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 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)

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 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)

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)

Bangladesh continues to experience stubbornly high levels of rural malnutrition amid steady economic growth and poverty reduction. The policy response to tackling malnutrition shows an overwhelmingly technocratic bias, which depoliticizes the broader question of how the agro-food regime is structured. Taking an agrarian and human rights-based approach, this paper argues that rural malnutrition must be analyzed as symptomatic of a deepening agrarian crisis in which the obsession with productivity increases and commercialization overrides people’s democratic right to culturally appropriate, good, nutritious (...) food. Using qualitative insights from a case study of three villages, this research illustrates how agricultural modernization and commercialization reproduce rural malnutrition by degrading local biodiversity and the rural poor’s access to nutrient-rich diets. In so doing, it undermines the official discourse’s simplistic and literal reading of malnutrition as a pathological health condition resulting from the mere absence of certain micronutrients in the human body, and thus questions the adequacy of the proposed solutions. Instead, this research suggests that solving malnutrition in large part involves facilitating the rural poor’s access to nutritious diets through democratizing and reorganizing the agriculture sector in a manner that is eco-friendly and unconstrained by market imperatives. It cautiously advances agroecology and food sovereignty as possible alternatives, while recognizing that overcoming the challenges agrarian class conflict, gender disparity and urban–rural divide pose would not be easy. (shrink)

Recent scholarship on gender and the state suggests that women's agency has been critical to the formation of welfare policy. Yet, nations with strong, mobilized feminist movements do not necessarily develop the most supportive welfare policies. By historically analyzing the emergence of British and French family allowance policy, the author suggests that the key to this conundrum lies in the interaction between women's movements and the value given to women's paid and unpaid labor. Woman-friendly state policy requires an active women's (...) movement and ideologies valuing women's paid and unpaid labor. In addition, women's movements must be able and willing to strategically use those ideologies to pursue their goals. (shrink)

Description: 'Religion is a doing and doing what is moral'. In Buddhism, particularly, there is such a great emphasis on moral doing that is very often designated as an 'ethical religion' (silaparaka dharma). The present work seeks to study Buddhist ethics as a development process not only in terms of inner dynamics of Buddhism inherent in its doctrinal and ethical formulations but also in terms of its response to various historical compulsions which motivated its followers to introduce in its general (...) framework novelties of forms and expressions. It is hoped that such an approach would lead to a greater appreciation of Buddhist ethics both as an emergent of a unique spiritual vision and a social force. The book which is divided in six chapters cover the entire range of Buddhist development in India. The work is novel both in its approach and treatment of the subject. It studies conceptual formulations in their proper historical contexts. Modern debates on various ethical problems have been taken into account to bring about greater clarity in discussions. (shrink)

The COVID-19 pandemic brought unprecedented strain on hospitals and, in particular, critical care settings. Early in the pandemic, multiple plans were developed to ration ventilators in anticipatio...

Contains eight essays by the late Professor G. Misra who was the first Indian philosopher to employ the rigorous methods of modern linguistic and logical analysis to understand the key doctrines of Advaita Ved?nta.

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)

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

This volume showcases key contemporary developments in Indian psychology. Psychology in India, being largely an Euro-American transplant, tends to be imitative. Written by eminent psychologists, teachers, young scholars, and practitioners from the field, the contributors voice the legitimate concerns of a culturally responsive psychology. The book also clearly emphasizes that contemporary research has moved beyond traditional thinking in terms of methodology, theory, and application. The chapters include discussions on conceptual foundation, methodological perspectives, perspectives on self and identity, human development and (...) social processes, health and wellbeing, and emerging concerns in the field of psychology. (shrink)

Commentary on Patañjali's Yogasūtra; includes complete text.

ABOUT THE BOOK:Sri Aurobindo has developed an original system of the Vedanta called Integral Advaitism. This book gives a systematic, thorough and authentic exposition of his thought. The fundamental and living issues, namely, the concept of the Absol.

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)

Commentary on Judith Shklar's skepticism has ranged from the claim that it was not the central characteristic of her thought to the argument that it seriously hobbled her thinking about justice. In fact Shklar's uniqueness as a thinker resides precisely in the fact that she combined a sweeping skepticism with a strong commitment to liberal justice. Skepticism interacted with her liberal moral commitments to inspire her account of injustice, without which her views about justice are impossible to grasp. Shklar's skepticism (...) produced her laser-like focus on sources of injustice and oppression for the individual, whom she perceived to be potentially threatened no less by tribe, nation, family, or a democratic citizens' community than by the state itself. It produced not only her highly original insights into the inadequacy of all existing models of justice, but also her subtle yet concerted effort to render democracy safe for liberalism in political theory while at the same make liberalism more egalitarian. (shrink)

With the end of the Cold War, political and ideological competition has decreased as a stated reason for space exploration. The possibility of establishing a settlement on Mars is being seriously evaluated by state and commercial space agencies, which includes objectives to expand human civilization and ensure the continuity of the human species. The technological challenges associated with space settlement continue to receive significant attention, but the success of space settlement will also depend on other human factors. This study presents (...) a high-level overview of some potential issues that could arise with the development of a permanent populationand a space economyon Mars. This study highlights some of the anticipated problems of overnance, trade, production, and proliferation that will need pragmatic solutions to ensure the sustainability of a martian settlement. This paper is intended to instigate further discussion and research regarding human and economic factors that could enable or constrain future settlements on Mars. (shrink)

The behavior of Lyapunov exponents λ and dynamical entropies h, whose positivity characterizes chaotic motion, under Lorentz and Rindler transformations is studied. Under Lorentz transformations, λ and h are changed, but their positivity is preserved for chaotic systems. Under Rindler transformations, λ and h are changed in such a way..

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.

This essay examines debates over alternative ethical formulations that break from the Kantian model through contemporary fiction—Kiran Desai’s The Inheritance of Loss (2006), Kazuo Ishiguro’s Never Let Me Go (2005) and Zadie Smith’s On Beauty (2005). The essay returns to the theory, the ethics of care, put forward by Carol Gilligan in In a Different Voice (1982), which has regained significance in the context of questions surrounding care in contemporary ethical thinking. While the three novels are concerned with ideas of (...) care, beauty, justice and the tyranny of the mainstream, this essay examines particular themes in particular texts which suggest that ideas with otherwise subversive potential—like care or beauty or justice—lose their radicalism when they are incorporated within the impersonal, masculinist mainstream. Carol Gilligan’s feminine ethics of care, with its respect for the particular, is not only still important as the stimulus to thinking about alternatives to overarching ethical discourses, but it could also re-confer these concepts of care, beauty and justice their revolutionary potential. (shrink)

The present paper investigates investor decision-making from a psychological standpoint and explores the role of consciousness and mindfulness on investors’ analytical ability and investment efficacy. A comprehensive survey instrument including sub-scales of different behavioural constructs is administered to 222 individual investors. We find evidence supporting the positive influence of cognitive capability on investment efficacy. The findings also suggest that mindfulness reliably mediates consciousness to cause an effect on cognitive capability. Higher cognitive capability will manifest in the form of detailed analysis (...) and interpretation of available information and improve stock selection, asset allocation, and market timing, thus increasing investment efficacy. A mindful investor can mitigate negative stimuli, emotional turmoil, dilemmas and distress in stock trading in a far more superior way to mediate consciousness for higher cognitive capability. The implications of the study indicate that consciousness and mindfulness-based interventions may facilitate making the investors stronger to manage difficult times and perform a careful rational assessment to eventually become successful investors. (shrink)