Inferential Steps Research Articles

Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

ABSTRACTThis article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems.

Using corpus linguistics to examine the extrapolation inference in the validity argument for a high-stakes speaking assessment

Investigations of the validity of a number of high-stakes language assessments are conducted using an argument-based approach, which requires evidence for inferences that are critical to score interpretation (Chapelle, Enright, & Jamieson, 2008b; Kane, 2013). The current study investigates the extrapolation inference for a high-stakes test of spoken English, the Michigan English Language Assessment Battery (MELAB) speaking task. This inference requires evidence that supports the inferential step from observations of what test takers can do on an assessment to what they can do in the target domain (Chapelle et al., 2008b; Kane, 2013). Typically, the extrapolation inference has been supported by evidence from a criterion measure of language ability. This study proposes an additional empirical method, namely corpus-based register analysis (Biber & Conrad, 2009), which provides a quantitative framework for examining the linguistic relationship between performance assessments and the domains to which their scores are extrapolated. This approach extends Bachman and Palmer’s (2010) focus on the target language use (TLU) domain analysis in their study of assessment use arguments by providing a quantitative approach for the study of language. We first explain the connections between corpus-based register analysis and TLU analysis. Second, an investigation of the MELAB speaking task compares the language of test-taker responses to the language of academic, professional, and conversational spoken registers, or TLU domains. Additionally, the language features at different performance levels within the MELAB speaking task are investigated to determine the relationship between test takers’ scores and their language use in the task. Following previous studies using corpus-based register analysis, we conduct a multi-dimensional (MD) analysis for our investigation. The comparison of the language features from the MELAB with the language of TLU domains revealed that support for the extrapolation inference varies across dimensions of language use.

Dispelling five myths about hypothesis testing in biological systematics

The emphasis on testing phylogenetic hypotheses has been prominent since the English language introductions of Willi Hennig’s Phylogenetic Systematics (1966) and Karl Popper’s (1959) Logic of Scientific Discovery. While the mechanics of hypothesis and theory testing are well established in other fields of science, adherence to those prescriptions in biological systematics has rarely been formally recognized. The consequence has been the development of potentially contradictory approaches to empirically evaluating phylogenetic hypotheses under the guise of testing. In his brief review of the topic, Assis (Cladistics, 30:240–242, 2014) identified five different views on phylogenetic hypothesis testing: (1) total evidence, (2) taxonomic congruence, (3) reciprocal illumination, (4) homology assessment, and (5) taxa sampling. The present paper examines the validity of these views against the actual inferential steps required to infer hypotheses and subsequently engage in testing, i.e., abduction, deduction, and induction (sensu stricto), respectively. It is shown that none of the tests discussed by Assis are valid, and while it is straightforward to outline what is required to properly test phylogenetic hypotheses, the feasibility of accomplishing such tests is operationally impractical in most instances.

Where is procedural meaning located? Evidence from discourse connectives and tenses

The main goal of this article is to make a proposal about where procedural meaning is located. Procedural meaning is defined as guiding the processing of conceptual information, whereas conceptual meaning includes information about the representation of entities, for instance objects or events. Conceptual information for connectives is described at the level of entailment, explicature and implicature, and may indicate possible causal relations among the events described, whereas procedural information for causal connectives is restricted to indicating the direction of the causal relation (forward or backward). Conceptual information for tenses specifies temporal coordinates, while procedural meaning specifies directional and subjective properties of events, using features such as [±narrative] or [±subjective]. A second goal is to answer a central question for pragmatics: what is the contribution of connectives, that is, what is the difference between discourses with and without connectives? The pragmatic framework adopted, which is based on Relevance Theory, gives the following answer: in a discourse without connectives, the accessibility of the intended interpretation depends solely on the context, whereas the use of connectives allows a simpler route, reducing the number of inferential steps and helping to determine semantic and pragmatic contents such as entailments, explicatures and implicatures.

What’s the Point of Complete Rigour?

Complete inferential rigour is achieved by breaking down arguments into steps that are as small as possible: inferential ‘atoms’. For example, a mathematical or philosophical argument may be made completely inferentially rigorous (‘atomized’) by decomposing its inferential steps into the type of step found in a natural deduction system. It is commonly thought that atomization, paradigmatically in mathematics but also more generally, is pro tanto epistemically valuable. The paper considers some plausible candidates for the epistemic value arising from atomization and finds that none of them fits the bill. In particular, atomized arguments do not ground the correctness of their unatomized counterparts; they are typically not credence-preserving; and they need not reveal the source of inferential disagreement. The moral this suggests is that complete rigour is not even a defeasible epistemic ideal.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving.

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load.

An evolutionary computational theory of prefrontal executive function in decision-making.

The prefrontal cortex subserves executive control and decision-making, that is, the coordination and selection of thoughts and actions in the service of adaptive behaviour. We present here a computational theory describing the evolution of the prefrontal cortex from rodents to humans as gradually adding new inferential Bayesian capabilities for dealing with a computationally intractable decision problem: exploring and learning new behavioural strategies versus exploiting and adjusting previously learned ones through reinforcement learning (RL). We provide a principled account identifying three inferential steps optimizing this arbitration through the emergence of (i) factual reactive inferences in paralimbic prefrontal regions in rodents; (ii) factual proactive inferences in lateral prefrontal regions in primates and (iii) counterfactual reactive and proactive inferences in human frontopolar regions. The theory clarifies the integration of model-free and model-based RL through the notion of strategy creation. The theory also shows that counterfactual inferences in humans yield to the notion of hypothesis testing, a critical reasoning ability for approximating optimal adaptive processes and presumably endowing humans with a qualitative evolutionary advantage in adaptive behaviour.

Analyzing jokes with the Intersecting Circles Model of humorous communication

In previous research, I have claimed that relevance theory (Sperber and Wilson 1995) is a valid cognitive pragmatics framework to explain how humorous effects are generated, both from the processing of jokes (Yus 1997, 2003, 2008, 2012a, 2012b) and from the processing of longer discourses such as stand-up comedy monologues (Yus 2002, 2004, 2005). This paper aims to show how the speaker’s humorous intention is devised and how humorous effects are generated in the audience by analyzing 1000 randomly collected jokes and checking how they fit into any of the seven types of jokes that are predicted in the Intersecting Circles Model of humorous communication (Yus forthcoming). The paper is organized as follows: First, I provide a brief comment on the cognitive foundation of relevance theory and the inferential steps that hearers go through in the interpretation of utterances according to this theory. Second, I comment on how these steps can be manipulated for the sake of humor. Next, comments on a previous classification of jokes are provided. Finally, the Intersecting Circles Model of humorous communication (henceforth ICM) is outlined and the corpus of jokes is analyzed to check how they fit into the seven types of jokes that this Model comprises.

Re-Assessing the Speech Act Schema: Twenty-First Century Reflections

Bach and Harnish’s (1979) Speech Act Schema (SAS) breaks down into a series of inferential steps the process involved in understanding an utterance as a particular kind of speech act. At the heart of the SAS lies the notion of illocutionary intention, a special kind of reflexive intention whose fulfilment consists in its recognition. This article re-assesses Bach and Harnish’s Speech Act Schema in two ways. First, I discuss three types of indirect speech acts—acts exchanged between intimates, alerts, and ritual indirectness—arguing that in all three cases, a perlocutionary effect of re-affirming or testing the degree of sharedness between speaker and addressee is also achieved, making all three types of acts overt collateral acts in Bach and Harnish’s terminology. Second, I consider cases when the speaker’s illocutionary intention exists in only a rudimentary form, such as children’s early directives and metaphorical utterances expressing feelings. In such cases, the hearer is called upon to play a more active role, by constructing (rather than recognizing) an understanding based on the linguistic material provided by the speaker. The need to account for this second set of acts challenges the centrality of the speaker’s illocutionary intention as the ultimate arbitrator of communicative outcomes and forces us to accord at least equal weight to the contribution of the hearer. The end result is a novel emphasis on the intersubjective aspects of linguistic communication, which were given less prominence in more traditional models, such as the SAS.

Towards more Accessible Conceptions of Statistical Inference

SummaryThere is a compelling case, based on research in statistics education, for first courses in statistical inference to be underpinned by a staged development path. Preferably over a number of years, students should begin working with precursor forms of statistical inference, much earlier than they now do. A side benefit is giving younger students more straightforward and more satisfying ways of answering interesting real world questions. We discuss the issues that are involved in formulating precursor versions of inference and then present some specific and highly visual proposals. These build on novel ways of experiencing sampling variation and have intuitive connections to the standard formal methods of making inferences in first university courses in statistics. Our proposal uses visual comparisons to enable the inferential step to be made without taking the eyes off relevant graphs of the data. This allows the time and conceptual distances between questions, data and conclusions to be minimized, so that the most critical linkages can be made. Our approach was devised for use in high schools but is also relevant to adult education and some introductory tertiary courses.

Towards naturalness scales of pragmatic complexity

This paper is an attempt to handle pragmatic complexity within the framework of Natural Linguistics. Specifically it aims at building two naturalness scales of the complexity of pragmatic inferences based on the naturalness parameters of trans-parency–opacity and of biuniqueness–ambiguity, illustrated mainly with French examples. The scales are complementary: transparency–opacity deals with hierarchized meanings, biuniqueness–ambiguity with exclusive alternative meanings. Pragmatic complexity is intended here as a function of the number and types of inferences or inferential steps included in the description of an utterance meaning. It is defined quantitatively and qualitatively and converges with cognitive complexity. The scales distinguish phenomena that are to varying degrees opaque or ambiguous (indirect, elliptic or non-literal) according to whether there is flouting or violation of a Gricean maxim and how this takes place. The number of cotextual and/or contextual dimensions as well as variable cog-nitive operations, modes of reasoning and meaning relations are taken as measures of pragmatic complexity. The paper also discusses the relation between complexity and markedness. This issue reveals a conflict between the perspectives of speaker and hearer.

On the Soundness of Inferring Modern Language from Symbolic Behaviour

At issue in this article is the soundness of archaeological inferences which proceed stepwise from data about the material culture of Middle Stone Age humans, via assumptions about their symbolic behaviour, to the conclusion that they had modern language. Taking as paradigmatic the inference that the humans who inhabited Blombos Cave in South Africa some 75,000 years ago had fully syntactical language, the article argues that the inferential step from symbolic behaviour to modern language lacks the required warrant. This step, it is shown, is not underpinned by an adequate bridge theory of the putative links between symbolic behaviour and modern language. The bridge theories invoked to date to shore up the Blombos inference are flawed, for instance, in that they incorporate untenable assumptions about language, including an incorrect view of the expressive power of relatively simple linguistic means.

The A Simili Argument: An Inferentialist Setting

AbstractThe A Simili Argument draws the conclusion that a target case has a normative property Q since it shares a relevant property P with a source case. It can be seen as a complex inference constituted by three inferential steps: An abduction of the relevant property P, an induction of the class having that property, and a deduction of the target's having property Q. A major problem of this argument is the characterization of the property relevance. The standard answer refers to the notion of ratio: It is the ratio that fixes what is relevant for what. But the determination of the ratio is often a difficult and controversial task. This issue is considered here from an inferentialist point of view, claiming that the ratio and relevance are determined by the normative statuses reciprocally attributed by the speakers in the context of legal argumentation.

Modern behavioral experiments are not economic history

It is ironic that an article titled “Recordkeeping alters economic history by promoting reciprocity” (1) contains no evidence at all from economic history. “Economic history” is typically defined as the empirical record of past economic practices and processes. The fact that recordkeeping by modern subjects alters the result of a game is not directly informative about past economies; a crucial inferential step is left out. These results may indeed help us understand the origins of recordkeeping and accounting. But descriptions of what modern subjects do in an experimental setting do not constitute historical data. Historians and archaeologists actually have considerable empirical information on the origins of recordkeeping in various parts of the world (2–5), but economists typically ignore historical and archaeological data, preferring instead to theorize about the way ancient economies may have operated. Researchers will welcome this study as an addition to our array of analogical data that can contribute to the study of past economies. But the title of this article is incorrect and misleading because the article presents no data on economic history.

ConTrack: Finding the most likely pathways between brain regions using diffusion tractography

Magnetic resonance diffusion-weighted imaging coupled with fiber tractography (DFT) is the only non-invasive method for measuring white matter pathways in the living human brain. DFT is often used to discover new pathways. But there are also many applications, particularly in visual neuroscience, in which we are confident that two brain regions are connected, and we wish to find the most likely pathway forming the connection. In several cases, current DFT algorithms fail to find these candidate pathways. To overcome this limitation, we have developed a probabilistic DFT algorithm (ConTrack) that identifies the most likely pathways between two regions. We introduce the algorithm in three parts: a sampler to generate a large set of potential pathways, a scoring algorithm that measures the likelihood of a pathway, and an inferential step to identify the most likely pathways connecting two regions. In a series of experiments using human data, we show that ConTrack estimates known pathways at positions that are consistent with those found using a high quality deterministic algorithm. Further we show that separating sampling and scoring enables ConTrack to identify valid pathways, known to exist, that are missed by other deterministic and probabilistic DFT algorithms.

Prehistoric shell beads as a window on language evolution

Humans had “fully syntactical language” as early as 75,000 years ago. This has been inferred from properties of a number of Middle Stone Age (MSA) shell beads excavated at Blombos Cave in South Africa. Addressing the question “Can one learn something about the evolution of language from prehistoric shell beads?”, the article analyses the chain of inferential steps by which this conclusion was reached. It argues that some of these steps are problematic in not being underpinned by well-articulated theories of what “fully syntactical language” is and of why a complex form of syntax is a requisite for transmitting MSA symbolic meanings. At a more general level, the article, moreover, fleshes out the concept of a “window on language evolution” by contrasting the shell bead window with the window provided by pidgin languages in regard to the form of inference they embody and the purpose for which they are used.

A gênese do conceito freudiano de inconsciente

Durante toda sua obra, Freud concebe os processos psíquicos como derivados da atividade do cérebro. Aqui é proposta uma reconstituição dos passos inferenciais (constituindo uma seqüência lógica e não cronológica), possibilitados por essa concepção psiconeural, que levaram (sob a influência dos fatos clínicos) ao conceito psicanalítico de inconsciente. Os processos neurofisiológicos subjacentes ao psíquico devem possuir complexidade suficiente para justificar as propriedades psíquicas conhecidas pela consciência. Para Freud, a consciência é uma espécie de percepção interna de processos psíquicos. Como a consciência não é inerente a esses processos, torna-se natural imaginar que eles possam também ocorrer sem serem percebidos (processos pré-conscientes). O conceito de inconsciente propriamente dito também se mostra tributário de sua concepção psiconeural.

Symposium on “Cognition and Rationality: Part I” The rationality of scientific discovery: abductive reasoning and epistemic mediators

Philosophers have usually offered a number of ways of describing hypotheses generation, but all aim at demonstrating that the activity of generating hypotheses is paradoxical, illusory or obscure, and then not analysable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. The “computational turn” gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. Creativity and discovery are no more seen as a mysterious irrational process, but, thanks to constructive accounts, as a complex relationship among different inferential steps that can be clearly analysed and identified. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems.

Experience in integrative negotiations: What needs to be learned?

In this research we focus on the roles of experience and understanding in fostering integrative negotiation performance. We report on two experiments in which we distinguish between understanding opponents’ general priorities among issues versus understanding their specific gains for particular offers. Although experience enhanced integrative performance even in the absence of understanding, we found that understanding the specific gains had an incremental effect on performance. We conclude that while generally acknowledging opponents’ interests is not sufficient, the additional inferential step of assessing their specific gains throughout the negotiation process is advantageous.

Experience in Integrative Negotiations: What Needs to Be Learned?

Focusing on the roles of experience and understanding in fostering integrative negotiation performance, we report two experiments in which we particularly distinguish between understanding opponents' general priorities among issues versus understanding their specific gains for particular offers. Although experience enhanced integrative performance even in the absence of understanding, we found that understanding the specific gains had an incremental effect. We conclude that while generally acknowledging opponents' interests is not sufficient, the additional inferential step of assessing their specific gains throughout the negotiation process is advantageous.