Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear (...) subintervals. As a result of non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

The famous Allen's interval relations constraint propagation algorithm was intended for linear time. Its 13 primitive relations define all the possible mutual locations of two intervals on the time-axis. In this paper an application of the algorithm for non-linear time is suggested. First, a new primitive relation is added. It is called excludes since an occurrence of one event in a certain course of events excludes an occurrence of the other event in this course. Next, (...) new composition rules for relations between intervals are presented: some of the old rules are extended by the relation excludes, and entirely new ones are formulated for composing the relation excludes with the other relations. Four different composition tables are considered. The choice of a composition table depends on whether time is branching or not, and whether intervals can contain non-collinear subintervals or not. (shrink)

This article examines how non-linear time and circularity are deployed in the historical novel Nehanda, written by Zimbabwean author Yvonne Vera. Using Adriana Cavarero’s work on inclination...

Humankind is currently confronted with a critical challenge that determines its very existence, not only on an individual, racial, or national level but as a whole species: the fight against climate change and environmental degradation. To win this battle, humanity needs innovations and non-linear thinking. Nature has long been a substantial information source for unthinkable discoveries that save human lives. The paper suggests that by understanding the nature, emergence, and mechanism of serendipity, the survival skill of humans, humanity can (...) capitalize on it to learn from nature and generate nature-based innovations that can address the climate and environmental degradation crises. In the era of Artificial Intelligence (AI) proliferation, AI will be a vital tool providing navigational and useful information to leverage the power of serendipity in climate and sustainability science. However, an eco-surplus culture that incorporates core values pertaining to nature and sees environmental sustainability as the conscience of the times needs to be built to direct and control the immense power of AI-leveraged serendipity. Insights applied in this paper are drawn from the book titled “A New Theory of Serendipity: Nature, Emergence and Mechanism”. (shrink)

In the industrial context, steel is a broadly-used raw material with applications in many different fields. Due to its high impact in the activity of many industries all over the world, forecasting its price is of utmost importance for a huge amount of companies. In this work, non-linear neural models are applied for the first time to different datasets in order to validate their suitability when predicting the price of this commodity. In particular, the NAR, NIO and NARX (...) neural network models are innovatively applied for the first time to forecast the price of hot rolled steel in Spain. Besides these variety of models, different datasets consisting of a set of heterogenous variables from the last seven years and related to the price of this commodity are benchmarked and analyzed. The results showed that NARX is the best performing model when the price of raw materials used to produce steel and the stock market prices of three major global steel producing companies are employed as input to this predictive model. Consequently, this result may boost the application of Machine Learning in companies, in order to schedule the supplying operations according to the price forecasting. (shrink)

Related to the research of working conditions, the link between organizational factors and health was traditionally analyzed using linear models. However, the literature analysis suggests inconsistencies in linear models predicting workers’ health levels. To clarify this issue, this exploratory research compares the linear and non-linear relationships between job demands-resources, and the psychological and physical symptoms of employees working in the main five service subsectors: commerce, horeca, public administration, education, and healthcare. With a final sample of 4,047 (...) participants, our study data were extracted from the II Andalusian Working Conditions Survey. Following the theoretical framework of JD-R Model and considering the Vitamin Model theoretical approach for non-linear relationships, our results showed that there were significant differences among the five subsectors analyzed regarding the linear and non-linear relationships between job demands-resources and psychological and physical symptoms of employees. Furthermore, task complexity generated non-linear relationships in higher proportion than time pressure and contact with users. Likewise, non-linear relationships found showed a U-shape. Moreover, the findings of non-linear relationships suggested that medium levels of task complexity should not be exceeded to avoid further negative impact on psychological and physical symptoms for service sector employees, preserving their health. Finally, some general practical implications of work environment interventions are suggested. (shrink)

In the past 2 decades latent variable modeling has become a standard tool in the social sciences. In the same time period, traditional linear structural equation models have been extended to include non-linear interaction and quadratic effects (e.g., Klein and Moosbrugger, 2000 ), and multilevel modeling (Rabe-Hesketh et al., 2004 ). We present a general non-linear multilevel structural equation mixture model (GNM-SEMM) that combines recent semiparametric non-linear structural equation models (Kelava and Nagengast, 2012 ; Kelava (...) et al., 2014 ) with multilevel structural equation mixture models (Muthén and Asparouhov, 2009 ) for clustered and non-normally distributed data. The proposed approach allows for semiparametric relationships at the within and at the between levels. We present examples from the educational science to illustrate different submodels from the general framework. (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.

Here, for the first time, development studies encounters the set of ideas popularly known as 'Chaos Theory'. Samir Rihani applies to the processes of economic development, ideas from complex adaptive systems like uncertainty, complexity, and unpredictability. Rihani examines various aspects of the development process - including the World Bank, debt, and the struggle against poverty - and demonstrates the limitations of fundamentally linear thinking in an essentially non-linear world.

The question of form in Peirce’s early thought constitutes the starting point of his reflection on the connection models of the parts of continua. I will show how, interpreted as reason rather than as cause, form becomes a productive event. In this productive event the form, as “condition of possibility of the relation of the elementary parts of representation” becomes a modeling dynamic which, starting from interpretation, allows initiation of the process of the passage from substance to being. The problem (...) of this passage is the problem of a continuity that cannot be thought by the classical linear model of time. (shrink)

Mental imagery is an important topic in classical and modern philosophy, as it is central to the study of knowledge; since subjects can recall features of perceptual experiences in different ways and times, even modifying their structure, in this brief essay we will focus on non-perceptive mental images and to this purpose we will analyse, on the one hand, the nature of perceptive mental images ; on the other hand, NPMI generation according to different strategic conditions and retrieval modalities and, (...) so, their structural relationships with PMI. Thus, we will clarify what NPMI amounts to and, to this purpose, we will address the issue of epistemic correlation and semantic reference. As regards the former, we will adopt the notion of ‘belief’, both to describe which attitude supports the use of an NPMI and to account for its relationship with a PMI. As regards the latter, we will talk about weak ontology between an NPMI and the world, to conceive ‘the way in which’ mental imagery, despite the absence of a sensorial modification, refers to physical objects. As the subject’s mental contents determine, but do not constrain, what NPMI is like, we will deal with the ‘involvement’ of prior knowledge and the notion of meaningful space to underline that its generation is always the result of a wide process which involves perceptive visual information already processed and stored together with further mental contents. So, though some Authors consider mental imagery to be a ‘percept-like’ image and, somehow, espouse the theory of reactivation, we will pose a challenge to this theory – i.e. to what we call mental imagery standard framework – describing an NPMI in terms of configurational setting and indeterminacy. Consequently, we will propose a non-linear dynamic framework of mental imagery generation , according to which an NPMI is not reducible to a mere recalling of figural features of a perceptive image. (shrink)

As time-shifting technologies and digital convergence are facilitating and encouraging increasingly individualized and personalized television viewing practices, the social role and function of traditional linear television might be changing as well. Through empirical audience research, using TV diaries and interviews, this article investigates the social dimensions of engaged viewers’ reception of TV drama and explores how audiences themselves experience contemporary television as a social medium. The qualitative analysis reveals three social dimensions in viewers’ engagement with TV drama and (...) indicates that television is generally still perceived as a social medium. Time-shifting technologies do not only fracture audiences, they also create new opportunities for social connections with peer viewers. (shrink)

The present study focused on the dynamics and factors underpinning domestic abuse survivors’ decisions to end the abusive relationship. The experiences and opinions of 12 female DA survivors and 18 support workers were examined through in-depth, one-to-one, semi-structured interviews. Hybrid thematic analysis was conducted to retrieve semantic themes and explore relationships among the themes identified and the differences in survivors’ and professionals’ narratives of the separation process. The findings highlighted that separation decisions derived from the joint action of two sets (...) of factors, the “promoters” and the “accelerators.” Whilst the “promoters” are factors leading to the separation from the abuser over time, the “accelerators” bear a stronger and more direct connection with survivors’ decision to end the abusive relationship. Despite their differences, both these factors acted as propelling forces, leading survivors to actively pursue the separation from the perpetrator. To portray the dynamic links among these factors, we propose a conceptualisation drawn from Newton’s laws of motion. Our findings also highlighted important differences in the views of survivors and support workers, as the former conceived themselves as proactive in ending the abuse, whereas the latter described the leaving process as mainly led by authorities and services supporting survivors. This study has potential implications for research, policy and clinical practice, as it suggests that far from being a linear sequence of multiple stages, leaving an abusive relationship results from a complex interplay of factors that facilitate or drastically accelerate the separation process. We argue that future research should aim at improving our current understanding of the subjective and situational factors that can act as “accelerators” or “promoters” for women’s leaving decisions. Moreover, clinicians and policymakers should invest in creating interventions that aid victims to recognise and leverage promoters and accelerators, thus increasing their readiness to end the abuse. (shrink)

We describe a unification of old and recent ideas for formulating graphical models to explain time series data, including Granger causality, semi-automated search procedures for graphical causal models, modeling of contemporaneous influences in times series, and heuristic generalized additive model corrections to linear models. We illustrate the procedures by finding a structure of exogenous variables and mediating variables among time series of remote geospatial indices of ocean surface temperatures and pressures. The analysis agrees with known exogenous drivers (...) of the indices, not assumed in the analysis. Automated search applied to the residuals after regressing each series on its lags and the lags of its Granger causes yields a graphical model of “comtemporaneous” causal relations identical with the qualitative graphical relations from the time series. A similar analysis produces reasonable results when applied to candidate climate indices obtained by a clustering method from sea surface temperature and sea level pressure data. (shrink)

The appearance of nonlinear equations in science, engineering, economics, and medicine cannot be denied. Solving such equations requires numerical methods having higher-order convergence with cost-effectiveness, for the equations do not have exact solutions. In the pursuit of efficient numerical methods, an attempt is made to devise a modified strategy for approximating the solution of nonlinear models in either scalar or vector versions. Two numerical methods of second-and sixth-order convergence are carefully merged to obtain a hybrid multi-step numerical method with twelfth-order (...) convergence while using seven function evaluations per iteration, resulting in the efficiency index of about 1.4262. The convergence is also ascertained theoretically, and the asymptotic error constant is computed. Furthermore, various numerical methods of varying orders are used to compare the numerical results obtained with the proposed hybrid method in approximate solution, number of iterations, absolute error, absolute functional value, and the machine time measured in seconds. The obtained results outperformed the chosen methods when applied models arising from physical and natural fields were solved. Finally, to observe the convergence graphically, some complex polynomials are plotted as polynomiographs, wherein the rapid convergence of the proposed method is guaranteed. (shrink)

A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a (...) resource indexed non-commutative logic RN[l] is also shown. This theorem is intended to state that “time” is regarded as a “resource”. (shrink)

This paper seeks to understand the transmission and reception of legal rules as a component of the regulatory compliance process. It adopts a frontline approach to regulatory compliance that traces the grassroot functioning of compliance processes from regulator, to compliance managers to individual employees. Through a multilevel and multi-sited ethnography of worker safety protection in Chinese construction industry, this paper shows that in the cases studied there is a fundamental disconnect in the transmission and reception of law from regulator to (...) organization and within the regulated organization. Yet at the same time, the paper finds that employees did comply with the law, and that thus compliance can exist without a full transmission and reception of legal rules into and within the regulated organization. By expanding the frontline approach to study regulation and compliance to look at the grassroots operation across three different frontlines, this study has been able to assess the legal assumptions inherent in existing regulatory compliance research. Not only does it find that compliance in these cases was not a top-down process and that we need to look at the grassroots operation inside organizations, it also shows that law does not always play a central role in regulatory compliance and that we need to reassess the implicit focus on law in regulatory compliance scholarship. (shrink)

We present a nonparametric approach to prediction of the n-back n \in {1, 2} task as a proxy measure of mental workload using Near Infrared Spectroscopy (NIRS) data. In particular, we focus on measuring the mental workload through hemodynamic responses in the brain induced by these tasks, thereby realizing the potential that they can offer for their detection in real world scenarios (e.g., difficulty of a conversation). Our approach takes advantage of intrinsic linearity that is inherent in the components of (...) the NIRS time series to adopt a one step regression strategy. We demonstrate the correctness of our approach through its mathematical analysis. Furthermore, we study the performance of our model in an inter-subject setting in contrast with state-of-the-art techniques in the literature to show a significant improvement on prediction of these tasks (82.50% and 86.40% for female and male participants, respectively). Moreover, our empirical analysis suggest a gender difference effect on the performance of the classifiers (with male data exhibiting a higher non-linearity) along with the left-lateralized activation in both genders with higher specificity in females. (shrink)

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different (...) from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system. (shrink)

We describe a unification of old and recent ideas for formulating graphical models to explain time series data, including Granger causality, semi-automated search procedures for graphical causal models, modeling of contemporaneous influences in times series, and heuristic generalized additive model corrections to linear models. We illustrate the procedures by finding a structure of exogenous variables and mediating variables among time series of remote geospatial indices of ocean surface temperatures and pressures. The analysis agrees with known exogenous drivers (...) of the indices, not assumed in the analysis. Automated search applied to the residuals after regressing each series on its lags and the lags of its Granger causes yields a graphical model of “comtemporaneous” causal relations identical with the qualitative graphical relations from the time series. A similar analysis produces reasonable results when applied to candidate climate indices obtained by a clustering method from sea surface temperature and sea level pressure data. (shrink)

Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between (...) class='Hi'>time and knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi. (shrink)

ABSTRACT The question of axiomatizability of first-order temporal logics is studied w.r.t. different semantics and several restrictions on the language. The validity problem for logics admitting flexible interpretations of the predicate symbols or allowing at least binary predicate symbols is shown to be ?1 1-complete. In contrast, it is decidable for temporal logics with rigid monadic predicate symbols but without function symbols and identity.

Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic (...) notions are defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications. (shrink)

Linear mixed-effect models (LMMs) are being increasingly widely used in psychology to analyse multi-level research designs. This feature allows LMMs to address some of the problems identified by Speelman and McGann ( 2013 ) about the use of mean data, because they do not average across individual responses. However, recent guidelines for using LMM to analyse skewed reaction time (RT) data collected in many cognitive psychological studies recommend the application of non-linear transformations to satisfy assumptions of normality. (...) Uncritical adoption of this recommendation has important theoretical implications which can yield misleading conclusions. For example, Balota et al. ( 2013 ) showed that analyses of raw RT produced additive effects of word frequency and stimulus quality on word identification, which conflicted with the interactive effects observed in analyses of transformed RT. Generalized linear mixed-effect models (GLMM) provide a solution to this problem by satisfying normality assumptions without the need for transformation. This allows differences between individuals to be properly assessed, using the metric most appropriate to the researcher's theoretical context. We outline the major theoretical decisions involved in specifying a GLMM, and illustrate them by reanalysing Balota et al.'s datasets. We then consider the broader benefits of using GLMM to investigate individual differences. (shrink)

Central to the functioning of colonialism and coloniality is a specific construction of time, in terms of which the spatial ordering of the world also translates into a temporal ordering. Anthropologist Johannes Fabian argues that there is a specific rhetorical device at work here, namely the ‘denial of coevalness’, which is a colonial distancing strategy through which other worlds are robbed of validity on account of not existing within the same time as the West. In this article, I (...) aim to add to analyses of scholars like Fabian, Chakrabarty and Mignolo by arguing that this colonial temporal ordering, which persists today, is also thoroughly gendered. As a point of departure I use Walter Mignolo’s idea that the denial of coevalness relies on two distinctions, namely nature versus culture, and tradition versus modernity. I argue that the discursive construction of nature (as opposed to culture) and tradition (as opposed to modernity) centres on gendered assumptions and an obsession with control over women’s bodies. In the course of making this argument, I also point out the overlaps, as well as key differences, between woman’s exclusion from Western linear time, on the one hand, and the temporal distancing of the colonised, on the other. In particular, I show how Western linear chronology positions Western women and previously colonised women in vastly different ways. I argue that if one considers the extent to which the denial of coevalness relies on colonial gender discourses, the erasure of indigenous sexuate knowledges that contradict the colonial gender discourses is not one erasure among many, but one of the key erasures that colonial temporality hinges on. A crucial implication of my analysis is that the process of undoing, deconstructing or dismantling the colonial denial of coevalness is also inherently a feminist project. (shrink)

This paper presents a new correctness criterion for marked Danos-Reginer graphs (D-R graphs, for short) of Multiplicative Cyclic Linear Logic MCLL and Abrusci's non-commutative Linear Logic MNLL. As a corollary we obtain an affirmative answer to the open question whether a known quadratic-time algorithm for the correctness checking of proof nets for MCLL and MNLL can be improved to linear-time.

_Time, Space, and Phantasy_ examines the connections between time, space, phantasy and sexuality in clinical practice. It explores the subtleties of the encounter between patient and analyst, addressing how aspects of the patient’s unconscious past are actualised in the present, producing new meanings that can be re-translated to the past. Perelberg’s analysis of Freud’s Multi-dimensional model of temporality suggests that he always viewed the constitution of the individual as non-linear. In Freud’s formulations, the individual is decentred and ruled (...) by different temporalities, most of which escape their consciousness. Perelberg identifies the similarities between this and Einstein’s theory of relativity which states that rather than being absolute, time depends on the relative position and speed of the observing individual suggesting that rather than being a reality, time is an abstraction, connecting objects and events. Throughout this text, Perelberg draws together connections between time, mental space, and phantasy showing how time is constantly reshaped in the light of new events and experiences. This book will be of interest to psychoanalysts, psychotherapists, psychologists, and social workers. (shrink)

This paper examines the theoretical background and actual behavior in a gaming tournament with endogenous timing where a person has more incentive, structure, and time to form a strategy. The baseline treatment suggests that subgame perfection is a reasonable predictor of behavior –- subjects made 170 of 208 theoretically predicted choices of best actions, with the majority of mistakes made in timing choices by the players who did not survive the cut to the second round. Four sensitivity treatments established (...) that the design feature that lead to more predictable behavior was time to think –- 745 of 960 correctly predicted decisions with more time versus 595 of 960 with less time. A random effects Probit model suggests that the key design feature that closed the gap between predicted and observed behavior was not necessarily the non-linear payoffs created by the tournament design, but rather that the key was providing people with more time to think about their strategy. (shrink)

In Time After Time, David Wood accepts, without pessimism, the broad postmodern idea of the end of time. Wood exposes the rich, stratified, and non-linear textures of temporal complexity that characterize our world. Time includes breakdowns, repetitions, memories, and narratives that confuse a clear and open understanding of what it means to occupy time and space. In these thoughtful and powerful essays, Wood engages Kierkegaard, Nietzsche, Heidegger, and Derrida to demonstrate how repetition can preserve (...) sameness and how creativity can interrupt time. Wood’s original thinking about time charts a course through the breakdown in our trust in history and progress and poses a daring and productive way of doing phenomenology and deconstruction. (shrink)

This contribution analyzes the rhetoric surrounding natural disasters in historiographic sources, challenging our assumptions about the eschatological nature of late antique and medieval historical consciousness. Contrary to modern expectations, a large number of late antique and medieval sources indicate that earthquakes and other natural disasters were understood as signs from God, relating to theophanic encounters or divine wrath in the present time. Building on recent research on premodern concepts of time and historical consciousness, the article underscores the fact (...) that eschatological models of time and history-that is, the relentless linear, teleological progression of time towards the End of Days-was not how premodern people perceived the relationship between past, present, and future. The textual evidence presented here is supported by a fragmented and littleknown illuminated historiographic text, the Ravennater Annalen, housed today in the cathedral library in Merseburg. This copy of a sixth-century illustrated calendar from Ravenna contains unique depictions of earthquakes in the form of giants breathing fire. Like the textual sources, this visual document should not be read as a premonition of the End of Days, rather it visualizes the belief that divine agency and wrath caused natural disasters. (shrink)

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the (...) choice of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”. (shrink)

After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take (...) Linear Temporal Logic (LTL) as case study for this defeasible aspect. LTL has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of LTL, called defeasible linear temporal logic (LTL ~ ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with LTL. We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of LTL ~ sentences. Based on Sistla and Clarke's work on the complexity of the classical LTL language, we show the bounded-model property of two fragments of LTL ~ language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments. (shrink)

This paper explores the relationship of time and value in the history of economics, using the contributions of Girard, Achterhuis, Kula and Mirowski. In the ‘anthropometric stage’ time and value are intertwined: value and time are not abstract concepts, but they express a concrete process which incorporates the social positions of individuals. In the ‘lineamentric stage’ the concepts of time and value remain cyclical, but they receive an abstract character. The economy reproduces itself cyclically, because the (...) origin of value – human labour – reproduces itself in each production period. In the ‘syndetic stage’ the cyclical conception of the economy is abandoned through the perception of a non-reproductive system. Time and value are detached from each other, and linear time enters economic theory as an analytical tool. The labour theory of value is replaced by external denominants of value: utility and external scarcity. (shrink)

This essay illustrates senses in which linear time can be proven to be non existent. Yet, as the essay agrees, the practical use of linear time, as an organizational principle in life, is unquestionable. Do we live a lie by relying on the non existent to undergird our lives? Or is lie a misleading, and naïve, word for our solution to this state of affairs?

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

What does it mean to teach, live, and imagine one’s futures amidst a global pandemic? How to respond to the reality of unequal and overlapping crises, COVID-19 being one of them? Can alternative understandings of time help us create a more just post-pandemic university? Drawing on environmental humanities, disaster and critical time studies, in conversation with qualitative data, this article theorizes a ‘pedagogy of scale’: a practical and conceptual centering on multiple temporalities and diverse interpretative frames. The analysis (...) argues for the need to attend to overlapping, non-linear, and changeable scales of time, reference, and meaning that students draw on in order to make sense of crises: every crisis, even as unprecedented as COVID-19, is embedded in environmental processes, long-term vulnerabilities and injustices. These overlooked and overlapping scales interweave personal, planetary, and theological notions of time—from ecological deep time to the divine time—meaning, and self. In its focus on asynchronicity, overlap and multiplicity, the analysis extends current theorizations of temporality and crisis in higher education, challenges paradigms of mastery, advocates for epistemic plurality, and embraces decolonial notions of human subjectivity, providing a much-needed critical model for the post-pandemic university. (shrink)

In his Poetics, Aristotle articulated certain ideas on the structure of drama that dominated both dramatic literature and theatre practices for the centuries to come. In this article I show how the thorough analysis of his statements leads us to believe that he endorses causality, narrativity, and temporal linearity as primary factors in the organization of dramatic and stage texts. Tracing various modifications of causality throughout theatre history, I use the work of the two prominent contemporary directors, Eimuntas Nekrosius and (...) Anatoly Vasilyev, to demonstrate how postmodernist theatre has arrived at non-Aristotelian theatrical model based on the unity of a time–space continuum rather than temporal development. (shrink)

In this research we employ an inter-disciplinary project that uses active learning theory to help bridge the gap between a university’s extensive liberal arts core and its business program. We believe this project will improve and enrich classroom discussions of the more complex and nuanced issues found in the application of business principles. To redress the fact that many undergraduate students do not have extensive work experience to draw on when discussing the application of business ethics principles, we present a (...) project that uses a classic novel, Hard Times, to improve students’ abilities to contextualize and apply common business ethics frameworks. The project focuses on active learning and non-linear thinking, and aims to immerse the student in a fictional environment that models the complexity of, without being identical to, a real world business setting. (shrink)

In this paper we show that properties of non-linear time structures have not been studied enough. Axioms forcing the existence of a branching point in a branching area of a structure are presented for various classes of structures. We show also that the classical Dedekind continuity axiom does not work well in non-linear structures and we suggest stronger versions. Finally, some interdependencies between the axioms presented are proved.

This paper rereads John Dewey's works in the light of complexity theory and self‐organising systems. Dewey's pragmatic inquiry is posited as inspirational for developing a logic of education and learning that would incorporate novelty and creativity, these artistic elements being part and parcel of the science of complexity. Dewey's philosophical concepts are explored against the background of such founders of dynamical systems theory as Ludwig von Bertalanffy, Ervin Laszlo, and Erich Jantsch. If, in this process, Dewey's thought appears to undergo (...) some transformation, this would only confirm Jim ) belief that Dewey would welcome, in accord with his own philosophical project, the reconstruction of his own ideas so as to better respond to contingencies and challenges of new times, places and contexts. The paper introduces some elements of non‐linear dynamics, relating them to the problematic of learning and the transformation of habits. Finally, the paper addresses a delicate balance between novelty and confirmation in a self‐organised system, positing it as an issue of pedagogical significance. (shrink)

The article fits into the debate regarding space, time and nature in dialogue with the world lived by subjects that build up themselves or are built as mythological heroes, source of speech and spacial concrete practices. It's a poorly explored field in Geography that recently approaches to the cultural dynamic debate, to the symbolic field and also to their spacialization processes. The aim is to discuss the possibility of understanding in the present time about the space organization processes (...) related to the society's previous moments, in a space/time dialectics which articulate the present and past times in a complex and non linear way. Methodologically, starting from a literature review about the theme, the present study was linked to the field and documental research about migration to the vicinal ways of Transamazônica Highway (BR-230 Highway), the creation of the "Centro Espírita União do Vegetal", a religion that arises in the Amazon and set up its headquarters in Brasília and the construction of Brasilia as a modern metropolis without a past. The conclusion points at the possibility of space/time nexuses linking the Myth of Nature to the Creation of Heroes, constantly appropriated and with new meanings, in order to support speeches and new actions dialectically throughout the Brazilian contemporaneous space. (shrink)

This paper examines the theoretical background and actual behavior in a gaming tournament with endogenous timing where a person has more incentive, structure, and time to form a strategy. The baseline treatment suggests that subgame perfection is a reasonable predictor of behavior –- subjects made 170 of 208 theoretically predicted choices of best actions, with the majority of mistakes made in timing choices by the players who did not survive the cut to the second round. Four sensitivity treatments established (...) that the design feature that lead to more predictable behavior was time to think –- 745 of 960 correctly predicted decisions with more time versus 595 of 960 with less time. A random effects Probit model suggests that the key design feature that closed the gap between predicted and observed behavior was not necessarily the non-linear payoffs created by the tournament design, but rather that the key was providing people with more time to think about their strategy. (shrink)

In 1958 J. Lambek introduced a calculusL of syntactic types and defined an equivalence relation on types: x y means that there exists a sequence x=x1,...,xn=y (n 1), such thatx i x i+1 or xi+ x i (1 i n). He pointed out thatx y if and only if there is joinz such thatx z andy z. This paper gives an effective characterization of this equivalence for the Lambeck calculiL andLP, and for the multiplicative fragments of Girard's and Yetter's (...) class='Hi'>linear logics. Moreover, for the non-directed Lambek calculusLP and the multiplicative fragment of Girard's linear logic, we present linear time algorithms deciding whether two types are equal, and finding a join for them if they are. (shrink)

The main aim of this study was to analyze the patterns of changes in Approximate Number Sense precision from grade 1 to grade 9 in a sample of Russian schoolchildren. To fulfill this aim, the data from a longitudinal study of two cohorts of children were used. The first cohort was assessed at grades 1–5, and the second cohort was assessed at grades 5–9. ANS precision was assessed by accuracy and reaction time in a non-symbolic comparison test. The patterns (...) of change were estimated via mixed-effect growth models. The results revealed that in the first cohort, the average accuracy increased from grade 1 to grade 5 following a non-linear pattern and that the rate of growth slowed after grade 3. The non-linear pattern of changes in the second cohort indicated that accuracy started to increase from grade 7 to grade 9, while there were no changes from grade 5 to grade 7. However, the RT in the non-symbolic comparison test decreased evenly from grade 1 to grade 7, and the rate of processing non-symbolic information tended to stabilize from grade 7 to grade 9. Moreover, the changes in the rate of processing non-symbolic information were not explained by the changes in general processing speed. The results also demonstrated that accuracy and RT were positively correlated across all grades. These results indicate that accuracy and the rate of non-symbolic processing reflect two different processes, namely, the maturation and development of a non-symbolic representation system. (shrink)

Julia Kristeva’s work on the concept of revolt is marked by a temporal analysis that takes revolt to be a movement of return into the past that makes possible change, rebirth, and an open future. Such temporal revolt is, according to Kristeva, intimate, in that it touches on unconscious psychic structures and operates on the level of thought and creativity. But Kristeva simultaneously inherits Freud’s notion that the unconscious is timeless. How, I ask, can revolt be defined as a temporal (...) movement of return while at the same time being rooted in timelessness? I examine both Freud’s and Kristeva’s discussions of the timelessness of the unconscious and suggest that it needs to be understood not as non-temporal or outside of time, but rather as a temporal structure that challenges traditional philosophical conceptions of time. As such, the timelessness of the unconscious is far from being yet another instantiation of metaphysical presence. Rather, I see it as offering a challenge to both metaphysical presence and linear time, and indeed as making possible the retrospective movement of return that revolt for Kristeva must be. (shrink)

In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a “Klein paradox.” To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the “Klein paradox” disappears. In the case of Coulomb interaction, the revised nonlinear (...) equation can be linearized to give energy solutions for Hydrogen-like ions without singularity when nuclear number Z>137, showing a reversed energy order pending for experimental tests such as Zeeman effects. In non-relativistic limit, this nonlinear equation reduces to nonlinear Schrödinger equation with soliton-like solutions. Moreover, particle conjugation and electron-proton scattering with a nonsingular current-potential interaction are discussed. Finally the explicit form of gauge function is found, the uniqueness of Lorentz gauge is proven and the Lagrangian density of quantum electrodynamics (QED) is revised as well. The implementation of unitary time inversion leads to the ultimate derivation of nonlinear QED. (shrink)