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.

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.     

A formalisation of violation, error recovery, and enforcement in the bit transmission problem

The design of complex multi-agent systems is increasingly having to confront the possibility that agents may not behave as they are supposed to. In addition to analysing the properties that hold if protocols are followed correctly, it is also necessary to predict, test, and verify the properties that would hold if these protocols were to be violated. We illustrate how the formal machinery of deontic interpreted systems can be applied to the analysis of such problems by considering three variations of the bit transmission problem. The first, an example in which an agent may fail to do something it is supposed to do, shows how we deal with violations of protocols and specifications generally. The second, an example in which an agent may do something it is not supposed to do, shows how it is possible to specify and analyse remedial or error-recovery procedures. The third combines both kinds of faults and introduces a new component into the system, a controller, whose role is to enforce compliance with the protocol. In each case the formal analysis is used to test whether critical properties of the system are compromised, in this example, the reliable communication of information from one agent to the other.     

An Axiomatisation for the Multi-modal Logic of Knowledge and Linear Time LTK

The paper aims at providing the multi-modal propositional logicLTK with a sound and complete axiomatisation. This logic combinestemporal and epistemic operators and focuses on m odeling thebehaviour of a set of agents operating in a system on the backgroundof a temporal framework. Time is represented as linear and discrete,whereas knowledge is modeled as an S₅-like modality. A furthermodal operator intended to represent environment knowledge isadded to the system in order to achieve the expressive powersufficient to describe the piece of information available tothe agents at each moment in the flow of time.     

First Order Extensions of Classical Systems of Modal Logic; The role of the Barcan schemas

The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).     

Competing roles for the subfactors of need for closure in committing the fundamental attribution error

Webster’s (1993) finding that the need for closure (NFC) trait predicts the fundamental attribution error (FAE) is well-cited but has mixed support. After detailing failed replications and contradictory findings, this article reports an attempt to verify the positive NFC–FAE relation using the questioner–contestant paradigm. Rarely investigated but potentially vital to the field, this research also considered the two orthogonal subfactors of NFC, decisiveness and need for structure (Neuberg, Judice, & West, 1997). Results showed that need for structure predicted, overall NFC partially predicted, but decisiveness attenuated the FAE. Thus, Webster’s finding was both replicated and reversed by different aspects of NFC. Decisiveness adds to a short list of trait moderators of the FAE. Implications are discussed for how to measure NFC.     

Three decades of lay epistemics: The why,how, and who of knowledge formation

A conceptual integration and review are presented of three separate research programmes informed by the theory of lay epistemics (Kruglanski, 1989 Kruglanski, A. W. 1989. Lay epistemics and human knowledge: Cognitive and motivational bases, New York: Plenum. [Crossref] , [Google Scholar]). They respectively address the “why”, “how”, and “who” questions about human knowledge formation. The “why” question is treated in work on the need for cognitive closure that propels epistemic behaviour and affects individual, interpersonal, and group phenomena. The “how” question is addressed in work on the unimodel (Kruglanski, Pierro, Mannetti, Erb, & Chun, 2007 Kruglanski, A. W., Pierro, A., Mannetti, L., Erb, H. P. and Chun, W. Y. 2007. “On the parameters of social judgement”. In Advances in experimental social psychology, Edited by: Zanna, M. P. Vol. 39, 255–296. New York: Academic Press.  [Google Scholar]) depicting the process of drawing conclusions from the “information given”. The “who” question is addressed in work on “epistemic authority” highlighting the centrality of source effects (including oneself as a source) in human epistemic behaviour. These separate research paradigms explore facets of epistemic behaviour that jointly produce human knowledge, of essential significance to people's’ individual and social functioning.     

Logic of Knowledge and Utterance and the Liar

We extend the ordinary logic of knowledge based on the operator K and the system of axioms S₅ by adding a new operator U, standing for the agent utters , and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in [3] for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU.     

Epistemic luck and the generality problem

Epistemic luck has been the focus of much discussion recently. Perhaps the most general knowledge-precluding type is veritic luck, where a belief is true but might easily have been false. Veritic luck has two sources, and so eliminating it requires two distinct conditions for a theory of knowledge. I argue that, when one sets out those conditions properly, a solution to the generality problem for reliabilism emerges.

Completeness of Certain Bimodal Logics for Subset Spaces

Subset Spaces were introduced by L. Moss and R. Parikh in [8]. These spaces model the reasoning about knowledge of changing states.In [2] a kind of subset space called intersection space was considered and the question about the existence of a set of axioms that is complete for the logic of intersection spaces was addressed. In [9] the first author introduced the class of directed spaces and proved that any set of axioms for directed frames also characterizes intersection spaces.We give here a complete axiomatization for directed spaces. We also show that it is not possible to reduce this set of axioms to a finite set.     

Complete Axiomatizations for Reasoning about Knowledge and Branching Time

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with respect to a version of the bundle semantics.     

错误加工意识水平与错误相关脑电成分

错误加工的意识水平包括有意识水平、无意识水平以及介于两者之间的意识水平。意识水平的划分通常通过错误报告范式实现。根据其对意识水平的划分, 可以将相关研究分为二元意识水平研究和多元意识水平研究。已有研究, 主要关注于意识水平与错误诱发的Ne、Pe的关系。两类研究一致表明, Pe受意识水平的调节, 但是并没有得到fMRI研究的一致支持。对Ne的激活是否独立于意识, 研究者们仍存在争议。还有研究考察了注意对错误意识水平的影响, 结果支持Pe与意识水平共变的观点, 但是对注意如何影响错误意识水平还存在质疑。在对以上研究进行整理与分析的基础上, 对将来的研究提出了建议。     

Power,participation and partnerships: reflections on the co-creation of knowledge

Narrative writing was used to critically reflect on the reasons for the success and failure of two research partnerships: one between the authors and a community group, the other between the authors and academic colleagues. The reflections relate to a vignette constructed on the experiences of the authors and somewhat fictionalised, but brought together to highlight the contrasts, whereby one research partnership was successful in producing outcomes while the other was not. An analysis of these reflections was informed by Wenger’s Communities of Practice framework. This helped draw out issues around power and participation as fundamental for successful research partnerships, particularly multidisciplinary partnerships, intent on the co-creation of knowledge. Such issues related to recognising partnerships and the underlying assumptions when these partnerships cross boundaries include transparent communication, power and decision-making processes, critical self-awareness, and negotiated meaning and identity.     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

Instructor and student knowledge of study strategies

Students' self-reported study skills and beliefs are often inconsistent with empirically supported (ES) study strategies. However, little is known regarding instructors' beliefs about study skills and if such beliefs differ from those of students. In the current study, we surveyed college students' and instructors' knowledge of study strategies and had both groups evaluate the efficacy of learning strategies described in six learning scenarios. Results from the survey indicated that students frequently reported engaging in methods of studying that were not optimal for learning. Instructors' responses to the survey indicated that they endorsed a number of effective study skills but also held several beliefs inconsistent with research in learning and memory (e.g., learning styles). Further, results from the learning scenarios measure indicated that instructors were moderately more likely than students to endorse ES learning strategies. Collectively, these data suggest that instructors exhibited better knowledge of effective study skills than students, although the difference was small. We discuss several notable findings and argue for the improvement of both students' and instructors' study skill knowledge.     

Statistical inference for false positive and false negative error rates in mastery testing

This paper describes an asymptotic inferential procedure for the estimates of the false positive and false negative error rates. Formulas and tables are described for the computations of the standard errors. A simulation study indicates that the asymptotic standard errors may be used even with samples of 25 cases as long as the Kuder-Richardson Formula 21 reliability is reasonably large. Otherwise, a large sample would be required.This work was performed pursuant to Grant No NIE-G-78-0087 with the National Institute of Education, Department of Health, Education and Welfare, Huynh Huynh, Principal Investigator. Points of view or opinions stated do not necessarily reflect NIE position or policy and no official endorsement should be inferred. The editorial assistance of Joseph C. Saunders is gratefully acknowledged.     

Knowledge of Results for Motor Learning: Relationship Between Error Estimation and Knowledge of Results Frequency

The authors of the present study investigated the apparent contradiction between early and more recent views of knowledge of results (KR), the idea that how one is engaged before receiving KR may not be independent of how one uses that KR. In a 2 × 2 factorial design, participants (N = 64) practiced a simple force-production task and (a) were required, or not required, to estimate error about their previous response and (b) were provided KR either after every response (100%) or after every 5th response (20%) during acquisition. A no-KR retention test revealed an interaction between acquisition error estimation and KR frequencies. The group that received 100% KR and was required to error estimate during acquisition performed the best during retention. The 2 groups that received 20% KR performed less well. Finally, the group that received 100% KR and was not required to error estimate during acquisition performed the poorest during retention. One general interpretation of that pattern of results is that motor learning is an increasing function of the degree to which participants use KR to test response hypotheses (J. A. Adams, 1971; R. A. Schmidt, 1975). Practicing simple responses coupled with error estimation may embody response hypotheses that can be tested with KR, thus benefiting motor learning most under a 100% KR condition. Practicing simple responses without error estimation is less likely to embody response hypothesis, however, which may increase the probability that participants will use KR to guide upcoming responses, thus attenuating motor learning under a 100% KR condition. The authors conclude, therefore, that how one is engaged before receiving KR may not be independent of how one uses KR.