Notion Of Substitution Research Articles

Tight typings and split bounds, fully developed

Abstract Multi types – aka non-idempotent intersection types – have been used. to obtain quantitative bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the same time the number of evaluation steps and the size of the result. Recent results show that the number of steps can be taken as a reasonable time complexity measure. At the same time, however, these results suggest that multi types provide quite lax complexity bounds, because the size of the result can be exponentially bigger than the number of steps. Starting from this observation, we refine and generalise a technique introduced by Bernadet and Graham-Lengrand to provide exact bounds. Our typing judgements carry counters, one measuring evaluation lengths and the other measuring result sizes. In order to emphasise the modularity of the approach, we provide exact bounds for four evaluation strategies, both in the λ-calculus (head, leftmost-outermost, and maximal evaluation) and in the linear substitution calculus (linear head evaluation). Our work aims at both capturing the results in the literature and extending them with new outcomes. Concerning the literature, it unifies de Carvalho and Bernadet & Graham-Lengrand via a uniform technique and a complexity-based perspective. The two main novelties are exact split bounds for the leftmost strategy – the only known strategy that evaluates terms to full normal forms and provides a reasonable complexity measure – and the observation that the computing device hidden behind multi types is the notion of substitution at a distance, as implemented by the linear substitution calculus.

Tight typings and split bounds

Multi types—aka non-idempotent intersection types—have been used to obtain quantitative bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the same time the number of evaluation steps and the size of the result. Recent results show that the number of steps can be taken as a reasonable time complexity measure. At the same time, however, these results suggest that multi types provide quite lax complexity bounds, because the size of the result can be exponentially bigger than the number of steps. Starting from this observation, we refine and generalise a technique introduced by Bernadet & Graham-Lengrand to provide exact bounds for the maximal strategy. Our typing judgements carry two counters, one measuring evaluation lengths and the other measuring result sizes. In order to emphasise the modularity of the approach, we provide exact bounds for four evaluation strategies, both in the λ-calculus (head, leftmost-outermost, and maximal evaluation) and in the linear substitution calculus (linear head evaluation). Our work aims at both capturing the results in the literature and extending them with new outcomes. Concerning the literature, it unifies de Carvalho and Bernadet & Graham-Lengrand via a uniform technique and a complexity-based perspective. The two main novelties are exact split bounds for the leftmost strategy—the only known strategy that evaluates terms to full normal forms and provides a reasonable complexity measure—and the observation that the computing device hidden behind multi types is the notion of substitution at a distance, as implemented by the linear substitution calculus.

Everybody's Got To Be Somewhere

The key to any nameless representation of syntax is how it indicates the variables we choose to use and thus, implicitly, those we discard. Standard de Bruijn representations delay discarding maximally till the leaves of terms where one is chosen from the variables in scope at the expense of the rest. Consequently, introducing new but unused variables requires term traversal. This paper introduces a nameless 'co-de-Bruijn' representation which makes the opposite canonical choice, delaying discarding minimally, as near as possible to the root. It is literate Agda: dependent types make it a practical joy to express and be driven by strong intrinsic invariants which ensure that scope is aggressively whittled down to just the support of each subterm, in which every remaining variable occurs somewhere. The construction is generic, delivering a universe of syntaxes with higher-order metavariables, for which the appropriate notion of substitution is hereditary. The implementation of simultaneous substitution exploits tight scope control to avoid busywork and shift terms without traversal. Surprisingly, it is also intrinsically terminating, by structural recursion alone.

Precarious work or sustainable livelihoods? Aligning Prestea's Programme with the development dialogue on artisanal and small‐scale mining

Alternative livelihoods programmes (ALPs) are extensively executed in mining communities, often as models of development dialogue on artisanal and small‐scale mining (ASM). This paper assesses whether Prestea's ALP aligns with the development dialogue on artisanal mining. The conceptual design of ALP in Ghana's Prestea is based on the notions of substitution, homogenous community, and impact scalability. This paper argues that the Prestea ALP is not aligned with the development dialogue on artisanal mining, and therefore it is difficult to understand the role and function of environmentally‐damaging behaviours within livelihood strategies. The paper contends that it would be appropriate to concentrate on improving the existing artisanal miners’ operation of those most susceptible to resource access restrictions. Further, it may be more prudent to utilize livelihood‐centered interventions that create strong connections with sustainable development as a way of creating regular community engagements. Additionally, this paper argues that the term for the intervention programme on artisanal mining should be replaced with the broader term ‘livelihood‐centered intervention’. The replacement of the term ‘ALP’ avoids the tacit belief that ALP can adequately replace artisanal mining operations. Livelihood‐centered intervention should not necessarily utilize alternative livelihoods as direct behavioural change instruments.

Substitution in a sense

The Reference Principle (RP) states that co-referring expressions are everywhere intersubstitutable salva congruitate. On first glance, (RP) looks like a truism, but a truism with some bite: (RP) transforms difficult philosophical questions about co-reference into easy grammatical questions about substitutability. This has led a number of philosophers to think that we can use (RP) to make short work of certain longstanding metaphysical debates. For example, it has been suggested that all we need to do to show that the predicate ‘( ) is a horse’ does not refer to a property is point out that ‘( ) is a horse’ and ‘the property of being a horse’ are not everywhere intersubstitutable salva congruitate. However, when we understand ‘substitution’ in the simplest and most straightforward way, (RP) is no truism; in fact, natural languages are full of counterexamples to the principle. In this paper, I introduce a new notion of substitution, and then develop and argue for a version of (RP) that is immune to these counterexamples. Along the way I touch on the following topics: the relation between argument forms and their natural language instances; the reification of sense; the difference between terms and predicates; and the relation between reference and disquotation. I end by arguing that my new version of (RP) cannot be used to settle metaphysical debates quite as easily as some philosophers would like.

The politics of justice: Levinas, violence, and the ethical–political relation

In the early and often ignored 1934 essay ‘Reflections on the Philosophy of Hitlerism’, Levinas identifies a historically dominant form of politics rooted in the ontological reduction of the other to the same that provides intellectual justification for physical violence against the other. The ethical relation aims to overcome this political violence by thinking from the alterity of the other. The turn away from the political to the ethical does, however, lead to a problem – the third (le tiers) – that cannot be resolved by the ethical relation and so necessitates a return to the political. The political returned to is not the same as that left, but privileges the ethical relation and involves decisions about how to realize a prior norm: justice. This has given rise to debate in the literature regarding the relationship between the ethical and political that pits an oppositional account against an entwined one. I defend the latter, but argue that it depends upon two issues that are problematic for Levinas’s attempted overcoming of ontological forms of violence. Specifically, his (1) claim that this form of politics entails a ‘good’ form of violence, and (2) insistence that the political decision required to realize the ethically inspired conception of politics is compatible with his theory of substitution. I argue that the former undermines his claim that an ethically inspired politics is fundamentally different to an ontologically inspired one, while the political decision upon which his ethically inspired politics depends is incompatible with his notion of substitution.

Relying on the Vibe of the Thing: The Colombian Constitutional Court's Doctrine on the Substitution of the Constitution

The defense of substantive limits on constitutional change has mainly taken two roads. One has been to claim that certain constitutional provisions cannot ever be changed, though they might be restricted or suspended under some conditions. A second road has been to claim that, ex ante, any provision can be amended, though the constitution’s essential structure either cannot or can only be amended following a more restricted procedure. In other words, this position claims that a “normal” process of constitutional change cannot “substitute” or replace the constitution. Courts have taken part in discussions around these limits. The notion of substitution or replacement—or close relatives—has been invoked by litigants and judges in such different countries as Ireland, Italy, and India, to mention a few. In Latin America, it has been employed in politically salient decisions in the past fifteen years or so by the Colombian Constitutional Court. This paper concerns itself with this notion, and critically analyzes the Court’s invocation of it. The Court has taken pains to present the doctrine on procedural grounds concerning both the constitution’s amendment provisions and the Court’s authorization to supervise changes, and the paper reviews that attempt. Yet the doctrine also deals with substantive questions about the nature and content of the (Colombian) constitution, the activation and limits of constituent power, and judicial review in a democracy. The paper engages these questions as well. What does it mean to say a constitution—and, in particular, the Colombian constitution—cannot be substituted? What exactly is the “constitution” implicated in the analysis? Should the Constitutional Court partake in these discussions? Given both the Court’s current use of the doctrine and the renewed discussions of constituent power in the region, these are all timely questions.

“After you, sir!”: Substitution in Kant and Levinas

ABSTRACTThis paper compares the later Levinas’ notion of “substitution” with Kant’s account of substitution in Religion within the Boundaries of Mere Reason. Kant’s account is modelled on the Christian doctrine of the vicarious substitution of Christ, and some recent commentators on Levinas have argued that Levinas’ account is also similar to this Christian doctrine. By bringing out what I see as major differences between the two accounts, I show that Levinas’ notion of substitution should not be understood in this way.

POÉTICA DA SUBSTITUIÇÃO

Resumo: O artigo procura desenvolver o tema levinasiano da substituição, central para a compreensão do conjunto da obra do filósofo que propõe a ética como filosofia primeira. Como viés interpretativo toma-se o conceito de literatura menor da obra de Deleuze e Guattari, Kafka: pour une littérature mineure. Sabe-se que a filosofia de Levinas propõe uma crítica radical da ontologia, segundo ele, responsável pelo psiquismo da violência e do mal radical. Mas, uma vez que o discurso filosófico é essencialmente ontológico, a ética como filosofia primeira vai se ver em constante luta e dor da expressão, como diz Levinas. A filosofia de Levinas, como a literatura de Kafka, é o resultado de um processo de estrangulamento ou de impossibilidade. A análise da substituição como uma poética justifica-se por ser tal discurso, ausente de condições, um processo criador. Levinas fala como um autêntico estrangeiro na terra da filosofia: o outro que se apropria da língua nativa de Platão e Aristóteles para comunicar uma filosofia nova. A substituição é o resultado mais bem elaborado desse processo de criação filosófica.Abstract: The article aims to develop Levinas’ notion of substitution, essential to the understanding of his work, in which he proposes Ethics as the first philosophy. It takes the concept of minor literature, in the work of Deleuze and Guattari, Kafka: pour une littérature mineure, as its interpretive framework. The philosophy of Levinas is known to propose a radical critique of ontology that, according to him, is responsible for the psychological trend to violence and for the radical evil. However, considering the essentially ontological character of philosophical discourse, Ethics as first philosophy will, according to Levinas, be constantly struggling and suffering in an attempt to express itself. Levinas’ philosophy, as well as Kafka’s literature, are the result of a process of strangling of discourse or the proof of its impossibility. The analysis of substitution as poetics is justified by the fact that such discourse is, because without any conditions, a creative process. Levinas speaks as a genuine stranger in the land of philosophy, as the other who uses the language of Plato and Aristotle to transmit a brand new philosophy. Substitution being the most successful result of this creative.

Do similarities or differences between CEO leadership and organizational culture have a more positive effect on firm performance? A test of competing predictions.

This study examines the nature of the interaction between CEO leadership and organizational culture using 2 common metathemes (task and relationship) in leadership and culture research. Two perspectives, similarity and dissimilarity, offer competing predictions about the fit, or interaction, between leadership and culture and its predicted effect on firm performance. Predictions for the similarity perspective draw upon attribution theory and social identity theory of leadership, whereas predictions for the dissimilarity perspective are developed based upon insights from leadership contingency theories and the notion of substitutability. Hierarchical regression results from 114 CEOs and 324 top management team (TMT) members failed to support the similarity hypotheses but revealed broad support for the dissimilarity predictions. Findings suggest that culture can serve as a substitute for leadership when leadership behaviors are redundant with cultural values (i.e., they both share a task- or relationship-oriented focus). Findings also support leadership contingency theories indicating that CEO leadership is effective when it provides psychological and motivational resources lacking in the organization's culture. We discuss theoretical and practical implications and delineate directions for future research. (PsycINFO Database Record

Reframing the concept of alternative livelihoods.

Alternative livelihood project (ALP) is a widely used term for interventions that aim to reduce the prevalence of activities deemed to be environmentally damaging by substituting them with lower impact livelihood activities that provide at least equivalent benefits. ALPs are widely implemented in conservation, but in 2012, an International Union for Conservation of Nature resolution called for a critical review of such projects based on concern that their effectiveness was unproven. We focused on the conceptual design of ALPs by considering their underlying assumptions. We placed ALPs within a broad category of livelihood‐focused interventions to better understand their role in conservation and their intended impacts. We dissected 3 flawed assumptions about ALPs based on the notions of substitution, the homogenous community, and impact scalability. Interventions based on flawed assumptions about people's needs, aspirations, and the factors that influence livelihood choice are unlikely to achieve conservation objectives. We therefore recommend use of a sustainable livelihoods approach to understand the role and function of environmentally damaging behaviors within livelihood strategies; differentiate between households in a community that have the greatest environmental impact and those most vulnerable to resource access restrictions to improve intervention targeting; and learn more about the social–ecological system within which household livelihood strategies are embedded. Rather than using livelihood‐focused interventions as a direct behavior‐change tool, it may be more appropriate to focus on either enhancing the existing livelihood strategies of those most vulnerable to conservation‐imposed resource access restrictions or on use of livelihood‐focused interventions that establish a clear link to conservation as a means of building good community relations. However, we recommend that the term ALP be replaced by the broader term livelihood‐focused intervention. This avoids the implicit assumption that alternatives can fully substitute for natural resource‐based livelihood activities.

Going for the Gold versus Distributing the Green: Foreign Policy Substitutability and Complementarity in Status Enhancement Strategies

Status and the relative ranking of states in international politics seem to be salient concerns for most foreign policymakers.2 Yet, the literature on how status rankings are attributed to states remains as scarce as research on the strategies utilized by states to maintain or enhance the status they are attributed. While there is more research conducted on both status attribution and status competition regarding major powers and rising powers,3 little systematic attention has focused on the larger population of states in international politics.4 One of the latest contributions to this literature is an analysis of successful competition in the summer Olympics as a state status-seeking strategy (Rhamey and Early 2013). The authors find that winning Olympic medals and hosting the Olympics have significant impacts on states' status rankings. We do not question these results and, in fact, applaud the effort to map out one strategy of status enhancement. However, we raise a cautionary note about the complex foreign policy choices faced by states as they may pursue additional status. Within the toolbox of policymakers, there are a variety of policies with which to pursue the same objective in international politics, be it status enhancement or other goals. Typically, this interchangeability of strategies has been referred to in the literature as foreign policy substitutability (Most and Starr 1984; Morgan and Palmer 2000; Palmer and Bhandari 2000). If in fact there are numerous policy options available for seeking enhanced status, then these policies should be examined—and evaluated—using a comparative policy perspective in order to determine whether or not they are substitutable and possibly complementary policies.

Analysing and determining substitutability of different granularity Web services

Substitutability of Web service is the key aspect for ensuring reliability of Web service-oriented software. Along with more large and coarse granularity services appear across the Internet continuously, it has become a new challenge that how to determine the substitutability between different granularity services. In this paper, we propose the notion of interface inverted dependence to reveal all functions and business logic of large granularity services. A formal model is bulit by extending the Martin-Löf's type theory. The model can clearly describe both large and small granularity services from three aspects: syntax, semantics, and behaviour. Based on the formalization, we introduce the notions of substitutability between different granularity services with different stringency through considering the context of services. In order to judge the substitutability, a mechanism based on subtyping theory is proposed. At last, the case study is given to show the effectiveness of the proposed substitutability.

Capital as a Single Magnitude and the Orthodox Theory of Distribution in Some Writings of the Early 1930s

Some writings of the early 1930s by Dennis Robertson and John Hicks present, with a clarity not easily found elsewhere, the reasons why marginalist economists, who until recent decades normally treated capital as a single magnitude, were in fact compelled to do so. This paper focuses on a first reason that emerges from these writings: namely the fact that only this treatment of capital can lend plausibility to the notion of substitutability between factors of production on which the orthodox theory of distribution is built.

Correctness of Specialization-Based Parallel Processing Algorithm for Constraint Satisfaction Problem

The purpose of this paper is to discuss the correctness of a method for constructing parallel processing programs from a problem description. The framework we adopt for this purpose is Equivalent Transformation Framework (ETF), which regards computation as transformation of definite clauses. In the framework, a problem's domain knowledge and a query are described in definite clauses, and its meaning is defined by a model of the set of definite clauses. Then meaning-preserving transformation rules for the query are generated. We propose a parallel processing method based on “specialization”, a part of operation in the transformations, and discuss new parallel processing method based on the specialization that maintains correctness of the computation. The specialization is generalized notion of substitution in logic programming, and it allows more rich representation. We examine the correctness of our approach based the specialization.

How many roads lead to Rome? Equifinality set-size and commitment to goals and means

Four studies examined the relation between the number of equifinal means to a goal, actors' commitment to that goal, and their commitment to the means. In Study 1, participants freely generated varying number of means to two of their work goals. In Study 2, they generated social means to their goals (people they viewed as helpful to goal attainment). In Studies 3 and 4, the number of means to participants' goals was experimentally manipulated. All four studies found that means commitment is negatively related, whereas goal commitment is positively related, to means number. Consistent support was also obtained for the notion that the relation between means number and goal commitment is mediated by the expectancy of goal attainment, and by goal importance. Conceptual and practical implications of the findings were considered that link together the notions of substitutability and dependency within a goal systemic framework. Copyright © 2010 John Wiley & Sons, Ltd.

Forecast and rolling horizons under demand substitution and production changeovers: analysis and insights

For most multi-period decision-making problems, it is generally well accepted that the influence of information about later periods on the optimal decision in the current period reduces as we move farther into the future. If and when this influence reduces to zero, the corresponding problem horizon is referred to as a forecast horizon. For real businesses, the problem of obtaining a minimal forecast horizon becomes relevant because the task of estimating reliable data for future periods gets progressively more challenging and expensive. This article investigates forecast horizons for a two-product dynamic lot-sizing model under (i) the possibility of substitution in one direction; that is, one product can be used to satisfy the demand of the other product but not vice versa; and (ii) a changeover cost when production switches from one product to the other. It is assumed that only one of the two products can be produced in a period. The notion of substitution, due to the inherent flexibility it offers, has recently been recognized as an effective tool to improve the efficiency of multi-product inventory systems. The concept of regeneration points is used to justify the use of a practically relevant restricted version of the problem to obtain forecast horizons. A dynamic programming-based polynomial-time algorithm for the restricted version is developed and, subsequently, an efficient procedure for obtaining minimal forecast horizons by establishing the monotonicity of the regeneration points is obtained. Using a comprehensive test bed of instances, useful insights are obtained on the impact of substitution and production changeovers on the length of the minimal forecast horizons. Finally, for infinite-horizon problems, a practical rolling-horizon procedure is developed that uses forecasting costs to balance the benefit of additional information. It is shown that, instead of fixing the duration of the rolling horizon at a predetermined value, changing it dynamically based on the lengths of the minimal forecast horizons can significantly reduce the combined production and forecasting cost. [Supplemental materials are available for this article. Go to the publisher’s online edition of IIE Transactions to view the supplemental file.]

Forecast and Rolling Horizons Under Demand Substitution and Production Changeovers: Analysis and Insights

For most multi-period decision-making problems, it is generally well-accepted that the influence of information about later periods on the optimal decision in the current period reduces as we move farther into the future. If and when this influence reduces to zero, the corresponding problem horizon is referred to as a forecast horizon. For real businesses, the problem of obtaining a minimal forecast horizon becomes relevant because the task of estimating reliable data for future periods gets progressively challenging and expensive. We investigate forecast horizons for a two-product dynamic lot-sizing problem under (a) the possibility of substitution in one direction; that is, one product can be used to satisfy the demand of the other product but not vice-versa and (b) a changeover cost when production switches from one product to the other. The notion of substitution, due to the inherent flexibility it offers, has recently been recognized as an effective tool to improve the efficiency of multi-product inventory systems. Using the concept of regeneration points, we first justify the use of a practically-relevant restricted version of the problem for obtaining forecast horizons. Next, we develop a dynamic programming-based polynomial-time algorithm for the restricted version and, subsequently, an efficient procedure for obtaining minimal forecast horizons by establishing the monotonicity of the regeneration points. Using a comprehensive test bed of instances, we obtain useful insights on the impact of substitution and production changeovers on the length of the minimal forecast horizons. Finally, for infinite-horizon problems, we develop a practical rolling-horizon procedure that uses forecasting costs to balance the benefit of additional information. We show that, instead of fixing the duration of rolling horizon at a pre-determined value, changing it dynamically based on the lengths of the minimal forecast horizons can significantly reduce the combined production and forecasting cost.

Confluence and termination of fuzzy relations

Confluence and termination are essential properties connected to the idea of rewriting and substituting which appear in abstract rewriting systems. The aim of the present paper is to investigate confluence, termination, and related properties from the point of view of fuzzy logic leaving the ordinary notions a particular case when the underlying structure of truth degrees is two-valued Boolean algebra. The main motivation of this study is the fact that in several natural situations, the notion of substitutability is inherently fuzzy rather than crisp.

Explicit substitutions calculi with one step Eta-reduction decided explicitly

It has long been argued that the notion of substitution in the λ-calculus needs to be made explicit. This resulted in many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions have been atomised. In contrast to the great variety of developments for making explicit formalisations of the Beta rule, less work has been done for giving explicit definitions of the conditional Eta rule. In this paper constructive Eta rules are proposed for both the λσand the λse-calculi of explicit substitutions. Our results can be summarised as follows: 1) we introduce constructive and explicit definitions of the Eta rule in the λσand the λse-calculi, 2) we prove that these definitions are correct and preserve basic properties such as subject reduction. In particular, we show that the explicit definitions of the eta rules coincide with the Eta rule for pure λ-terms and that moreover, their application is decidable in the sense that Eta redices are effectively detected (and contracted). The formalisation of these Eta rules involves the development of specific calculi for explicitly checking the condition of the proposed Eta rules while constructing the Eta contractum.