The probabilistic approach to human reasoning

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning.     

Mental models and probabilistic thinking

This paper outlines the theory of reasoning based on mental models, and then shows how this theory might be extended to deal with probabilistic thinking. The same explanatory framework accommodates deduction and induction: there are both deductive and inductive inferences that yield probabilistic conclusions. The framework yields a theoretical conception of strength of inference, that is, a theory of what the strength of an inference is objectively: it equals the proportion of possible states of affairs consistent with the premises in which the conclusion is true, that is, the probability that the conclusion is true given that the premises are true. Since there are infinitely many possible states of affairs consistent with any set of premises, the paper then characterizes how individuals estimate the strength of an argument. They construct mental models, which each correspond to an infinite set of possibilities (or, in some cases, a finite set of infinite sets of possibilities). The construction of models is guided by knowledge and beliefs, including lay conceptions of such matters as the “law of large numbers”. The paper illustrates how this theory can account for phenomena of probabilistic reasoning.     

Husserl’s Foundation of the Formal Sciences in his “Logical Investigations”

This article is composed of three sections that investigate the epistemological foundations of Husserl’s idea of logic from the Logical Investigations. First, it shows the general structure of this logic. Husserl conceives of logic as a comprehensive, multi-layered theory of possible theories that has its most fundamental level in a doctrine of meaning. This doctrine aims to determine the elementary categories that constitute every possible meaning (meaning-categories). The second section presents the main idea of Husserl’s search for an epistemological foundation for knowledge, science and logic. Their epistemological clarification can only be reached through a detailed analysis of the structure of those intentions that give us what is meant in our intentions. To reveal the intuitive giveness of logical forms is the ultimate aim of Husserl’s epistemology of logic. Logical forms and meaning-categories can only be given in a certain higher-order intuition that Husserl calls categorical intuition. The third section of this article distinguishes different kinds of categorical intuition and shows how the most basic logical categories and concepts are given to us in a categorical abstraction.     

Map-based navigation in mobile robots:: I. A review of localization strategies

For a robot, an animal, and even for man, to be able to use an internal representation of the spatial layout of its environment to position itself is a very complex task, which raises numerous issues of perception, categorization and motor control that must all be solved in an integrated manner to promote survival. This point is illustrated here, within the framework of a review of localization strategies in mobile robots. The allothetic and idiothetic sensors that may be used by these robots to build internal representations of their environment, and the maps in which these representations may be instantiated, are first described. Then map-based navigation systems are categorized according to a three-level hierarchy of localization strategies, which respectively call upon direct position inference, single-hypothesis tracking, and multiple-hypothesis tracking. The advantages and drawbacks of these strategies, notably with respect to the limitations of the sensors on which they rely, are discussed throughout the text.     

Perceptual simulations can be as expressive as first-order logic

Theories asserting that human reasoning is based on perceptual simulations often suppose these simulations are of concrete individual objects and the specific relations that hold among them. However, much human knowledge involves assertions about which relations do not hold, generalities over large numbers of objects and conditional facts. Can simulation theories explain how the mind represents these forms of knowledge, or are they inferior in their expressive power to knowledge representation schemes based on logical formalisms designed specifically to deal with negative, conditional and quantificational knowledge? In this paper, we show how assertions about mental simulations can in fact straightforwardly express all the concepts that comprise first-order logic, including negation, conditionals and both universal and existential quantification. We also speculate on how to extend this approach to deal with probabilistic and more expressive logics.     

A Probabilistic Constraints Approach to Language Acquisition and Processing

This article provides an overview of a probabilistic constraints framework for thinking about language acquisition and processing. The generative approach attempts to characterize knowledge of language (i.e., competence grammar) and then asks how this knowledge is acquired and used. Our approach is performance oriented: the goal is to explain how people comprehend and produce utterances and how children acquire this skill. Use of language involves exploiting multiple probabilistic constraints over various types of linguistic and nonlinguistic information. Acquisition is the process of accumulating this information, which begins in infancy. The constraint satisfaction processes that are central to language use are the same as the bootstrapping processes that provide entry to language for the child. Framing questions about acquisition in terms of models of adult performance unifies the two topics under a set of common principles and has important consequences for arguments concerning language learnability.     

Korsgaard’s Constitutivism and the Possibility of Bad Action

Neo-Kantian accounts which try to ground morality in the necessary requirements of agency face the problem of “bad action”. The most prominent example is Christine Korsgaard’s version of constitutivism that considers the categorical imperative to be indispensable for an agent’s self-constitution. In my paper I will argue that a constitutive account can solve the problem of bad action by applying the distinction between constitutive and regulative rules to the categorical imperative. The result is that an autonomous agent can violate the categorical imperative in so far as it amounts to a regulative rule of morality; however, an agent cannot call into question the categorical imperative as a constitutive rule of the practice of morality without losing her or his identity as a moral agent. The paper then compares this approach to bad action with the one Korsgaard provides and outlines also a new way of grounding the categorical imperative.     

Aristotelian diagrams for semantic and syntactic consequence

Several authors have recently studied Aristotelian diagrams for various metatheoretical notions from logic, such as tautology, satisfiability, and the Aristotelian relations themselves. However, all these metalogical Aristotelian diagrams focus on the semantic (model-theoretical) perspective on logical consequence, thus ignoring the complementary, and equally important, syntactic (proof-theoretical) perspective. In this paper, I propose an explanation for this discrepancy, by arguing that the metalogical square of opposition for semantic consequence exhibits a natural analogy to the well-known square of opposition for the categorical statements from syllogistics, but that this analogy breaks down once we move from semantic to syntactic consequence. I then show that despite this difficulty, one can indeed construct metalogical Aristotelian diagrams from a syntactic perspective, which have their own, equally elegant characterization in terms of the categorical statements. Finally, I construct several metalogical Aristotelian diagrams that incorporate both semantic and syntactic consequence (and their interaction), and study how they are influenced by the underlying logical system’s soundness and/or completeness. All of this provides further support for the methodological/heuristic perspective on Aristotelian diagrams, which holds that the main use of these diagrams lies in facilitating analogies and comparisons between prima facie unrelated domains of investigation.

     

A Theory Of Irrationality As A ‘Reasonable’ Response To An Incomplete Specification

Suppose the principles explaining how the human mind (brain) reaches logical conclusions and judgments were different from – and independent of – thoseinvolved innormatively valid reasoning. Then such principles should affect both conclusion generation and recognition that particular conclusions are or are not justified. People, however, demonstrate a discrepancy between impaired performance in generating logical conclusions as opposed to rather impressive competence in recognizing rational (versus irrational) ones. This discrepancy is hypothesized to arise from often generating an incomplete specification of a logical or judgmental problem when attempting to solve it – versus a recognition of such incompleteness when it is pointed out. The basic argument is developed, with common examples, in the context of specifying or failing to specify all possible combinations in simple logical arguments and is then extended to probabilistic reasoning, where complete versus incomplete specification corresponds to attending to all or to only some components of Bayes theorem-based reasoning.     

Assembling a consistent set of sentences in relational probabilistic logic with stochastic independence

We examine the representation of judgements of stochastic independence in probabilistic logics. We focus on a relational logic where (i) judgements of stochastic independence are encoded by directed acyclic graphs, and (ii) probabilistic assessments are flexible in the sense that they are not required to specify a single probability measure. We discuss issues of knowledge representation and inference that arise from our particular combination of graphs, stochastic independence, logical formulas and probabilistic assessments.     

An Evolutionary Approach to Revising Modernization Theory: An Introduction to the Credible Polity

The future global distribution of the political regimes of countries, just like that of their economic incomes, displays a surprising tendency for polarization into only two clubs of convergence at the extrema. This, in itself, is a persuasive reason to analyze afresh the logical validity of an endogenous theory for political and economic development inherent in modernization theory. I suggest how adopting a simple evolutionary game theoretic view on the subject allows an explanation for these parallel clubs of convergence in political regimes and economic income within the framework of existing research in democratization theory. I also suggest how instrumental action can be methodically introduced into such a setup using learning strategies adopted by political actors. These strategies, based on the first principles of political competition, are motivated by introducing the theoretical concept of a Credible Polity.     

Community Science, Philosophy of Science, and the Practice of Research

Embedded in community science are implicit theories on the nature of reality (ontology), the justification of knowledge claims (epistemology), and how knowledge is constructed (methodology). These implicit theories influence the conceptualization and practice of research, and open up or constrain its possibilities. The purpose of this paper is to make some of these theories explicit, trace their intellectual history, and propose a shift in the way research in the social and behavioral sciences, and community science in particular, is conceptualized and practiced. After describing the influence and decline of logical empiricism, the underlying philosophical framework for science for the past century, I summarize contemporary views in the philosophy of science that are alternatives to logical empiricism. These include contextualism, normative naturalism, and scientific realism, and propose that a modified version of contextualism, known as perspectivism, affords the philosophical framework for an emerging community science. I then discuss the implications of perspectivism for community science in the form of four propositions to guide the practice of research.Portions of this paper are based on an invited paper presented at the May 1997 Pre-Conference Workshop of the Biennial Conference of the Society for Community Research and Action, Columbia, South Carolina.     

Probabilistic argumentation

Argumentation in the sense of a process of logical reasoning is a very intuitive and general methodology of establishing conclusions from defeasible premises. The core of any argumentative process is the systematical elaboration, exhibition, and weighting of possible arguments and counter-arguments. This paper presents the formal theory of probabilistic argumentation, which is conceived to deal with uncertain premises for which respective probabilities are known. With respect to possible arguments and counter-arguments of a hypothesis, this leads to probabilistic weights in the first place, and finally to an overall probabilistic judgment of the uncertain proposition in question. The resulting probabilistic measure is called degree of support and possesses the desired properties of non-monotonicity and non-additivity. Reasoning according to the proposed formalism is an simple and natural generalization of the two classical forms of probabilistic and logical reasoning, in which the two traditional questions of the probability and the logical deducibility of a hypothesis are replaced by the more general question of the probability of a hypothesis being logically deducible from the available knowledge base. From this perspective, probabilistic argumentation also contributes to the emerging area of probabilistic logics.     

Who is susceptible to conjunction fallacies in category-based induction?

Recent evidence suggests that the conjunction fallacy observed in people’s probabilistic reasoning is also to be found in their evaluations of inductive argument strength. We presented 130 participants with materials likely to produce a conjunction fallacy either by virtue of a shared categorical or a causal relationship between the categories in the argument. We also took a measure of participants’ cognitive ability. We observed conjunction fallacies overall with both sets of materials but found an association with ability for the categorical materials only. Our results have implications for accounts of individual differences in reasoning, for the relevance theory of induction, and for the recent claim that causal knowledge is important in inductive reasoning.     

Theory learning as stochastic search in the language of thought

We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While their subsymbolic representations provide a smooth error surface that supports efficient gradient-based learning, our symbolic representations are better suited to capturing children's intuitive theories but give rise to a harder learning problem, which can only be solved by exploratory search. Our algorithm attempts to discover the theory that best explains a set of observed data by performing stochastic search at two levels of abstraction: an outer loop in the space of theories and an inner loop in the space of explanations or models generated by each theory given a particular dataset. We show that this stochastic search is capable of learning appropriate theories in several everyday domains and discuss its dynamics in the context of empirical studies of children's learning.     

How to use probabilities in reasoning

Conclusions Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated.     

Wayfinding behavior and spatial knowledge of adults and children in a virtual environment: The role of landmarks

This study investigated the effect of different organizations of landmark-location pairings as fine-space information on wayfinding behavior and spatial knowledge on a total of 90 participants: 30 second graders, 30 sixth graders, and 30 adults. All participants had to find their way to a goal in a virtual environment with either randomized or categorical landmarks, or without any landmarks. Thereafter, they had to find the shortest way from the start position to the goal in two consecutive trials (wayfinding performance), and they had to solve a number of spatial knowledge tasks. The results showed that independent of their categorical function, the existence of landmarks influenced the way-finding performance of adults and children in the same way. Whereas the presence of landmarks had no effect on spatial survey knowledge, landmark knowledge itself was influenced by the categorical function of the landmarks presented. Moreover, second graders showed limited achievement compared to adults independent of the existence of landmarks. The main results implicate firstly that children at school age indeed are able to use landmark-location pairings as fine-space information like adults during learning an unknown environmental space, and secondly that a dissociation between wayfinding behavior and spatial knowledge might exist.     

Beyond subgoaling: A dynamic knowledge generation framework for creative problem solving in cognitive architectures

In this paper we propose a computational framework aimed at extending the problem solving capabilities of cognitive artificial agents through the introduction of a novel, goal-directed, dynamic knowledge generation mechanism obtained via a non monotonic reasoning procedure. In particular, the proposed framework relies on the assumption that certain classes of problems cannot be solved by simply learning or injecting new external knowledge in the declarative memory of a cognitive artificial agent but, on the other hand, require a mechanism for the automatic and creative re-framing, or re-formulation, of the available knowledge. We show how such mechanism can be obtained trough a framework of dynamic knowledge generation that is able to tackle the problem of commonsense concept combination. In addition, we show how such a framework can be employed in the field of cognitive architectures in order to overcome situations like the impasse in SOAR by extending the possible options of its subgoaling procedures.