First Order Common Knowledge Logics

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies.     

Cut-free common knowledge

Starting off from the infinitary system for common knowledge over multi-modal epistemic logic presented in [L. Alberucci, G. Jäger, About cut elimination for logics of common knowledge, Annals of Pure and Applied Logic 133 (2005) 73–99], we apply the finite model property to “finitize” this deductive system. The result is a cut-free, sound and complete sequent calculus for common knowledge.     

An experimental investigation into the effects of uncertainty on rational behaviour in two person symmetric games

This paper reports the results of two experiments to investigate the effects of payoff alterations in two-person symmetric games. The initial experiment involved 60 subjects, each of whom could earn from £0 to £15, depending on the interaction of their decisions and the unknown decisions of one other person. All decisions were made without feedback to isolate the impact on subjects' behaviour of the game's parameters. A primary aim was to see if the games had strategically distinct structures, or whether uncertainty over the choice rule of others would influence choice behaviour and lessen this independence. An alternative model of rational choice, making allowance for uncertainty in the decision environment, was proposed to capture subjects' behaviour. The results indicated that the frontiers of most of the games had no impact on choice behaviour other than through the magnitude of the change in payoffs. The model received strong support across an identifiable set of ‘frontierless’ games. However, the variety of games was not sufficient to provide a comprehensive test. A second experiment was recently held to close these gaps. Fifty subjects took part, each of whom earned from A$0 to A$24, averaging A$17. The findings provided broad additional support for the theory.     

Williamson on inexact knowledge

Timothy Williamson claims that margin for error principles govern all cases of inexact knowledge. I show that this claim is unfounded: there are cases of inexact knowledge where Williamson’s argument for margin for error principles does not go through. The problematic cases are those where the value of the relevant parameter is fixed across close cases. I explore and reject two responses to my objection, before concluding that Williamson’s account of inexact knowledge is not compelling.

Mutual support in games: Some properties of Berge equilibria

The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n-player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems.     

Knowing full well: the normativity of beliefs as performances

Belief is considered a kind of performance, which attains one level of success if it is true (or accurate), a second level if competent (or adroit), and a third if true because competent (or apt). Knowledge on one level (the animal level) is apt belief. The epistemic normativity constitutive of such knowledge is thus a kind of performance normativity. A problem is posed for this account by the fact that suspension of belief seems to fall under the same sort of epistemic normativity as does belief itself, yet to suspend is of course precisely not to perform, certainly not with the aim of truth. The paper takes up this problem, and proposes a solution that distinguishes levels of performance norrmativity, including a first order where execution competence is in play, and a second order where the performer must assess the risks attendant on issuing a first-order performance. This imports a level of reflective knowledge that ascends above the animal level.

Establishing conventional communication systems: Is common knowledge necessary?

How do communities establish shared communication systems? The Common Knowledge view assumes that symbolic conventions develop through the accumulation of common knowledge regarding communication practices among the members of a community. In contrast with this view, it is proposed that coordinated communication emerges a by‐product of local interactions among dyads. A set of multi‐agent computer simulations show that a population of “egocentric” agents can establish and maintain symbolic conventions without common knowledge. In the simulations, convergence to a single conventional system was most likely and most efficient when agents updated their behavior on the basis of local rather than global, system‐level information. The massive feedback and parallelism present in the simulations gave rise to phenomena that are often assumed to result from complex strategic processing on the part of individual agents. The implications of these findings for the development of theories of language use are discussed.     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

Measuring inaccuracy of uncertain doxastic states in many-valued logical systems

I will propose an alternative philosophical approach to the representation of uncertain doxastic states. I will argue that the current account of measuring inaccuracy of uncertain doxastic states is inadequate for Belnap's four-valued logic. Specifically, a situation can be found in which either an inaccuracy measure returns a completely wrong result or an agent's inaccuracy score is inadequate relative to the mistake in her doxastic attitude. This will motivate an alternative representation of uncertain doxastic states based on ordered pairs. I will describe a possible inaccuracy measure that is suitable for ordered pairs, and I will show that it has all the qualities that are required for an inaccuracy measure to be legitimate. Finally, I will introduce conditions of rationality for uncertain doxastic states represented by ordered pairs.     

The virtues of epistemic conservatism

Although several important methodologies implicitly assume the truth of epistemic conservatism, the view that holding a belief confers some measure of justification on the belief, recent criticisms have led some to conclude that epistemic conservatism is an implausible view. That conclusion is mistaken. In this article, I propose a new formulation of epistemic conservatism that is not susceptible to the criticisms leveled at earlier formulations of epistemic conservatism. In addition to withstanding these criticisms, this formulation of epistemic conservatism has several benefits. First, this formulation has the benefits of earlier formulations of epistemic conservatism, that is to say it makes sense of our intuitions about justification in regard to both memory beliefs and beliefs for which we have forgotten our evidence. Second, it provides a good way of responding to the skeptic’s challenge concerning the possibility of possessing knowledge of the external world posed by the Alternative Hypotheses argument. Third, it provides responses to both forms of a new skeptical problem plaguing basic knowledge structure theories, the Problem of Easy Knowledge formulated by Stewart Cohen. I argue that given the many benefits of this formulation of epistemic conservatism and the fact that it is not vulnerable to the criticisms that undermine earlier formulations of epistemic conservatism, this formulation of epistemic conservatism is a plausible view to maintain.     

Inconsistency and uncertainty in multi-attribute judgment of human performance

This paper examines the effect of uncertainty and inconsistency on the judgment of human performance. The results indicate that the effect of inconsistency on judgment is not mediated by subjective uncertainty. We find that both the level and the extremity of judgment decrease with uncertainty. These effects are explained, respectively, by uncertainty aversion and by regressiveness. We also find that both the level and the extremity of judgment of human performance increase with inconsistency. These effects are explained by reliance on integration rules in which judgment is based primarily on some aspects of the information, while other aspects are, to some extent, ignored.     

On the assessment of procedural knowledge: From problem spaces to knowledge spaces

By generalizing and completing the work initiated by Stefanutti and Albert (2003, Journal of Universal Computer Science, 9, 1455), this article provides the mathematical foundations of a theoretical approach whose primary goal is to construct a bridge between problem solving, as initially conceived by Newell and Simon (1972, Human problem solving. Englewood Cliffs, NJ: Prentice-Hall.), and knowledge assessment (Doignon and Falmagne, 1985, International Journal of Man-Machine Studies, 23, 175; Doignon and Falmagne, 1999, Knowledge spaces. Berlin, Germany: Springer-Verlag.; Falmagne et al., 2013, Knowledge spaces: Applications in education. New York, NY: Springer-Verlag; Falmagne and Doignon, 2011, Learning spaces: Interdisciplinary applied mathematics. Berlin, Germany: Springer-Verlag.). It is shown that the collection of all possible knowledge states for a given problem space is a learning space. An algorithm for deriving a learning space from a problem space is illustrated. As an example, the algorithm is used to derive the learning space of a neuropsychological test whose problem space is well known: the Tower of London (TOL; Shallice, 1982, Philosophical Transactions of the Royal Society of London B: Biological Sciences, 298, 199). The derived learning space could then be used for adaptively assessing individual planning skills with the TOL.     

Integrating different types of knowledge in supervision

The present article examines ways to integrate two, often contradictory, types of knowledge in supervision, which are sometimes represented either by supervisors or supervisees, and sometimes by different parts in the supervisee. These types of knowledge are in a dialectic relationship: they may define each other and at the same time influence and shape each other, yet remain two separate sources for understanding the therapeutic experience. One type is the primary, vague, and intuitive knowledge about patients and therapist–patient interactions, derived from actual participation in the therapeutic relationship. The other type is knowledge derived from theory, experience acquired mainly outside of the specific therapy, and dialog with colleagues.     

Contextual information in situations of uncertainty: The value of explicit-information provision depends on expertise level,knowledge acquisition and prior-action congruency

In behavioral control, contextual information is used alongside incoming sensory inputs to reduce uncertainties about the unfolding situation. However, our understanding of this weighting process is limited; particularly regarding the applied question of whether individuals should be provided with information or whether they should rather generate it by themselves. We thus compared the provision of more or less valid (i.e., “true”) contextual information with a self-generation condition by examining the performance of elite and near-elite youth handball players (N = 30 + 27) in a virtual-reality defensive task. We measured response correctness, positioning as a function of the teammates’ defensive behaviors and the degree to which the experimentally induced patterns in the teammates’ strengths were detected. The results show that providing individuals with uncertain information neither enhances nor harms performance decisively. However, valid information enhances performance in congruent situations while degrading performance in incongruent situations, more pronouncedly in elite than in near-elite players. Consequently, individuals should be provided with explicit contextual information only if (i) their expertise level is not adequate enough to rely on self-generation, (ii) the situation-specific knowledge base cannot be sufficiently self-generated, and (iii) the instructor is sufficiently certain that the explicit information actually meets the upcoming situation.     

Intolerance of uncertainty,causal uncertainty,causal importance,self-concept clarity and their relations to generalized anxiety disorder

Although numerous studies have provided support for the notion that intolerance of uncertainty plays a key role in pathological worry (the hallmark feature of generalized anxiety disorder (GAD)), other uncertainty-related constructs may also have relevance for the understanding of individuals who engage in pathological worry. Three constructs from the social cognition literature, causal uncertainty, causal importance, and self-concept clarity, were examined in the present study to assess the degree to which these explain unique variance in GAD, over and above intolerance of uncertainty. N = 235 participants completed self-report measures of trait worry, GAD symptoms, and uncertainty-relevant constructs. A subgroup was subsequently classified as low in GAD symptoms (n = 69) or high in GAD symptoms (n = 54) based on validated cut scores on measures of trait worry and GAD symptoms. In logistic regressions, only elevated intolerance of uncertainty and lower self-concept clarity emerged as unique correlates of high (vs. low) GAD symptoms. The possible role of self-concept uncertainty in GAD and the utility of integrating social cognition theories and constructs into clinical research on intolerance of uncertainty are discussed.     

Inexact Knowledge with Introspection

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.     

Discrimination in measures of knowledge monitoring accuracy

Knowledge monitoring predicts academic outcomes in many contexts. However, measures of knowledge monitoring accuracy are often incomplete. In the current study, a measure of students’ ability to discriminate known from unknown information as a component of knowledge monitoring was considered. Undergraduate students’ knowledge monitoring accuracy was assessed and used to predict final exam scores in a specific course. It was found that gamma, a measure commonly used as the measure of knowledge monitoring accuracy, accounted for a small, but significant amount of variance in academic performance whereas the discrimination and bias indexes combined to account for a greater amount of variance in academic performance.     

Differentiating intolerance of uncertainty from three related but distinct constructs

Individual differences in uncertainty have been associated with heightened anxiety, stress and approach-oriented coping. Intolerance of uncertainty (IU) is a trait characteristic that arises from negative beliefs about uncertainty and its consequences. Researchers have established the central role of IU in the development of problematic worry and maladaptive coping, highlighting the importance of this construct to anxiety disorders. However, there is a need to improve our understanding of the phenomenology of IU. The goal of this paper was to present hypotheses regarding the similarities and differences between IU and three related constructs – intolerance of ambiguity, uncertainty orientation, and need for cognitive closure – and to call for future empirical studies to substantiate these hypotheses. To assist with achieving this goal, we conducted a systematic review of the literature, which also served to identify current gaps in knowledge. This paper differentiates these constructs by outlining each definition and general approaches to assessment, reviewing the existing empirical relations, and proposing theoretical similarities and distinctions. Findings may assist researchers in selecting the appropriate construct to address their research questions. Future research directions for the application of these constructs, particularly within the field of clinical and health psychology, are discussed.