The speed-accuracy trade-off effect refers to the behavioral trade-off between fast yet error-prone respones and accurate but slow responses. Multiple theories on the cognitive mechanisms behind SAT exist. One theory assumes that SAT is a consequence of strategically adjusting the amount of evidence required for overt behaviors, such as perceptual choices. Another theory hypothesizes that SAT is the consequence of the mixture of multiple categorically different cognitive processes. In this paper, these theories are disambiguated by assessing whether the fixed-point property (...) of mixture distributions holds, in both simulations and data. I conclude that, at least for perceptual decision making, there is no evidence for a mixture of different cognitive processes to trade off accuracy of responding for speed. (shrink)

This article discusses how sequential sampling models can be integrated in a cognitive architecture. The new theory Retrieval by Accumulating Evidence in an Architecture (RACE/A) combines the level of detail typically provided by sequential sampling models with the level of task complexity typically provided by cognitive architectures. We will use RACE/A to model data from two variants of a picture–word interference task in a psychological refractory period design. These models will demonstrate how RACE/A enables interactions between sequential sampling and long-term (...) declarative learning, and between sequential sampling and task control. In a traditional sequential sampling model, the onset of the process within the task is unclear, as is the number of sampling processes. RACE/A provides a theoretical basis for estimating the onset of sequential sampling processes during task execution and allows for easy modeling of multiple sequential sampling processes within a task. (shrink)

The speed‐accuracy trade‐off (SAT) effect refers to the behavioral trade‐off between fast yet error‐prone respones and accurate but slow responses. Multiple theories on the cognitive mechanisms behind SAT exist. One theory assumes that SAT is a consequence of strategically adjusting the amount of evidence required for overt behaviors, such as perceptual choices. Another theory hypothesizes that SAT is the consequence of the mixture of multiple categorically different cognitive processes. In this paper, these theories are disambiguated by assessing whether the fixed‐point (...) property of mixture distributions holds, in both simulations and data. I conclude that, at least for perceptual decision making, there is no evidence for a mixture of different cognitive processes to trade off accuracy of responding for speed. (shrink)

Between‐trial effects in Stroop‐like interference tasks are linked to differences in the amount of cognitive control. Trials following an incongruent trial show less interference, an effect suggested to result from the increased control caused by the incongruent previous trial (known as the Gratton effect). In this study, we show that cognitive control not only results in a different amount of interference but also in a different locus of the interference. That is, the stage of the task that shows the most (...) interference changes as a function of the preceding trial. Using computational cognitive modeling, we explain these effects by a difference in the amount of processing of the irrelevant dimension of the stimulus. (shrink)

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the first (...) experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., “Most of the gleerbs are feezda.”) based on the numerical information provided in the second sentence, (e.g., “60% of the gleerbs are feezda”). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics. (shrink)

Parametric cognitive models are increasingly popular tools for analyzing data obtained from psychological experiments. One of the main goals of such models is to formalize psychological theories using parameters that represent distinct psychological processes. We argue that systematic quantitative reviews of parameter estimates can make an important contribution to robust and cumulative cognitive modeling. Parameter reviews can benefit model development and model assessment by providing valuable information about the expected parameter space, and can facilitate the more efficient design of experiments. (...) Importantly, parameter reviews provide crucial—if not indispensable—information for the specification of informative prior distributions in Bayesian cognitive modeling. From the Bayesian perspective, prior distributions are an integral part of a model, reflecting cumulative theoretical knowledge about plausible values of the model's parameters (Lee,2018). In this paper we illustrate how systematic parameter reviews can be implemented to generate informed prior distributions for the Diffusion Decision Model (DDM; Ratcliff and McKoon,2008), the most widely used model of speeded decision making. We surveyed the published literature on empirical applications of the DDM, extracted the reported parameter estimates, and synthesized this information in the form of prior distributions. Our parameter review establishes a comprehensive reference resource for plausible DDM parameter values in various experimental paradigms that can guide future applications of the model. Based on the challenges we faced during the parameter review, we formulate a set of general and DDM-specific suggestions aiming to increase reproducibility and the information gained from the review process. (shrink)

The parameters governing our behavior are in constant flux, and capturing these dynamics in cognitive models remains a challenge. We demonstrate how a mapping between ACT‐R's model of declarative memory and the linear ballistic accumulator enables efficient estimation of memory parameters from data. The resulting estimates provide a cognitively meaningful explanation for observed differences in behavior over time and between individuals.

The parameters governing our behavior are in constant flux. Accurately capturing these dynamics in cognitive models poses a challenge to modelers. Here, we demonstrate a mapping of ACT-R's declarative memory onto the linear ballistic accumulator (LBA), a mathematical model describing a competition between evidence accumulation processes. We show that this mapping provides a method for inferring individual ACT-R parameters without requiring the modeler to build and fit an entire ACT-R model. Existing parameter estimation methods for the LBA can be used, (...) instead of the computationally expensive parameter sweeps that are traditionally done. We conduct a parameter recovery study to confirm that the LBA can recover ACT-R parameters from simulated data. Then, as a proof of concept, we use the LBA to estimate ACT-R parameters from an empirical dataset. The resulting parameter estimates provide a cognitively meaningful explanation for observed differences in behavior over time and between individuals. In addition, we find that the mapping between ACT-R and LBA lends a more concrete interpretation to ACT-R's latency factor parameter, namely as a measure of response caution. This work contributes to a growing movement towards integrating formal modeling approaches in cognitive science. (shrink)

An agent who receives information in the form of an indicative conditional statement and who trusts her source will modify her credences to bring them in line with the conditional. I will argue that the agent, upon the acquisition of such information, should, in general, expand her prior credence function to an indeterminate posterior one; that is, to a set of credence functions. Two different ways the agent might interpret the conditional will be presented, and the properties of the resulting (...) indeterminate posteriors compared. The cause of the expansion from a single prior credence function to a set of credence functions forming the indeterminate posterior one will be explained. The expansion undermines the Bayesian dogma that the result of assimilating new information into a determinate prior credence functions is always a determinate posterior one. (shrink)

The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to all cases (...) in which new information is traditionally handled by minimizing the relative entropy. (shrink)

An infinite lottery experiment seems to indicate that Bayesian conditionalization may be inconsistent when the prior credence function is finitely additive because, in that experiment, it conflicts with the principle of reflection. I will show that any other form of updating credences would produce the same conflict, and, furthermore, that the conflict is not between conditionalization and reflection but, instead, between finite additivity and reflection. A correct treatment of the infinite lottery experiment requires a careful treatment of finite additivity. I (...) will show that the results of the experiment, paradoxical though they may be, are not inconsistent, but that they conflict with one particular version of reflection . I will reject that version and I will propose a slight modification of a different version of reflection such that the modified version does maintain the mutual consistency of finite additivity, reflection and conditionalization. As a result, I will strengthen the case for finite additivity by showing that Bayesian conditionalization is fully consistent with it. (shrink)

Dans ce volume considérable, on été réunies les contributions d'un Congrès international tenu à Louvain en 1998 pour marquer l'achèvement de la première édition de la Théologie Platonicienne de Proclus. Ces contributions, toutes rigoureusement centrées sur la Théol. Plat. concernent (1) les principes et les sources de la Théol. plat. (2) Les méthodes théologiques de Proclus (3) La postérité de la Théol. plat. dans le monde grec, païen comme chrétien, et dans le monde islamique. Des indices très détaillés permettent de (...) retrouver tous les passages cités et commentés dans ce volume. (shrink)

Diagnosis theory reasons about incomplete knowledge and only considers the past. It distinguishes between violations and non-violations. Qualitative decision theory reasons about decision variables and considers the future. It distinguishes between fulfilled goals and unfulfilled goals. In this paper we formalize normative diagnoses and decisions in the special purpose formalism DIO2 as well as in extensions of the preference-based deontic logic PDL. The DIagnostic and DEcision-theoretic framework for DEontic reasoning DIO2 formalizes reasoning about violations and fulfillments, and is used to (...) characterize the distinction between normative diagnosis theory and decision theory. The extension of the preference-based deontic logic PDL shows how normative diagnostic and decision-theoretic reasoning — i.e. reasoning about violations and fulfillments — can be formalized as an extension of deontic reasoning. (shrink)

John Pell worked in the Netherlands from 1643 until 1652. He therefore deserves a place in a survey of mathematics c. 1650 in the Netherlands. During his stay he was mainly concerned with refuting a quadrature of the circle that was published in 1644 in Amsterdam by the Danish astronomer and mathematician Longomontanus. We therefore make Pell's refutation the main theme of this paper, but other aspects of Pell's work and some biographical information will be discussed within this framework. This (...) paper includes a discussion of the refuted quadrature, and the first publication of a copy of the original one-leaf refutation, which was thought to be lost. In addition, we survey Pell's correspondence about the affair and in that connection discuss some unknown letters from Mersenne. (shrink)

Hans van Maanen is professor of art and society at the Department of Arts, Culture & Media Studies of the University of Groningen, the Netherlands.

A letter written by Christiaan Huygens to David Gregory is published here for the first time. After an introduction about the contacts between the two correspondents, an annotated English translation of the letter is given. The letter forms part of the wider correspondence about the ‘new calculus’, in which L'Hospital and Leibniz also participated, and gives some new evidence about Huygens's ambivalent attitude towards the new developments. Therefore, two mathematical passages in the letter are discussed separately. An appendix contains the (...) original Latin text. (shrink)

Amsterdam University Press is a leading publisher of academic books, journals and textbooks in the Humanities and Social Sciences. Our aim is to make current research available to scholars, students, innovators, and the general public. AUP stands for scholarly excellence, global presence, and engagement with the international academic community.

Sounds are heard, sometimes even felt, but in most cases they remain unseen. This ephemeral and invisible nature of sound was already considered a problem when the science of acoustics took form in the seventeenth century. The fact that sound could not be seen was described as a significant hindrance to its understanding. But it was precisely during this time that a wide variety of sounds attracted broad scientific attention across Europe. Scholars, natural philosophers, and mathematicians investigated and experimented with (...) sound and musical instruments and developed theories of hearing. This article looks at the role of images, diagrams, and visualization techniques in late seventeenth-century acoustics, bringing together the history of sound and the history of scientific images. Focusing on water and light as the dominant analogies for sound, the article demonstrates that visualization was an important tool for thinking about sound and allowed for the circulation of theories and experiments. At the same time, the epistemic status of these images remained contested, as there was no single model that could explain the different ways sound behaves as it moves through space and that could be visualized. (shrink)

Diagnosis theory reasons about incomplete knowledge and only considers the past. It distinguishes between violations and non-violations. Qualitative decision theory reasons about decision variables and considers the future. It distinguishes between fulfilled goals and unfulfilled goals. In this paper we formalize normative diagnoses and decisions in the special purpose formalism DIO(DE)2 as well as in extensions of the preference-based deontic logic PDL. The DIagnostic and DEcision-theoretic framework for DEontic reasoning DIO(DE)2 formalizes reasoning about violations and fulfillments, and is used to (...) characterize the distinction between normative diagnosis theory and (qualitative) decision theory. The extension of the preference-based deontic logic PDL shows how normative diagnostic and decision-theoretic reasoning — i.e. reasoning about violations and fulfillments — can be formalized as an extension of deontic reasoning. (shrink)

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They (...) are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels. (shrink)

The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field. The first part provides a general and historical perspective on the field. The second part gives a comprehensive coverage of the argumentation formalisms (...) available in the literature at various levels of abstraction. The third part is devoted to cover some of the many dialogical aspects of argumentation, while the fourth one deals with algorithmic, computational and implementation issues. Finally, the fifth part provides some deeper analyses on the previously introduced topics. The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the first outcome. Further volumes are planned to cover topics not included in the present one and the initiative is conceived to grow by the support and feeding it receives from the community members. (shrink)

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They (...) are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels. (shrink)

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, (...) considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourr6n/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step. (shrink)

In this paper I propose violation games as the basis of formal logics to represent and reason about norms, i.e. as the foundation of deontic logic. Deontic logic is an applied non-classical logic reflecting a way in which we conceptualize normative reasoning. By introducing violation games as a fundamental principle of deontic logic, I am introducing a new way of looking at familiar problems in normative reasoning, with the aim of introducing a new approach for handling norms in intelligent systems.

The principle-based approach is a methodology to classify and analyse argumentation semantics. In this paper we classify seven of the main alternatives for argumentation semantics using a set of new robustness principles. These principles complement Baroni and Giacomin’s original classification and deal with the behaviour of a semantics when the argumentation framework changes due to the addition or removal of an attack between two arguments. We distinguish so-called persistence principles and monotonicity principles, where the former deal with the question of (...) whether a labelling or extension of an argumentation framework under a given semantics persists after a change, and the latter with the question of whether new labellings or extensions are created after a change. We furthermore show in which sense labelling-based and extension-based semantics lead to subtly different principles and results. Our results can be used for choosing a semantics for a particular application, or to guide the search for new argumentation semantics, but they have been used also in the design of algorithms. (shrink)

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen (...) and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission. (shrink)

In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s abstract arguments with meta-arguments using a technique called flattening. (...) We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. (shrink)