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)

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)

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)

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)

We examined proactive and reactive control effects in the context of task-relevant happy, sad, and angry facial expressions on a face-word Stroop task. Participants identified the emotion expressed by a face that contained a congruent or incongruent emotional word. Proactive control effects were measured in terms of the reduction in Stroop interference as a function of previous trial emotion and previous trial congruence. Reactive control effects were measured in terms of the reduction in Stroop interference as a function of current (...) trial emotion and previous trial congruence. Previous trial negative emotions exert greater influence on proactive control than the positive emotion. Sad faces in the previous trial resulted in greater reduction in the Stroop interference for happy faces in the current trial. However, current trial angry faces showed stronger adaptation effects compared to happy faces. Thus, both proactive and reactive control mechanisms are dependent on emotional valence of task-relevant stimuli. (shrink)

Individuals across organizations and roles are increasingly seeking a meaningful and fulfilling experience in their activities. Towards that, the Bhagavad Gita advises the practice of Karma Yoga. However, the conceptualization of Karma Yoga in extant management literature is shrouded in confusion with little agreement on its dimensionalities. In this article, employing qualitative method, we offer an alternative conceptualization of the construct. Accordingly, we define Karma Yoga as a persistent positive state of mind that is characterized by absorption and service consciousness. (...) Furthermore, the findings also suggest the importance of sense control and equanimity as the necessary prerequisites for individuals to practise Karma Yoga. (shrink)

Study on the philosophy of Atharvaveda, Hindu canonical text.

Dissipative structures exist at all scales, systems, and at different levels of complexity. A thermodynamic theory integrating simple and complex DS is introduced, which addresses existence of growing/decaying DS based on their entropy analysis. Two entropy-based dimensionless ratios are introduced, which explain negentropy-debt payment and existence of DS with growth or decay. It is shown that excess negentropy debt payment is needed and beneficial for growing DS; but for decaying DS, it hastens its approach to perish and is counter-productive. Growing (...) complex DS tend to pay lower negentropy debt to their surroundings, due to involvement in other activities enabled by complexity; e.g. mediation for survival that is linked to their mortality. Hence, disorder of complex DS increases, due to which, their growth can be un-sustained, leading to entry in decay-phase in spite of availability of adequate mass-energy in-flows. Proper handling or reduction of complexity enables growth in the direction of ideal growth, which is limited only by availability of adequate mass-energy in-flows. (shrink)

The ethical principle of respect for patient autonomy is essential for balanced doctor–patient relationship. Understanding and following proper procedure for informed consent is the goal for a healthcare provider. There are clinical scenarios which are often encountered and are still challenging. In this article, those cases are described which presented dilemma at the time of obtaining informed consent and an ethical approach is described.

The Yogic literatures are replete with examples of several unique mystical experiences in deeper states of meditation. These experiences have nevertheless remained largely untouched by the scientific community, possibly because of the extreme inexplicability of such states and the lack of sophistication in evaluating them. More amenable to scientific research, however, would seem to be the simpler states of awareness in meditation such as that of inner light perception. While a few studies have attempted to explore this state by objective (...) means, the subjective experience of this state remains largely unexplored. The present study originates from an interesting sub-theme identified in an earlier study focused on interpretative phenomenological analysis (IPA) of the experience of inner light perception among Vihangam Yogis. The original study found that the Yogis were very confident in differentiating their experience of inner light perception from other similar experiences. It was thus decided to use IPA to explore the clarity of the differences perceived by the Vihangam Yogis between these experiences. The present study reveals that the meditators could clearly differentiate the state colloquially termed "inner light perception" from (a) external light perception, (b) imagination and (c) dreams. The meditators gave detailed descriptions of their perception of the differences between these experiences, which suggests that the subjective state of inner light perception could be quite different from that of those experiences which the authors have termed differentials of inner light perception. The conclusion reached is that, in addition to further empirical study by means of the traditional modalities and measures, vigorous qualitative study of the subjective dimensions of the state of inner light perception is warranted, with this study indicating that IPA is especially effective in the latter regard. (shrink)

The Yogic literatures are replete with examples of several unique mystical experiences in deeper states of meditation. These experiences have nevertheless remained largely untouched by the scientific community, possibly because of the extreme inexplicability of such states and the lack of sophistication in evaluating them. More amenable to scientific research, however, would seem to be the simpler states of awareness in meditation such as that of inner light perception. While a few studies have attempted to explore this state by objective (...) means, the subjective experience of this state remains largely unexplored. The present study originates from an interesting sub-theme identified in an earlier study focused on interpretative phenomenological analysis of the experience of inner light perception among Vihangam Yogis. The original study found that the Yogis were very confident in differentiating their experience of inner light perception from other similar experiences. It was thus decided to use IPA to explore the clarity of the differences perceived by the Vihangam Yogis between these experiences. The present study reveals that the meditators could clearly differentiate the state colloquially termed “inner light perception” from external light perception, imagination and dreams. The meditators gave detailed descriptions of their perception of the differences between these experiences, which suggests that the subjective state of inner light perception could be quite different from that of those experiences which the authors have termed differentials of inner light perception. The conclusion reached is that, in addition to further empirical study by means of the traditional modalities and measures, vigorous qualitative study of the subjective dimensions of the state of inner light perception is warranted, with this study indicating that IPA is especially effective in the latter regard. (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)

While human rights law has evolved to provide guidance to governments in realizing human rights in public health emergencies, the COVID-19 pandemic has challenged the foundations of human rights in global health governance. Public health responses to the pandemic have undermined international human rights obligations to realize the rights to health and life, human rights that underlie public health, and international assistance and cooperation. As governments prepare for revisions of global health law, new opportunities are presented to harmonize global health (...) law and human rights law, strengthening rights-based governance to respond to future threats. (shrink)