We prove that for a finitely generated infinite nilpotent group $G$ with structure $(G,\cdot,\dots)$, the connected component ${G^*}^0$ of a sufficiently saturated extension $G^*$ of $G$ exists and equals \[ \bigcap_{n\in\N} \{g^n\colon g\in G^*\}. \] We construct an expansion of ${\mathbb Z}$ by a predicate $({\mathbb Z},+,P)$ such that the type-connected component ${{\mathbb Z}^*}^{00}_{\emptyset}$ is strictly smaller than ${{\mathbb Z}^*}^0$. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain (...) an optimality result for the van der Waerden theorem for finite partitions of groups. (shrink)

We analyze model-theoretic connected components in extensions of a given group by abelian groups which are defined by means of 2-cocycles with finite image. We characterize, in terms of these 2-cocycles, when the smallest type-definable subgroup of the corresponding extension differs from the smallest invariant subgroup. In some situations, we also describe the quotient of these two connected components. Using our general results about extensions of groups together with Matsumoto–Moore theory or various quasi-characters considered in bounded cohomology, we (...) obtain new classes of examples of groups whose smallest type-definable subgroup of bounded index differs from the smallest invariant subgroup of bounded index. This includes the first known example of a group with this property found by Conversano and Pillay, namely the universal cover of [Formula: see text], as well as various examples of different nature, e.g. some central extensions of free groups or of fundamental groups of closed orientable surfaces. As a corollary, we get that both non-abelian free groups and fundamental groups of closed orientable surfaces of genus [Formula: see text], expanded by predicates for all subsets, have this property, too. We also obtain a variant of the example of Conversano and Pillay for [Formula: see text] instead of [Formula: see text], which was not accessible by the previously known methods. (shrink)

We study the partial orderings of the form ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}, \subset\rangle}$$\end{document}, where X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} is a binary relational structure with the connectivity components isomorphic to a strongly connected structure Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} and P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} is the set of substructures of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {X}}$$\end{document} isomorphic to X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}. We show that, for example, for a countable X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}, the poset ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb {P}, \subset\rangle}$$\end{document} is either isomorphic to a finite power of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} or forcing equivalent to a separative atomless σ-closed poset and, consistently, to P/fin. In particular, this holds for each ultrahomogeneous structure X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} such that X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} or Xc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}^{c}}$$\end{document} is a disconnected structure and in this case Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} can be replaced by an ultrahomogeneous connected digraph. (shrink)

There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that (...) commutators with a “weakly connected” component often lack the fmp. Our results imply that the above positive result does not generalize to universally axiomatizable component logics, and even commutators without “transitive” components such as [K3,K] can lack the fmp. We also generalize the above negative result to cases where one of the component logics has frames of depth one only, such as [S4.3,S5] and the decidable product logic S4.3×S5. We also show cases when already half of commutativity is enough to force infinite frames. (shrink)

Prism adaptation is a form of visuomotor training that produces both sensorimotor and cognitive aftereffects depending on the direction of the visual displacement. Recently, a neural framework explaining both types of PA-induced aftereffects has been proposed, but direct evidence for it is lacking. We employed Structural Equation Modeling, a form of effective connectivity analysis, to establish directionality among connected nodes of the brain network thought to subserve PA. The findings reveal two distinct network branches: a loop involving connections from (...) the parietal cortices to the right parahippocampal gyrus, and a branch linking the lateral premotor cortex to the parahippocampal gyrus via the cerebellum. Like the sensorimotor aftereffects, the first branch exhibited qualitatively different modulations for left versus right PA, and critically, changes in these connections were correlated with the magnitude of the sensorimotor aftereffects. Like the cognitive aftereffects, changes in the second branch were qualitatively similar for left and right PA, with greater change for left PA and a trend correlation with cognitive aftereffects. These results provide direct evidence that PA is supported by two functionally distinct subnetworks, a parietal–temporal network responsible for sensorimotor aftereffects and a fronto-cerebellar network responsible for cognitive aftereffects. (shrink)

In this paper I evaluate the ICE-theory of function ascriptions to technical artefacts as proposed by Houkes and Vermaas, 2004a and Houkes and Vermaas, 2004b. This account adds non-structural concepts to functional description of artefacts, which are typically not employed by engineers when they ascribe functions to artefacts. The aim of this paper is to analyse to what extent the ICE-theory can reproduce the engineering view that artefacts have their functions in virtue of their physicochemical structure. It is shown that (...) this theory can reproduce this engineering view for components of artefacts but not for the artefacts themselves: engineers can ascribe functions to components on the basis of only the physicochemical structure of artefacts; but when engineers ascribe functions to artefacts as a whole, they have to consider explicitly the goals for which agents use artefacts and the actions that constitute this use.Keywords: Function theory; Technical artefacts; Components; Physics and chemistry; Engineering; Action theory. (shrink)

In the Shuowen, one of the earliest comprehensive character dictionaries of ancient China, when discussing where the Chinese characters derive their structural components, Xu Shen proposed the dual constitutive principle of “adopting proximally from the human body, and distally from things around.” This dual emphasis of “body” and “things around” corresponds largely to the phenomenological issues of body or corporeality on the one hand, and lifeworld on the other. If we borrow Heidegger’s definition of Dasein as Being-in-the world, we can (...) easily arrive at a reformulation of Xu Shen’s constitutive principle of the Chinese script as one that concerns “bodily Dasein.” By looking into various examples of script tokens we can further elaborate on how the Chinese make use not only of the body in general but various body parts, and how they differentiate their life world into material nature, living things, and a multifaceted world of equipment in forming a core basis of Chinese characters/components, upon which further symbolic manipulation such as “indication”, “phonetic borrowing”, semantic combination, and “annotative derivation”, etc. can be based. Finally, examples will be cited to show how in the Chinese scripts the human body might interact with other’s bodies or with “things around” in various ways to cover the social, environmental, ritual, technical, economical, and even intellectual aspects of human experience. Bodily Dasein, so to speak, provides us with a new perspective of understanding and appreciating the entire scope of the Chinese script. (shrink)

Accounts of causal explanation are standard in philosophy of science. Less common are accounts of experimentation to investigate causal relations: detailed discussions of the specific kinds of experiments scientists design and run. Silva, Landreth, and Bickle’s account of “connection experiments” derives directly from landmark experiments in “molecular and cellular cognition.” We start with its key components, and then using a detailed case study from recent social neuroscience we emphasize and extend three features of SLB’s account: a division of distinct types (...) of connection experiments, each providing a different type of evidence for a hypothesized causal relationship; the typically downward-looking nature of the experimental search for mediating causes in mainstream neurobiology; and most importantly, the centrality of multiple-experiment research programs, with each experiment designed such that if successful its results can be integrated with the others, toward the goal of confirming multiple-phenomena causal pathways. Our extension of SLB’s account complements existing philosophical work on experimentation in neurobiology. (shrink)

This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete (...) sequent calculi for S*fde, dS*fde, crossS*fde. Among the other accomplishments of the paper, we generalize the semantics from Bochvar, Hallden, Deutsch and Daniels, we provide a general recipe to define containment logics, we explore the single-premise/single-conclusion fragment of S*fde, dS*fde, crossS*fdeand the connections between crossS*fde and the logic Eq of equality by Epstein. Also, we present S*fde as a relevant logic of meaninglessness that follows the main philosophical tenets of Goddard and Routley, and we briefly examine three further systems that are closely related to our main logics. Finally, we discuss Routley's criticism to containment logic in light of our results, and overview some open issues. (shrink)

Support functions $s(h,e)=p(h\backslash e)-p(h)$ are widely used in discussion of explanation, causality and, recently, in connection with the possibility or otherwise of probabilistic induction. With this latter application in view, a rather complete analysis of the variety of support functions, their interrelationships and their "non-deductive" and "inductive" components is presented. With the restriction to two propositions, three variable probabilities are enough to discuss such problems. The analysis is illustrated by graphs, a Venn diagram and by using the Laplace Rule of (...) Succession as an illustrative example. It is concluded that within this framework one cannot prove or disprove the possibility of probabilistic induction. (shrink)

This paper outlines the process of verbal communication of emotion as this occurs through the phases of the referential process, including arousal of an emotion schema; detailed and specific descriptions of images and episodes that are exemplars of emotion schemas; and reflection and reorganization, which may include emotion labels and other types of categorical terms. The concepts of emotion schemas and the referential process are defined in the theoretical framework of multiple code theory which includes subsymbolic sensory, visceral and motoric (...) processes, symbolic images and words. Emotion schemas are defined as clusters of representations of events incorporating similar bodily, sensory and motoric processes activated in relation to different people in different contexts. Through the referential process subsymbolic components of a schema that have been activated in a speaker or writer and that may be connected only partially to words may be evoked in a listener or reader. The concept of the emotion schemas is examined in relation to current work in emotion theory and neuroscience. The unique effects of detailed descriptions of episodes in conveying complex aspects of emotional experience are discussed, as recognized by writers, and as demonstrated in empirical research. Computerized measures of the phases of the referential process are presented, focusing particularly on the central measure, the Weighted Referential Activity Dictionary which identifies points of narrative and imagery. The operation of the function words that dominate the WRAD are examined in relation to the structure of narrative expression underlying the verbal representation of emotion schemas. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under (...) control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete (...) for dimension greater than or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes. (shrink)

This paper describes the topological aspect of a logic-based, artificial intelligence approach to formalising the qualitative description of spatial properties and relations, and reasoning about those properties and relations. This approach, known as RCC theory, has been under development for several years at the University of Leeds. The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even where quantitative spatial data (...) are most important, they must be attached to the components of a perceived spatial structure if we are to make use of them. RCC theory covers other qualitative aspects of spatial description and reasoning, but the topological properties and relations of spatially extended entities are fundamental to our work. The topological formalisms used by mathematicians are, in general, not well suited to the task of formalising the kinds of ‘common-sense’ or ‘everyday’ qualitative spatial description and reasoning which are our primary interest. Nevertheless, we must come to grips with the concepts of topology as practised by mathematicians if we are not to risk constantly ‘reinventing wheels’. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under (...) control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Based on previous studies implicating increased functional connectivity within the self-referential brain network in major depressive disorder (MDD), and considering the functional roles of three distinct modules of such brain net (responsible for three-dimensional components of Selfhood) together with the documented abnormalities of self-related processing in MDD, we tested the hypothesis that patients with depression would exhibit increased connectivity within each module of the self-referential brain network and that the strength of these connections would correlate positively with depression severity. Applying (...) the electroencephalogram (EEG) operational synchrony analysis to extract three modules of the self-referential brain network in 12 medication-free depressive outpatients and 10 control subjects we have found an increase in the strength of EEG synchrony within all three modules in depressive patients (though non-significant for the right module). Furthermore, multiple regression analysis that used 3 factors (values of synchrony strength for all three modules) as input indicated that combined increase in the strength of synchrony in all three modules was positively associated with severity of depression. Taken together the findings of this study suggest that depression is primarily associated with hypersynchrony in all three modules of the brain self-referential network (the anterior module been responsible for “witnessing observation and first–person perspective”, the left posterior module been responsible for “reflective agency and narration” and the right posterior module been responsible for “bodily representational-emotional agency”), thus contributing to excessive self-focus, rumination, and body tension. (shrink)

The standard Lewis–Stalnaker semantics of counterfactuals, given the Strong Centering Thesis, implies that all true–true counterfactuals are trivially true. McGlynn developed a theory, based on Penczek, to rehabilitate the non-triviality of true–true counterfactuals. I show here that counterfactuals with true but irrelevant components are counterexamples to McGlynn’s account. I argue that an extended version of the connection hypothesis is sustainable, and grounds a full theory of counterfactuals explicable in a broadly standard way, if an indispensable asymmetry between semifacuals and other (...) counterfactuals is acknowledged. (shrink)

This paper describes the topological aspect of a logic-based, artificial intelligence approach to formalising the qualitative description of spatial properties and relations, and reasoning about those properties and relations. This approach, known as RCC theory, has been under development for several years at the University of Leeds. The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even where quantitative spatial data (...) are most important, they must be attached to the components of a perceived spatial structure if we are to make use of them. RCC theory covers other qualitative aspects of spatial description and reasoning, but the topological properties and relations of spatially extended entities are fundamental to our work. The topological formalisms used by mathematicians are, in general, not well suited to the task of formalising the kinds of ‘common-sense’ or ‘everyday’ qualitative spatial description and reasoning which are our primary interest. Nevertheless, we must come to grips with the concepts of topology as practised by mathematicians if we are not to risk constantly ‘reinventing wheels’. (shrink)

The author presents a version of the ontological scheme of Newton’s mechanistic worldview based on both the study of previous versions of its understanding and the text of the “Mathematical Principles of Natural Philosophy”. Newton developed a model of new universality or a homogeneous and isotropic world in which uniform laws operate. This model is based on several ontological postulates Newton introduced, which can be isolated from several provisions of his classic work. The new mechanistic worldview is based on the (...) imputation of the world of universal simplicity. The quantitative “unit” of a simple, homogeneous, physical-geometric universe is an ambivalent corpuscle-point. The main constants of the “mechanistic universe” are the diversity of the numbers of masses, motions, and forces connected by clear reciprocal relationships. Newton also introduced theoretical space and time as a privileged, absolute reference system. Finally, in the Newtonian version of the mechanistic worldview, there are compelled metaphysical ingredients or inexplicable and transcendental qualities. They are gravity, ether, and God. Thus, the ontological scheme of Newton’s mechanistic worldview is a construction based on the sequential mental experiment of presenting the universe exclusively from the side of its “objectivity” and “sensory certification”. (shrink)

One of the most prominent ethical concerns regarding emerging neurotechnologies is mental privacy. This is the idea that we should have control over access to our neural data and to the information about our mental processes and states that can be obtained by analyzing it. A key issue is whether this information needs more stringent protection than other kinds of personal information. I will articulate and support the view, underlying recent regulatory frameworks, that mental privacy requires a special treatment because (...) of its relation to relevant aspects of personal identity. It has been suggested that this approach could be supported by the idea that mental privacy constitutes a fundamental psychological dimension of privacy. The connection between this psychological view of privacy and identity can be traced back to Irwin Altman’s idea that privacy is an interpersonal boundary regulation process. However, it is not clear whether this notion of privacy can be associated with a conception of identity that is relevant in contemporary neuroethics. I will suggest that the narrative and relational approach to identity, a prominent view in recent ethical discussions of neurotechnology, lines up with key aspects of Altman’s proposal. I suggest that if mental privacy is an essential component of identity, the latter could be affected by technological mind-reading. (shrink)

Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called E-connection approach for combining modal logics to (...) an algebraic setting. (shrink)

We introduce and study the model-theoretic notions of absolute connectedness and type-absolute connectedness for groups. We prove that groups of rational points of split semisimple linear groups (that is, Chevalley groups) over arbitrary infinite fields are absolutely connected and characterize connected Lie groups which are type-absolutely connected. We prove that the class of type-absolutely connected group is exactly the class of discretely topologized groups with the trivial Bohr compactification, that is, the class of minimally almost periodic (...) groups. (shrink)

Abstract. The American dream of the “self-made man” is as central to the functioning of our capitalist society as Wall Street and as familiar as the Statue of Liberty. According to this dream, the tired masses have a shot at making it on their own if they have the will power, stamina, and intestinal fortitude to survive and compete. What do we do now that we are faced with scientific evidence that this very strategy is driving society into disconnection, despair, (...) and even poor health? Relational-cultural theory states that growth happens through and toward relationships not toward increased separation and autonomy. Relational-cultural theory describes empathy and mutuality as key components to healthy relationships. This essay will focus on the latest research in the neuroscience of relationships—the development of the capacity to connect within relationships, the systems that help us read and empathize with others, the adaptability and plasticity of the central nervous system, and the destructive nature of isolation. (shrink)

In previous published research (“Conditionals and Inferential Connections: A Hypothetical Inferential Theory,” Cognitive Psychology, 2018), we investigated experimentally what role the presence and strength of an inferential connection between a conditional’s antecedent and consequent plays in how people process that conditional. Our analysis showed the strength of that connection to be strongly predictive of whether participants evaluated the conditional as true, false, or neither true nor false. In this article, we re-analyse the data from our previous research, now focussing on (...) the semantics of conditionals rather than on how they are processed. Specifically, we use those data to compare the main extant semantics with each other and with inferentialism, a semantics according to which the truth of a conditional requires the presence of an inferential connection between the conditional’s component parts. (shrink)

Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a (...) better understanding of what are the common properties of any two constructors, say disjunction and conjunction. (shrink)

We investigate the partial orderings of the form 〈P(X),⊂〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}(\mathbb{X}), \subset \rangle}$$\end{document}, where X=〈X,ρ〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X} =\langle X, \rho \rangle }$$\end{document} is a countable binary relational structure and P(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} (\mathbb{X})}$$\end{document} the set of the domains of its isomorphic substructures and show that if the components of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} (...) are maximally embeddable and satisfy an additional condition related to connectivity, then the poset 〈P(X),⊂〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P} (\mathbb{X}), \subset \rangle }$$\end{document} is forcing equivalent to a finite power of (P(ω)/ Fin)+, or to the poset (P(ω × ω)/(fin × Fin))+, or to the product (P(Δ)/EDfin)+×((P(ω)/Fin)+)n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(P(\Delta )/\fancyscript{e}\fancyscript{d}_{\rm fin})^+ \times ((P(\omega )/{\rm Fin})^+)^n}$$\end{document}, for some n∈ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \in \omega}$$\end{document}. In particular we obtain forcing equivalents of the posets of copies of countable equivalence relations, disconnected ultrahomogeneous graphs and some partial orderings. (shrink)

Background and Objective: Understanding how trauma impacts the self-structure of individuals suffering from the Post-Traumatic Stress Disorder (PTSD) symptoms is a complex matter and despite several attempts to explain the relationship between trauma and the “Self”, this issue still lacks clarity. Therefore, adopting a new theoretical perspective may help understand PTSD deeper and to shed light on the underlying psychophysiological mechanisms. Methods: In this study, we employed the “three-dimensional construct model of the experiential selfhood” where three major components of selfhood (...) (phenomenal first-person agency, embodiment, and reflection/narration) are related to three Operational Modules (OMs) of the self-referential brain network. These modules can be reliably estimated through operational synchrony analysis of the Electroencephalogram (EEG). Six individuals with PTSD symptoms and twenty-nine sex-, age- and demographic- (race, education, marital status) matched healthy controls underwent resting state EEG signal acquisition with the following estimation of the synchrony strength within every OM. Results: Our results indicate that subjects with PTSD symptoms had significantly stronger EEG operational synchrony within anterior and right posterior OMs as well as significantly weaker EEG operational synchrony within left posterior OM compared to healthy controls. Moreover, increased the functional integrity of the anterior OM was positively associated with hyperactivity symptoms, reduced synchrony of the left posterior OM was associated with greater avoidance, and increased right posterior OM integrity was positively correlated with intrusion and mood symptoms. Conclusion: The results are interpreted in light of the triad model of selfhood and its theoretical and clinical implications (including a new treatment approach) are discussed. (shrink)

Timothy Williamson has presented several arguments that seek to cast doubt on the idea that cognition can be factorized into internal and external components. In the first section of this paper, I attempt to evaluate these arguments. My conclusion will be that these arguments establish several highly important points, but in the end these arguments fail to cast any doubt either on the idea that cognitive science should be largely concerned with internal mental processes, or on the idea that cognition (...) can be analysed in terms of the existence of a suitable connection between internal and external components. I shall present an argument for the conclusion that cognition involves certain causal processes that are entirely internal. (shrink)

We present a graduate science ethics course that connects cases from the historical record to present realities and practices in the areas of social responsibility, authorship, and human/animal experimentation. This content is delivered with mixed methods, including films, debates, blogging, and practicum; even the instructional team is mixed, including a historian of science and a research scientist. What really unites all of the course’s components is the experiential aspect: from acting in historical debates to participating in the current scientific enterprise. (...) The course aims to change the students’ culture into one deeply devoted to the science ethics cause. To measure the sought after cultural change, we developed and validated a relevant questionnaire. Results of this questionnaire from students who took the course, demonstrate that the course had the intended effect on them. Furthermore, results of this questionnaire from controls indicate the need for cultural change in that cohort. All these quantitative results are reinforced by qualitative outcomes. (shrink)

This paper focuses on the inferential configuration of arguments, generally referred to as argument scheme. After outlining our approach, denominated Argumentum Model of Topics (AMT, see Rigotti and Greco Morasso 2006, 2009; Rigotti 2006, 2008, 2009), we compare it to other modern and contemporary approaches, to eventually illustrate some advantages offered by it. In spite of the evident connection with the tradition of topics, emerging also from AMT’s denomination, its involvement in the contemporary dialogue on argument schemes should not be (...) overlooked. The model builds in particular on the theoretical and methodological perspective of pragma-dialectics in its extended version, reconciling dialectic and rhetoric; nevertheless, it also takes into account numerous other contributions to the study of argument schemes. Aiming at a representation of argument schemes able to monitor the inferential cohesion and completeness of arguments, AMT focuses on two components of argument scheme that could be distinguished, readapting pragma-dialectical terms, as procedural and material respectively. The procedural component is based on the semantic-ontological structure, which generates the inferential connection from which the logical form of the argument is derived. The material component integrates into the argument scheme the implicit and explicit premises bound to the contextual common ground (Rigotti 2006). In this paper, the comparison of the AMT to other approaches focuses on the inferential configuration of arguments and not on the typologies of argument schemes and on the principles they are based on, which the authors intend to tackle in a further paper. (shrink)

In recent years, scholars have increasingly dedicated their attention to analyse and reflect on the topic of leadership. However, the debate has often focused on the figure of the leader, as if being a leader were a self-sufficient function in itself, understood without finalities or independent of them. I would argue that leadership is not a position that can be assumed, but, rather, a relationship that is constructed. Similarly, the question of leaders has often given rise to a deconstruction of (...) its components, without any insight as to how the reality is put together. Leadership cannot be understood solely from a technical or instrumental perspective. It is not a mere relational skill that simply requires developing competencies. The exercise of leadership always includes—explicitly or implicitly—a connection with values. Therefore, developing leadership is impossible without a personal process that develops the person’s capacity for perception, learning, interiorisation, explicit sense-making and constructing meaning. These issues are truly important at a time in which the debate on business education and its contribution is completely open, targeting the very core of business education’s reason for being. Though open, the debate can only become a truly dynamic discussion if there is a real dialogue between the different positions and traditions. For this reason, this paper proposes an anthropological and non-denominational reading of some of the fundamental meditations found in the Spiritual Exercises of Saint Ignatius which could be used as a heuristic in the debate regarding what business schools propose. This paper represents an initial step in this direction, exploring some of the potentialities of the Spiritual Exercises for business schools that do not claim any religious tradition. (shrink)

Objectives: Recent fMRI studies have shown that it is possible to reliably identify the defaultmode network (DMN) in the absence of any task, by resting-state connectivity analyses in healthy volunteers. We here aimed to identify the DMN in the challenging patient population of disorders of consciousness encountered following coma. Experimental design: A spatial independent component analysis-based methodology permitted DMN assessment, decomposing connectivity in all its different sources either neuronal or artifactual. Three different selection criteria were introduced assessing anticorrelation-corrected connectivity (...) with or without an automatic masking procedure and calculating connectivity scores encompassing both spatial and temporal properties. These three methods were validated on 10 healthy controls and applied to an independent group of 8 healthy controls and 11 severely brain-damaged patients [locked-in syndrome (n ¼ 2), minimally conscious (n ¼ 1), and vegetative state (n ¼ 8)]. Principal observations: All vegetative patients showed fewer connections in the default-mode areas, when compared with controls, contrary to locked-in patients who showed nearnormal connectivity. In the minimally conscious-state patient, only the two selection criteria considering both spatial and temporal properties were able to identify an intact right lateralized BOLD connectivity pattern, and metabolic PET data suggested its neuronal origin. Conclusions: When assess-. (shrink)

This two-volume work, first published in 1843, was John Stuart Mill's first major book. It reinvented the modern study of logic and laid the foundations for his later work in the areas of political economy, women's rights and representative government. In clear, systematic prose, Mill (1806–73) disentangles syllogistic logic from its origins in Aristotle and scholasticism and grounds it instead in processes of inductive reasoning. An important attempt at integrating empiricism within a more general theory of human knowledge, the work (...) constitutes essential reading for anyone seeking a full understanding of Mill's thought. Volume 1 contains Mill's introduction, which elaborates upon his definition of logic as 'not the science of Belief, but the science of Proof, or Evidence'. It also features discussions of the central components of logical reasoning - propositions and syllogisms - in relation to Mill's theories of inductive reasoning and experimental method. (shrink)

I explored the association between components constituting the basis for moral and optimal human functioning, i.e., moral reasoning, moral identity, empathy, and purpose, via network analysis. I employed factor scores instead of composite scores that most previous studies used for better accuracy in score estimation in this study. Then, I estimated the network structure among collected variables and centrality indicators. For additional information, the structure and indicators were compared between two groups, participants who engaged in civic activities highly versus lowly. (...) The results demonstrated significant intra- and inter-scale associations in the network. The network structure was invariant across the two groups. Despite the network invariance, I found that the global connectivity between and centrality indicators of examined factors were higher among the high civic engagement group in general. I discussed the implications of the findings in research on moral functioning based on moral psychology and virtue ethics. (shrink)

The meaning of a formula built out of proof-functional connectives depends in an essential way upon the intensional aspect of the proofs of the component subformulas. We study three such connectives, strong equivalence (where the two directions of the equivalence are established by mutually inverse maps), strong conjunction (where the two components of the conjunction are established by the same proof) and relevant implication (where the implication is established by an identity map). For each of these connectives we give (...) a type assignment system, a realizability semantics, and a completeness theorem. This form of completeness implies the semantic completeness of the type assignment system. (shrink)

The article is devoted to the formation of linguistic, communicative and cultural competence among students bilinguals in teaching Russian language and speech culture. The authors put forward the thesis that the training of specialists in the conditions of bilingualism re quires not only a higher level of learning a second language, but also a qualitatively different level of comprehension. It is proved that the discipline ‘Russian and the culture of speech‘ assumes formation of communicative and culturological competence of the higher (...) education institutions, which are trained on two-profile offices taking into account a regional component. Relevance of research in this area is increasing each year since the treatment of the person as the center of all systems of cognition highlights in the pedagogical University the formation of the modern language personality, capable of effective professional activity. The functional approach provides detection of features of functioning of language units in different spheres of public work. The communicative principle means that acquisition of Russian as a means of communication happens in the course of speech practice most approached to process of communication in Russian. The detection of similarity and distinctions between languages, interlingual comparison promotes establishment and a lexical interference. The linguistic-cultural principle provides understanding of language as the phenomena of culture and is connected with ability to define national-cultural components of linguistic units - words, phraseological combinations, grammatical categories of the text. Involvement of regional component as a basis in practice of teaching Russian and culture of speech increases efficiency of all process of training of students of national branch. (shrink)

Joint Analysis of EEG and fMRI datasets can bring new insight into brain mechanisms. In this paper, we employed the recently introduced Correlated Coupled Tensor Matrix Factorization (CCMTF) method for analysis of the emotion regulation paradigm based on EEG frontal asymmetry neurofeedback in the alpha frequency band with simultaneous fMRI. CCMTF method assumes that the co-variations of the common dimension (temporal dimension) between EEG and fMRI are correlated and not necessarily identical. The results of the CCMTF method suggested that EEG (...) and fMRI had similar covariations during the transition of brain activities from resting states to task (view and upregulation) states and these covariations followed an increasing trend. The fMRI shared spatial component showed activations in the limbic system, DLPFC, OFC, and VLPC regions, which were consistent with the previous studies and were linked to EEG frequency patterns in the range of 1–15 Hz with a correlation value close to 0.75. The estimated regions from the CCMTF method were then used as the candidate nodes for dynamic functional connectivity (dFC) analysis, in which the changes in connectivity from view to upregulation states were examined. The results of the dFC analysis were compared with a Normalized Mutual information (NMI) based approach in two different frequency ranges (1–15 and 15–40 Hz) as the NMI method was applied to the vectors of dFC nodes of EEG and fMRI data. The results of the two methods illustrated that the relation between EEG and fMRI datasets was mostly in the frequency range of 1–15 Hz. These relations were both in the brain activations and the dFCs between the two modalities. This paper suggests that the CCMTF method is a capable approach for extracting the shared information between EEG and fMRI data and can reveal new information about brain functions and their connectivity without solving the EEG inverse problem or analyzing different frequency bands. (shrink)

A few years ago no one would have suspected that the well‐known disorder of connective tissue, Marfan syndrome, could be caused by mutations in a recently discovered extracellular component, fibrillin. Likewise, nobody would have predicted that fibrillin represents a small family of proteins that are associated with several pheno‐typically overlapping disorders. The fibrillins are integral constituents of the non‐collagenous microfibrils, with an average diameter of 10 nm. These aggregates are distributed in the extracellular matrix of virtually every tissue. Microfibrillar (...) bundles provide the external coating to elastin in elastic fibers, and serve an anchoring function in non‐elastic tissues. At higher resolution, individual microfibrils have a “beads‐on‐a‐string” appearance resulting from the head‐to‐tail polymerization of multiple fibrillin aggregates. Structurally, fibrillin contains a series of repeated sequences homologous to the epidermal growth factor calcium‐binding motif. Characterization of fibrillin mutations in Marfan syndrome patients, together with the elucidation of the structure of the fibrillin proteins, have provided new insights, and raised new questions, about the function of the 10 nm microfibrils. For example, it is possible that the fibrillins, in addition to serving a structural function, might also be involved in regulating cellular activities and morphogenetic programs. It is fitting that the long search for the Marfan syndrome gene has brought a novel group of proteins to the forefront of extracellular matrix biology. (shrink)

Students often have difficulty connecting theoretical and text-based scholarship to the real world. When teaching in Asia, this disconnection is exacerbated by the European/American focus of many canonical texts, whereas students' own experiences are primarily Asian. However, in my discipline of political philosophy, this problem receives little recognition nor is it comprehensively addressed. In this paper, I propose that the problem must be taken seriously, and I share my own experiences with a novel pedagogical strategy which might offer a possible (...) path forward. Recent scholarship has championed an active learning approach, where students engage in their own research, and deliver outward-facing products that have a meaning and purpose beyond the confines of the student-professor relationship. In this spirit, I have put into practice a strategy of course design, where active learning is used to overcome students' disconnection with the course content. In particular, as a major component of course assessment, students are required to write an 'opinion piece', which is then showcased on a public website. The opinion piece must address a real-world issue which the student himself or herself selects and deems important; furthermore, it must build on the theoretical tools of the course and be written in a style which makes it accessible to a wider audience. I discuss the implementation of this strategy in two political philosophy courses, including strategies to avoid 'dumbing down' and ‘diluting’ the process of critical thinking. While no formal analysis of impact of the strategy on learning outcomes has been conducted, an anonymous pedagogical survey has yielded an overwhelmingly positive response for students' self-reported perceptions of the curricular innovations. (shrink)

Background: Electroconvulsive therapy is one of the most effective treatments for major depressive disorder. Recently, there has been increasing attention to evaluate the effect of ECT on resting-state functional magnetic resonance imaging. This study aims to compare rs-fMRI of depressive disorder patients with healthy participants, investigate whether pre-ECT dynamic functional network connectivity network estimated from patients rs-fMRI is associated with an eventual ECT outcome, and explore the effect of ECT on brain network states.Method: Resting-state functional magnetic resonance imaging data were (...) collected from 119 patients with depression or depressive disorder, and 61 healthy participants, with an age mean of 52.25 years old. The pre-ECT and post-ECT Hamilton Depression Rating Scale were 25.59 ± 6.14 and 11.48 ± 9.07, respectively. Twenty-four independent components from default mode and cognitive control network were extracted, using group-independent component analysis from pre-ECT and post-ECT rs-fMRI. Then, the sliding window approach was used to estimate the pre-and post-ECT dFNC of each subject. Next, k-means clustering was separately applied to pre-ECT dFNC and post-ECT dFNC to assess three distinct states from each participant. We calculated the amount of time each subject spends in each state, which is called “occupancy rate” or OCR. Next, we compared OCR values between HC and DEP participants. We also calculated the partial correlation between pre-ECT OCRs and HDRS change while controlling for age, gender, and site. Finally, we evaluated the effectiveness of ECT by comparing pre- and post-ECT OCR of DEP and HC participants.Results: The main findings include depressive disorder patients had significantly lower OCR values than the HC group in state 2, where connectivity between cognitive control network and default mode network was relatively higher than other states, Pre-ECT OCR of state, with more negative connectivity between CCN and DMN components, is linked with the HDRS changes. This means that those DEP patients who spent less time in this state showed more HDRS change, and The post-ECT OCR analysis suggested that ECT increased the amount of time DEP patients spent in state 2.Conclusion: Our finding suggests that dynamic functional network connectivity features, estimated from CCN and DMN, show promise as a predictive biomarker of the ECT outcome of DEP patients. Also, this study identifies a possible underlying mechanism associated with the ECT effect on DEP patients. (shrink)

For five individuals, a social network was constructed from a series of his or her dreams. Three important network measures were calculated for each network: transitivity, assortativity, and giant component proportion. These were monotonically related; over the five networks as transitivity increased, assortativity increased and giant component proportion decreased. The relations indicate that characters appear in dreams systematically. Systematicity likely arises from the dreamer's memory of people and their relations, which is from the dreamer's cognitive social network. But (...) the dream social network is not a copy of the cognitive social network. Waking life social networks tend to have positive assortativity; that is, people tend to be connected to others with similar connectivity. Instead, in our sample of dream social networks assortativity is more often negative or near 0, as in online social networks. We show that if characters appear via a random walk, negative assortativity can result, particularly if the random walk is biased as suggested by remote associations. (shrink)

Regularization may be used as an alternative to dimensionality reduction when the number of variables in a model is much larger than the number of available observations. In a recent study from our group regularized regression was employed to quantify brain functional connectivity in a sample of healthy controls using a brain parcellation and resting state fMRI images. Here regularization is applied to evaluate resting state connectivity abnormalities at the voxel level in a sample of patients with schizophrenia. Specifically, ridge (...) regression is implemented with different degrees of regularization. Results are compared to those delivered by the weighted global brain connectivity method, which is based on averaged bivariate correlations and from the non-redundant connectivity method, a dimensionality reduction approach that applies supervised principal component regressions. Ridge regression is able to detect a larger set of abnormally connected regions than both GBC and NRC methods, including schizophrenia related connectivity reductions in fronto-medial, somatosensory and occipital structures. Due to its multivariate nature, the proposed method is much more sensitive to group abnormalities than the GBC, but it also outperforms the NRC, which is multivariate too. Voxel based regularized regression is a simple and sensitive alternative for quantifying brain functional connectivity. (shrink)

WORDNET, a ubiquitous tool for natural language processing, suffers from sparsity of connections between its component concepts (synsets). Through the use of human annotators, a subset of the connections between 1000 hand-chosen synsets was assigned a value of “evocation” representing how much the first concept brings to mind the second. These data, along with existing similarity measures, constitute the basis of a method for predicting evocation between previously unrated pairs.

Awareness of internal bodily sensations and its connection to complex socioemotional abilities like empathy has been postulated, yet the functional neural circuitry they share remains poorly understood. The present fMRI study employs independent component analysis to investigate which empathy facet shares resting-state functional connectivity and/or BOLD variability with IA. Healthy participants viewed an abstract nonsocial movie demonstrated to evoke strong rsFC in brain networks resembling rest, and resultant rsFC and rsBOLD data were correlated with self-reported empathy and IA questionnaires. (...) We demonstrate a bidirectional behavioral and neurobiological relationship between empathy and IA, depending on the type of empathy interrogated: Affective empathy and IA share both rsFC and rsBOLD, while Cognitive empathy and IA only share rsBOLD. Specifically, increased rsFC in the right inferior frontal operculum of a larger attention network was associated with increased vicarious experience but decreased awareness of inner body sensations. Furthermore, increased rsBOLD between brain regions of an interoceptive network was related to increased sensitivity to internal sensations along with decreased Affective empathy. Finally, increased rsBOLD between brain regions subserving a mentalizing network related to not only an improved ability to take someone’s perspective, but also a better sense of mind-body interconnectedness. Overall, these findings suggest that the awareness of one’s own internal body changes is related to the socioemotional ability of feeling and understanding another’s emotional state and critically, that this relationship is reflected in the brain’s resting state neuroarchitecture. Methodologically, this work highlights the importance of utilizing rsBOLD as a complementary window alongside rsFC to better understand neurological phenomena. Our results may be beneficial in aiding diagnosis in clinical populations such as autism spectrum disorder, where participants may be unable to complete tasks or questionnaires due to the severity of their symptoms. (shrink)

An important problem for decision-makers in society deals with the efficient and equitable allocation of scarce resources to individuals and groups. The significance of this problem is rapidly growing since there is a rising demand for scarce resources all over the world. Such resource dilemmas belong to a conceptually broader class of situations known as social dilemmas. In this type of dilemma, individual choices that appear ‘‘rational’’ often result in suboptimal group outcomes. In this article we study how people make (...) monetary allocation decisions between the community where they live and a neighbouring community, with the aim of finding out to what extent these decisions are subject to biased over-weighting. The manuscript reports four experiments that deal with the way individuals make such allocation decisions when the potential beneficiaries are such communities. The specific goal of these experiments is to gauge the amount of bias in the weights that people assign to the various beneficiaries. Taken together, the results from all the four experiments suggest that making the gain of the neighbouring community prominent to a higher extent de-biases the outcomes (the prominence effect) compared to when own community gain is made prominent. Place identity is discussed as a potentially important factor in this connection. Hence, it may be argued that there seems to be some kind of a pro-self component that is able to explain a large part of the variance observed for the prominence effect. Connections between such a factor and in-group favouritism are discussed. A strength of the study was that these major results appeared to be quite robust when considered as task effects, as the salience of the manipulated context factors in the studies (in terms of reliable main or interaction effects) did not distort them. (shrink)

Working in stochastic spin space and using POV measures as in the Davies and Lewis measurement scheme, we construct a formalism to describe the simultaneous measurement of incompatible spin components. The methods are illustrated with a new analysis of the Stern-Gerlach experiment, and with a discussion of spin dynamics in stochastic spin space. We also present a new short proof of a theorem on representations of spin-1/2 systems, find a joint spectral family for (noncommuting) spin components, and indicate the connection (...) of our result with the Riesz extension theorem. (shrink)

Understanding arithmetic word problems involves a complex interaction of text comprehension and mathematical processes. This article presents a computer simulation designed to capture the working memory demands required in “bottomup” comprehension of arithmetic word problems. The simulation's sentence‐level parser and text integration component reflect the importance of processing the problem from its original natural language presentation. Children's probability of solution was analyzed in exploratory regression analyses as a function of the simulation's sentence‐level and text integration processes. Working memory variables (...) measuring the combined effects of concepts to remember and text integration inferences account for a significant proportion of variance in children's solution probabilities across the first four grade levels (K‐3). Consistent with previous results from others, which highlighted the significance of small changes in problem wording, the simulation offers a process‐oriented perspective as to why natural language presentation constrains the comprehension of mathematical relationships. (shrink)