A Theory of Magnitude suggests that space, time, and quantities are processed through a generalized magnitude system. ATOM posits that task-irrelevant magnitudes interfere with the processing of task-relevant magnitudes as all the magnitudes are processed by a common system. Many behavioral and neuroimaging studies have found support in favor of a common magnitude processing system. However, it is largely unknown whether such cross-domain monotonic mapping arises from a change in the accuracy of the magnitude judgments or results from changes in (...) precision of the processing of magnitude. Therefore, in the present study, we examined whether large numerical magnitude affects temporal accuracy or temporal precision, or both. In other words, whether numerical magnitudes change our temporal experience or simply bias duration judgments. The temporal discrimination paradigm was used to present numerical magnitudes across varied durations. We estimated temporal accuracy and precision for each numerical magnitude. The results revealed that temporal accuracy for large numerical magnitude was significantly lower than that of small and identical magnitudes. This implies that the temporal duration was overestimated for large numerical magnitude compared to small and identical numerical magnitude, in line with ATOM’s prediction. However, no influence of numerical magnitude was observed on temporal precision. The findings of the present study suggest that task-irrelevant numerical magnitude selectively affects the accuracy of processing of duration but not duration discrimination itself. Further, we argue that numerical magnitude may not directly affect temporal processing but could influence via attentional mechanisms. (shrink)

Several canonical experimental paradigms have been proposed to study the typical behavioral phenomenon and the nature of learning in sequential keypress tasks. A characteristic feature of most paradigms is that they are representative of externally-specified sequencing—motor tasks where the environment or task paradigm extrinsically provides the sequence of stimuli, i.e., the responses are stimulus-driven. Previous studies utilizing such canonical paradigms have largely overlooked the learning behaviors in a more realistic class of motor tasks that involve internally-guided sequencing—where the sequence of (...) motor actions is self-generated or internally-specified. In this work, we use the grid-navigation task as an instance of internally-guided sequencing to investigate the nature of learning in such paradigms. The participants performed Grid-Sailing Task, which required navigating a 5 × 5 grid from start to goal position while using a particular key-mapping among the three cursor-movement directions and the three keyboard buttons. The participants performed two behavioral experiments—Single-SG and Mixed-SG condition. The Single-SG condition required performing GST on a single SG position repeatedly, whereas the Mixed-SG condition involved performing GST using the same KM on two novel SG positions presented in a random, inter-mixed manner. In the Single-SG condition, we show that motor learning contributes to the sequence-specific learning in GST with the repeated execution of the same trajectories. In the Mixed-SG condition, since the participants utilize the previously learned KM, we anticipate a transfer of learning from the Single-SG condition. The acquisition and transfer of a KM-specific internal model facilitates efficient trajectory planning on novel SG conditions. The acquisition of such a KM-specific internal model amounts to trajectory-independent cognitive learning in GST. We show that cognitive learning contributes to the learning in GST by showing transfer-related performance improvements in the Mixed-SG condition. In sum, we show the role of cognitive and motor learning processes in internally-guided sequencing and further make a case for using GST-like grid-navigation paradigms in investigating internally guided skill learning. (shrink)

Hastings Center Report, Volume 51, Issue 5, Page 53-55, September‐October 2021.

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

We investigate model theoretic characterisations of the expressive power of modal logics in terms of bisimulation invariance. The paradigmatic result of this kind is van Benthem’s theorem, which says that a first-order formula is invariant under bisimulation if, and only if, it is equivalent to a formula of basic modal logic. The present investigation primarily concerns ramifications for specific classes of structures. We study in particular model classes defined through conditions on the underlying frames, with a focus on frame classes (...) that play a major role in modal correspondence theory and often correspond to typical application domains of modal logics. Classical model theoretic arguments do not apply to many of the most interesting classes–for instance, rooted frames, finite rooted frames, finite transitive frames, well-founded transitive frames, finite equivalence frames–as these are not elementary. Instead we develop and extend the game-based analysis over such classes and provide bisimulation preserving model constructions within these classes. Over most of the classes considered, we obtain finite model theory analogues of the classically expected characterisations, with new proofs also for the classical setting. The class of transitive frames is a notable exception, with a marked difference between the classical and the finite model theory of bisimulation invariant first-order properties. Over the class of all finite transitive frames in particular, we find that monadic second-order logic is no more expressive than first-order as far as bisimulation invariant properties are concerned — though both are more expressive here than basic modal logic. We obtain ramifications of the de Jongh–Sambin theorem and a new and specific analogue of the Janin–Walukiewicz characterisation of bisimulation invariant monadic second-order for finite transitive frames. (shrink)

We consider fixed point logics, i.e., extensions of first order predicate logic with operators defining fixed points. A number of such operators, generalizing inductive definitions, have been studied in the context of finite model theory, including nondeterministic and alternating operators. We review results established in finite model theory, and also consider the expressive power of the resulting logics on infinite structures. In particular, we establish the relationship between inflationary and nondeterministic fixed point logics and second order logic, and we consider (...) questions related to the determinacy of games associated with alternating fixed points. (shrink)

articles like Anubhava, Jnana Karma Sammucyavada, Trsna and Viksepa contributed.

We consider Choiceless Polynomial Time , a language introduced by Blass, Gurevich and Shelah, and show that it can express a query originally constructed by Cai, Fürer and Immerman to separate fixed-point logic with counting from image. This settles a question posed by Blass et al. The program we present uses sets of unbounded finite rank: we demonstrate that this is necessary by showing that the query cannot be computed by any program that has a constant bound on the rank (...) of sets used, even in image, an extension of image with counting. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first-order definable over the class of finite directed graphs and that this class admits a first-order definable global linear order. We apply this last result to show that FO = FO.

We sketch out two basic paradigms informing banking practice: the economistic paradigm focusing on profit maximization and the humanistic one, serving the common good. We then highlight paradigmatic cases to explore how each of these business models fared during the quasi-natural experiment of the financial crisis. We find that many humanistic banks outperformed traditional economistic banks. Despite the uneven playing field humanistic banks fared remarkably well with regard to traditional financial performance judgements, muting criticisms of competitiveness. We find that overall (...) both paradigms can provide a basis for successful banking as long as social and financial value generation are blended. We conclude by providing lessons learned for better banking. (shrink)

We consider the problem of obtaining logical characterisations of oracle complexity classes. In particular, we consider the complexity classes LOGSPACENP and PTIMENP. For these classes, characterisations are known in terms of NP computable Lindström quantifiers which hold on ordered structures. We show that these characterisations are unlikely to extend to arbitrary structures, since this would imply the collapse of certain exponential complexity hierarchies. We also observe, however, that PTIMENP can be characterised in terms of Lindström quantifers , though it remains (...) open whether this can be done for LOGSPACENP. (shrink)

This book offers the first comparative account of the changes and stabilities of public perceptions of science within the US, France, China, Japan, and across Europe over the past few decades. The contributors address the influence of cultural factors; the question of science and religion and its influence on particular developments (e.g. stem cell research); and the demarcation of science from non-science as well as issues including the incommensurability versus cognitive polyphasia and the cognitive (in)tolerance of different systems of knowledge.

Much previous work has suggested that word order preferences across languages can be explained by the dependency distance minimization constraint (Ferrer‐i Cancho, 2008, 2015; Hawkins, 1994). Consistent with this claim, corpus studies have shown that the average distance between a head (e.g., verb) and its dependent (e.g., noun) tends to be short cross‐linguistically (Ferrer‐i Cancho, 2014; Futrell, Mahowald, & Gibson, 2015; Liu, Xu, & Liang, 2017). This implies that on average languages avoid inefficient or complex structures for simpler structures. But (...) a number of studies in psycholinguistics (Konieczny, 2000; Levy & Keller, 2013; Vasishth, Suckow, Lewis, & Kern, 2010) show that the comprehension system can adapt to the typological properties of a language, for example, verb‐final order, leading to more complex structures, for example, having longer linear distance between a head and its dependent. In this paper, we conduct a corpus study for a group of 38 languages, which were either Subject–Verb–Object (SVO) or Subject–Object–Verb (SOV), in order to investigate the role of word order typology in determining syntactic complexity. We present results aggregated across all dependency types, as well as for specific verbal (objects, indirect objects, and adjuncts) and nonverbal (nominal, adjectival, and adverbial) dependencies. The results suggest that dependency distance in a language is determined by the default word order of a language, and crucially, the direction of a dependency (whether the head precedes the dependent or follows it; e.g., whether the noun precedes the verb or follows it). Particularly we show that in SOV languages (e.g., Hindi, Korean) as well as SVO languages (e.g., English, Spanish), longer linear distance (measured as number of words) between head and dependent arises in structures when they mirror the default word order of the language. In addition to showing results on linear distance, we also investigate the influence of word order typology on hierarchical distance (HD; measured as number of heads between head and dependent). The results for HD are similar to that of linear distance. At the same time, in comparison to linear distance, the influence of adaptability on HD seems less strong. In particular, the results show that most languages tend to avoid greater structural depth. Together, these results show evidence for “limited adaptability” to the default word order preferences in a language. Our results support a large body of work in the processing literature that highlights the importance of linguistic exposure and its interaction with working memory constraints in determining sentence complexity. Our results also point to the possible role of other factors such as the morphological richness of a language and a multifactor account of sentence complexity remains a promising area for future investigation. (shrink)

Much has been said about the potential of digital health technologies for democratizing health care. But how exactly is democratization with digital health technologies conceptualized and what does it involve? We investigate debates on the democratization of health care with digital health and identify that democratization is being envisioned as a matter of access to health information, health care, and patient empowerment. However, taking a closer look at the growing pool of empirical data on digital health, we argue that these (...) technologies come short of materializing these goals, given the unequal health outcomes they facilitate. Building on this evidence, we argue that not only debates on democratization need to be connected to concerns of social determinants of health but also debates on the impact of digital health need to go far beyond democratization and engage with concerns of health justice. (shrink)