We continue the investigation of generalized Bosbach states that we began in Part I, restricting our research to the commutative case and treating further aspects related to these states. Part II is concerned with similarity convergences, continuity of states and the construction of the s-completion of a commutative residuated lattice, where s is a generalized Bosbach state.

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful (...) for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics. (shrink)

Bosbach and Riečan states on residuated lattices both are generalizations of probability measures on Boolean algebras. Just from the observation that both of them can be defined by using the canonical structure of the standard MV-algebra on the unit interval [0, 1], generalized Riečan states and two types of generalized Bosbach states on residuated lattices were recently introduced by Georgescu and Mureşan through replacing the standard MV-algebra with arbitrary residuated lattices as codomains. In the present paper, (...) the Glivenko theorem is first extended to residuated lattices with a nucleus, which gives several necessary and sufficient conditions for the underlying nucleus to be a residuated lattice homomorphism. Then it is proved that every generalized Bosbach state (of type I, or of type II) compatible with the nucleus on a nucleus-based-Glivenko residuated lattice is uniquely determined by its restriction on the nucleus image of the underlying residuated lattice, and every relatively generalized Riečan state compatible with the double relative negation on an arbitrary residuated lattice is uniquely determined by its restriction on the double relative negation image of the residuated lattice. Our results indicate that many-valued probability theory compatible with nuclei on residuated lattices reduces in essence to probability theory on algebras of fixpoints of the underlying nuclei. (shrink)

In this paper, we mainly investigate the existence of states based on the Glivenko theorem in bounded semihoops, which are building blocks for the algebraic semantics for relevant fuzzy logics. First, we extend algebraic formulations of the Glivenko theorem to bounded semihoops and give some characterizations of Glivenko semihoops and regular semihoops. The category of regular semihoops is a reflective subcategory of the category of Glivenko semihoops. Moreover, by means of the negative translation term, we characterize the Glivenko variety. Then (...) we show that the regular semihoop of regular elements of a free algebra in the variety of Glivenko semihoops is free in the corresponding variety of regular semihoops. Similar results are derived for the semihoop of dense elements of free Glivenko semihoops. Finally, we give a purely algebraic method to check the existence of states on Glivenko semihoops. In particular, we prove that a bounded semihoop has Bosbach states if and only if it has a divisible filter, and a bounded semihoop has Riečan states if and only if it has a semi-divisible filter. (shrink)

To what extent can we feel what someone else feels? Data from neuroscience suggest that empathy is supported by a simulation process, namely the neural activation of the same or similar regions that subserve the representation of specific states in the observer. However, expectations significantly modulate sensory input, including affective information. For example, expecting painful stimulation can decrease the neural signal and the subjective experience thereof. For an accurate representation of the other person’s state, such top-down processes would have (...) to be simulated as well. However, this is only partly possible, because expectations are usually acquired by learning. Therefore, it is important to be aware of possible misleading simulations that lead to misinterpretations of someone’s state. (shrink)

Here P is the density operator of the system under consideration, and σ ± and σ 3 are the usual Pauli matrices, acting on atom i whose states are |1 > or |0 >, representing, respectively, the atom being in an excited state or in the ground state. B and C are appropriate decay constants and s has been called the pumping parameter [1]. It varies from s = 0 for pure damping to s = 1 for full (...) laser action. To solve the corresponding quantum master equations, three approaches have been taken: First, one focuses on the case of one atom. Second, one truncates eq. (1) and derives semi-classical models. Third, one employs numerical simulation methods such as the quantum trajectory method. While the latter method is very popular, it should be noted that the numerical complexity of the problem increases exponentially with the number of atoms, and so numerical methods soon become unfeasible. (shrink)

The question of whether time is its own best representation is explored. Though there is theoretical debate between proponents of internal models and embedded cognition proponents (e.g. Brooks R 1991 Artificial Intelligence 47 139–59) concerning whether the world is its own best model, proponents of internal models are often content to let time be its own best representation. This happens via the time update of the model that simply allows the model’s state to evolve along with the state (...) of the modeled domain. I argue that this is neither necessary nor advisable. I show that this is not necessary by describing how internal modeling approaches can be generalized to schemes that explicitly represent time by maintaining trajectory estimates rather than state estimates. Though there are a variety of ways this could be done, I illustrate the proposal with a scheme that combines filtering, smoothing and prediction to maintain an estimate of the modeled domain’s trajectory over time. I show that letting time be its own representation is not advisable by showing how trajectory estimation schemes can provide accounts of temporal illusions, such as apparent motion, that pose serious difficulties for any scheme that lets time be its own representation. (shrink)

February 1, 2000 TABLE OF CONTENTS TABLE OF AUTHORITIES......................................................................................... .......................ii STATEMENT OF INTEREST............................................................................................ ................. v..

Explainable AI (XAI) provides methods to understand non-interpretable machine learning models. However, we have little knowledge about what legal experts expect from these explanations, including their legal compliance with, and value against European Union legislation. To close this gap, we present the Explanation Dialogues, an expert focus study to uncover the expectations, reasoning, and understanding of legal experts and practitioners towards XAI, with a specific focus on the European General Data Protection Regulation. The study consists of an online questionnaire and (...) follow-up interviews, and is centered around a use-case in the credit domain. We extract both a set of hierarchical and interconnected codes using grounded theory, and present the standpoints of the participating experts towards XAI. We find that the presented explanations are hard to understand and lack information, and discuss issues that can arise from the different interests of the data controller and subject. Finally, we present a set of recommendations for developers of XAI methods, and indications of legal areas of discussion. Among others, recommendations address the presentation, choice, and content of an explanation, technical risks as well as the end-user, while we provide legal pointers to the contestability of explanations, transparency thresholds, intellectual property rights as well as the relationship between involved parties. (shrink)

Reprinted 1999 by The Lawbook Exchange, Ltd. LCCN 98-32334. ISBN 1-886363-74-9. Cloth. $95. * Reprint of the first edition.

In the trust-health relationship, how trusting other people in society may promote good health is a topic often examined. However, the other direction of influence – how health may affect trust – has not been well explored. In order to investigate this possible effect, we employed Bayesian Mindsponge Framework (BMF) analytics to go deeper into the information processing mechanisms underlying the expressions of trust. Conducting Bayesian analysis on a dataset of 1237 residents from Cali, Colombia, we found that general health (...) status is positively associated with generalized trust, but recent experiences of illnesses/injuries have a negative moderating effect. Personalized trust is largely unchanged across different general health conditions, but the trust level becomes higher with recent experiences of illnesses/injuries. Psychophysiological mechanisms of increasing information filtering intensity toward unfamiliar sources during a vulnerable state of health is a plausible explanation of found patterns in generalized trust. Because established personal relationships are reinforced information channels, personalized trust is not affected as much. Rather, the results suggest that people may rely even more on loved ones when they are in bad health conditions. This exploratory study shows that the trust-health relationship can be examined from a different angle that may provide new insights. (shrink)

In the founding documents of this country one finds appeals both to the sovereignty of the people and to abstract notions of rights, "justice," and "the common good". These two ideas are evoked almost as if there were no sense on behalf of the framers that these two ideas simultaneously held create a philosophic tension. Yet as history informs us, they are often contradictory in content. This theme was explored by Rousseau in his distinction of the general will versus the (...) will of all. For Rousseau, the answer to political legitimacy was simple: it was found in the general will, the embodiment of transcendent political ideas. ;Rousseau's choice is one which mirrors that of the American founders. And in doing so they have taken a necessary step in law and state formation: the appeal to Platonism. But, ironically, this appeal does not mean that the popular will has no place in the law. In fact, a careful reading of Plato will render precisely the opposite conclusion: that a sound state built upon transcendent ideas must take into account a number of important empirical considerations, perhaps most significant among these being the will of the people. These ideas are not, however, the determinate Forms from the Phaedo, but rather the indeterminate concepts which guide the Athenian Stranger in his construction of the constitution of Magnesia in the Laws. Given this ontological characteristic of the Forms, the author of a state must have a broad understanding of empirical circumstances including human nature, while serving the demands of the universal ideas. In this light, one must realize that the law will be of no service to its highest aspirations unless it can be written in a manner that the people will act in accordance with it But the lawgiver also relies on this body for the articulation of the higher ideas. Thus the people are at once an obstacle to and a conduit of a higher law. To the extent, however, that democratic theory fails to confront its foundations in such a manner, it becomes mired in confusion. (shrink)

The opposition between behaviour- and mind-reading accounts of data on infants and non-human primates could be less dramatic than has been thought up to now. In this paper, I argue for this thesis by analysing a possible neuro-computational explanation of early mind-reading, based on a mechanism of associative generalization which is apt to implement the notion of mental states as intervening variables proposed by Andrew Whiten. This account allows capturing important continuities between behaviour-reading and mind-reading, insofar as both are supposed (...) to be just different kinds of generalization from perceptual experience. Specifically, I will argue that the projection of inner experiences to others which is involved in early mind-reading does not imply a computational leap beyond associative generalization from perceptual experience. (shrink)

Canonical economic agents act so as to maximize a single, representative, utility function. However, there is accumulating evidence that heterogeneity in thought processes may be an important determinant of individual behavior. This paper investigates the implications of a vector-valued generalization of the Expected Utility paradigm, which permits agents either to deliberate as per Homo economics, or to act impulsively. This generalized decision theory is applied to explain the crowding-out effect, irrational educational investment decisions, persistent social inequalities, the pervasive influence (...) of non-cognitive ability on socio-economic outcomes, and the dynamic relationships between non-cognitive ability, cognitive ability, and behavioral biases. These results suggest that the generalized decision theory warrants further investigation. (shrink)

A theorem is derived that enables a systematic enumeration of all the linear superoperators ℒ (associated with a two-level quantum system) that generate, via the law of motion ℒρ= $\dot \rho$ , mappings ρ(0) → ρ(t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state ρ(t → ∞) that is in some cases independent of (...) ρ(0). (shrink)

For a large proportion of our daily lives, spontaneously occurring thoughts tend to disengage our minds from goal-directed thinking. Previous studies showed that EEG features such as the P3 and alpha oscillations can predict mind-wandering to some extent, but only with accuracies of around 60%. A potential candidate for improving prediction accuracy is the Steady-State Visual Evoked Potential, which is used frequently in single-trial contexts such as brain-computer interfaces as a marker of the direction of attention. In this study, (...) we modified the sustained attention to response task that is usually employed to measure spontaneous thought to incorporate the SSVEP elicited by a 12.5-Hz flicker. We then examined whether the SSVEP could track and allow for the prediction of the stickiness and task-relatedness dimensions of spontaneous thought. Our results show that the SSVEP evoked by flickering words was able to distinguish between more and less sticky thinking but not between whether a participant was on- or off-task. This suggests that the SSVEP is able to track spontaneous thinking when it is strongly disengaged from the task but not off-task thought in general. Future research should determine the exact dimensions of spontaneous thought to which the SSVEP is most sensitive. (shrink)

Analytical jurisprudence often proceeds with two key assumptions: that all law is either contained in or traceable back to an authorizing law-state, and that states are stable and in full control of the borders of their legal systems. What would a general theory of law be like and do if these long-standing presumptions were loosened? The Unsteady State aims to assess the possibilities by enacting a relational approach to explanation of law, exploring law's relations to the environment, security, (...) and technology. The account provided here offers a rich and renewed perspective on the preconditions and continuity of legal order in systemic and non-systemic forms, and further supports the view that the state remains prominent yet is now less dominant in the normative lives of norm-subjects and as an object of legal theory. (shrink)

This paper studies the dynamic characteristics of triopoly models that are constructed based on a 3-dimensional Cobb–Douglas utility function. The paper presents two parts. The first part introduces a competition among three rational firms on which their prices are isoelastic functions. The competition is described by a 3-dimensional discrete dynamical system. We examine the impact of rationality on the system’s steady state point. Studying the stability/instability of this point, which is Nash equilibrium and is unique in those models, is (...) illustrated. Numerically, we give some global analysis of Nash point and its stability. The second part deals with heterogeneous scenarios. It consists of two different models. In the first model, we assume that one competitor adopts the local monopolistic approximation mechanism while the other opponents are rational. The second model assumes two heterogeneous players with LMA mechanism against one rational firm. Studies show that the stability of NE point of those models is not guaranteed. Furthermore, simulation shows that when firms behave rational with symmetric costs, the stability of NE point is achievable. (shrink)

This paper develops a method for extracting from data the quantum theoretical state representation belonging to any reproducible empirical scheme for preparing a physical system, provided only that at least one observable has its possible values limited to a finite set. In Part I, we formulate a general systematic procedure, based on the concept of irreducible tensor operators, for the selection of sets of observables sufficiently large to permit the unambiguous determination of an unknown quantum state.

The Warring States period was without doubt a time when reason thrived. The Confucians, Mohists, and Daoists, respectively, displayed three of its intellectual inclinations. One was reason with an exceptionally prominent moral flavor, and the cultivation of human character as its object. It calls on men to uphold the dignity, tranquillity, and loftiness of their inner selves. One was reason with a very strong practical flavor, and the realization of beneficent profit as its object. It leads men to address ways (...) of maintaining the stability of society, material wealth to support men's livelihoods, and individual survival. Apart from these two, there was reason that has spiritual transcendence and human immortality as its object, and which was manifested as a tendency toward anti-intellectualism. It tries to protect individual survival and freedom of the spirit, despite social pressures. As for those mystical ideas and techniques that seemed absurd, they gradually regressed into simplistic ceremonies, fables, and symbols among the cultural workers who pursued reason. The psychological attitude of "sacrificing to spirits as if they were present" led many cultural aristocrats to distance themselves from mystical ideas and techniques. Mysticism gradually disappeared from among men of culture, especially once it became increasingly difficult for those divination methods and technical arts, used merely to satisfy concrete needs, to avoid the scrutiny of reason. Some late Warring States period texts can help us understand the direction this way of thinking took. "Xian xue" in the Hanfeizi says,When the shaman priests pray for someone, they say, "May you live a thousand autumns and ten thousand years!" But the "thousand autumns and ten thousand years" are only a noise dinning on the ear: No one has ever proven [zheng] that such prayers add so much as a day to anyone"s life. For this reason people despise the shaman priests.". (shrink)

This volume aims to clarify the epistemic potential of applying evolutionary thinking outside biology, and provides a survey of the current state of the art in research on relevant topics in the life sciences, the philosophy of science, and the various areas of evolutionary research outside the life sciences. By bringing together chapters by evolutionary biologists, systematic biologists, philosophers of biology, philosophers of social science, complex systems modelers, psychologists, anthropologists, economists, linguists, historians, and educators, the volume examines evolutionary thinking (...) within and outside the life sciences from a multidisciplinary perspective. While the chapters written by biologists and philosophers of science address theoretical aspects of the guiding questions and aims of the volume, the chapters written by researchers from the other areas approach them from the perspective of applying evolutionary thinking to non-biological phenomena. Taken together, the chapters in this volume do not only show how evolutionary thinking can be fruitfully applied in various areas of investigation, but also highlight numerous open problems, unanswered questions, and issues on which more clarity is needed. As such, the volume can serve as a starting point for future research on the application of evolutionary thinking across disciplines. (shrink)

Here, we offer concrete illustrations of the state determination method developed abstractly in Part I of this work. Quorums are found for finite-dimensional magnetic multipole problems as well as for the harmonic oscillator with an energy cutoff. There is, in addition, a discussion of general procedures for empirically distinguishing pure states from mixed states.

IntroductionGeneralized Anxiety Disorder is a prevalent emotional disorder associated with increased dysfunctionality, which has a lasting impact on the individual’s quality of life. Besides medication, Cognitive-Behavioral Therapy represents the golden standard psychotherapeutic approach for GAD, integrating multilevel techniques and various delivery formats that enable the development of tailored treatment protocols. The objective of this study was to compare the efficiency of a standard CBT protocol targeting worries, dysfunctional beliefs, and intolerance of uncertainty with an integrative and multimodal CBT intervention augmented (...) with Virtual Reality.Materials and methodsThis study included 66 participants with moderate GAD symptoms that were randomized to the standard CBT group and the Integrative and Multimodal CBT augmented with VR group. The interventions comprised 10 weekly sessions conducted by trained CBT therapists, including cognitive restructuring, problem-solving, behavioral exposure, and relaxation techniques. Baseline and post-assessments were conducted with both groups. Primary outcome measures included the Hamilton Anxiety Rating Scale and Penn-State Worry Questionnaire to evaluate the severity of GAD symptoms and worries, respectively. Secondary outcomes involved the administration of Automatic Thoughts Questionnaire, Dysfunctional Attitudes Scale and Unconditional Self-Acceptance Questionnaire.ResultsBoth interventions determined statistically significant effects on both primary and secondary outcomes in the expected direction. However, CBTs was associated with higher effect sizes for anxiety and worries, in contrast to IM-VRCBT. Also, secondary analyses revealed positive correlations between changes in anxiety and worries level and the reduction of dysfunctional cognitive processes.ConclusionThis research emphasized the effectiveness of CBT interventions for treating adults with moderate GAD symptomatology. Specifically, both interventions were efficient for reducing anxiety symptomatology present at individuals with GAD. However, regarding cognitive dysfunctions like worries, the standard CBT protocol performed better, as compared to the IM-VRCBT. In addition, we conclude that VR could be integrated within CBT interventions in a single protocol for GAD treatment. (shrink)

Higher education is seeing renewed calls for strengthening ethics education, yet there remains a dearth of research on the state of ethics education across undergraduate curricula. Research about ethics in higher education tends to be localized and often isolated to fields of graduate study. In contribution to a contemporary, landscape understanding of ethics education, we collected data on the placement and prevalence of ethics instruction within the general education curricula at 507 major U.S. colleges and universities. Our findings suggest (...) that 1) most schools in our study’s population do not explicitly require ethics as a part of their general education curricula; and 2) a school’s religiosity and research status are positively associated with explicitly requiring ethics instruction for its undergraduate student body. (shrink)

The present study was conducted with the aim of constructing and validating a short form of the Profile of Mood States. The POMS is a widely-applied measure for the assessment of an individual's mood. Thus, it is of great relevance for many research questions in clinical and social psychology. To develop the short scale, we first examined psychometric properties and found the optimal 16-item solution among all valid combinations of the full POMS in an exploratory subsample of our complete representative (...) sample of the German general population. We then validated this model in a confirmatory subsample. Additionally, we examined its invariance across age groups and sex, as well as its reliability. Our results indicate that the POMS-16 is a valid and reliable measure of mood states with minimal losses compared to the 35-item version. Particularly where brevity and an economical assessment is desired, the POMS-16 should be considered. (shrink)

Some legal theorists deny that states can conceivably act extra-legally, in the sense of acting contrary to domestic law. This position finds its most robust articulation in the writings of Hans Kelsen, and has more recently been taken up by David Dyzenhaus in the context of his work on emergencies and legality. This paper seeks to demystify their arguments and, ultimately, contend that we can intelligibly speak of the state as a legal wrongdoer or a legally unauthorized actor.

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a (...) modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states. (shrink)

In recent years, the Minnesota Attorney General’s Office and the Minnesota Department of Health have cultivated a productive partnership to strengthen the state’s multidisciplinary response to overlapping health equity and social justice issues. This article describes shared efforts in three areas: post-conviction justice, drug overdose, and human trafficking/exploitation.