It is argued that the subjects did not give evidence of having acquired the characteristics of Piaget's “formal operational thought.”     

Communication Between Spouses as a Resilience Factor in Families in Which a Parent Has Depression: A Condensed Report

This study focused on communication as a family resilience factor in families in which an adult suffers from a depressive disorder. Six partners of depressive adults were interviewed. Results revealed two groups of couples. The “talkative couples” have many conversations during the depression and a facilitating factor was having insight into the depression. The other group, the “taciturn couples,” indicated large difficulties in having conversations, resulting in silence being the dominant contact between the partners. The majority of the participants stated that the absence of conversation would have meant the end of their relationship.     

Goal-directed decision making as probabilistic inference: a computational framework and potential neural correlates

Recent work has given rise to the view that reward-based decision making is governed by two key controllers: a habit system, which stores stimulus-response associations shaped by past reward, and a goal-oriented system that selects actions based on their anticipated outcomes. The current literature provides a rich body of computational theory addressing habit formation, centering on temporal-difference learning mechanisms. Less progress has been made toward formalizing the processes involved in goal-directed decision making. We draw on recent work in cognitive neuroscience, animal conditioning, cognitive and developmental psychology, and machine learning to outline a new theory of goal-directed decision making. Our basic proposal is that the brain, within an identifiable network of cortical and subcortical structures, implements a probabilistic generative model of reward, and that goal-directed decision making is effected through Bayesian inversion of this model. We present a set of simulations implementing the account, which address benchmark behavioral and neuroscientific findings, and give rise to a set of testable predictions. We also discuss the relationship between the proposed framework and other models of decision making, including recent models of perceptual choice, to which our theory bears a direct connection.     

How to reason without words: inference as categorization

The idea that reasoning is a singular accomplishment of the human species has an ancient pedigree. Yet this idea remains as controversial as it is ancient. Those who would deny reasoning to nonhuman animals typically hold a language-based conception of inference which places it beyond the reach of languageless creatures. Others reject such an anthropocentric conception of reasoning on the basis of similar performance by humans and animals in some reasoning tasks, such as transitive inference. Here, building on the modal similarity theory of Vigo [J Exp Theor Artif Intell, 2008 (in press)], we offer an account in which reasoning depends on a core suite of subsymbolic processes for similarity assessment, discrimination, and categorization. We argue that premise-based inference operates through these subsymbolic processes, even in humans. Given the robust discrimination and categorization abilities of some species of nonhuman animals, we believe that they should also be regarded as capable of simple forms of inference. Finally, we explain how this account of reasoning applies to the kinds of transitive inferences that many nonhuman animals display.