In this paper, we develop the system LZF of set theory with the unrestricted comprehension in full linear logic and show that LZF is a conservative extension of ZF– i.e., the Zermelo-Fraenkel set theory without the axiom of regularity. We formulate LZF as a sequent calculus with abstraction terms and prove the partial cut-elimination theorem for it. The cut-elimination result ensures the subterm property for those formulas which contain only terms corresponding to sets in ZF–. This implies that LZF (...) is a conservative extension of ZF– and therefore the former is consistent relative to the latter. (shrink)

An observer attempts to infer the unobserved ranking of two ideal objects, A and B, from observed rankings in which these objects are `accompanied' by `noise' components, C and D. In the first ranking, A is accompanied by C and B is accompanied by D, while in the second ranking, A is accompanied by D and B is accompanied by C. In both rankings, noisy-A is ranked above noisy-B. The observer infers that ideal-A is ranked above ideal-B. This commonly used (...) inference rule is formalized for the case in which A,B,C,D are sets. Let X be a finite set and let be a linear ordering on 2X. The following condition is imposed on . For every quadruple (A,B,C,D)∈Y, where Y is some domain in (2X)4, if and , then . The implications and interpretation of this condition for various domains Y are discussed. (shrink)

In this research, we shed new light on the empirical link between corporate social performance (CSP) and corporate financial performance (CFP) via the application of empirical models and methods new to the CSP–CFP literature. Applying advanced financial models to a uniquely constructed panel dataset, we demonstrate that a significant overall CSP–CFP relationship exists and that this relationship is, in part, conditioned on firms’ industry-specific context. To accommodate the estimation of time-invariant industry and industry-interaction effects, we estimate linear mixed models (...) in our test of the CSP–CFP relationship. Our results show both a significant overall CSP effect as well as significant industry effects between CSP and CFP. In conflict with expectations, the unweighted average effect of CSP on CFP is negative. Our industry analysis, however, shows that in over 17% of the industries in our sample, the effect of CSP on CFP for socially responsible firms is positive. We also examine the multidimensional nature of the CSP construct in an industry context by exploring the CSP dimension–industry nexus and identify dimensions of social performance that are associated with either better or worse financial performance. Our results confirm the existence of disparate CSP dimension–industry effects on CFP, thus our results provide important and actionable information to decision makers considering whether and how to commit corporate resources to social performance. (shrink)

In [1], Bull gave completeness proofs for three axiom systems with respect to tense logic with time linear and rational, real and integral. The associated varieties, Dens, Cont and Disc, are generated by algebras with frames {ℚ, }, {ℝ, } and {ℤ, }, respectively. In this paper we consider the subvariety [MATHEMATICAL SCRIPT CAPITAL V] generated by the finite members of Disc. We prove that V is locally finite and we determine its lattice of subvarieties. We also prove that (...) [MATHEMATICAL SCRIPT CAPITAL V] = Disc ∩ Dens = Disc ∩ Cont. (shrink)

We carry out a systematic investigation of the definability of linear order on classes of finite rigid structures. We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in finite model theory, such as least fixpoint logic LFP, partial fixpoint logic PFP, infinitary logic Lω∞ω with a finite number of variables, as well as the closures of these logics under implicit definitions. Moreover, we show that the upper and (...) lower bounds established here cannot be made substantially tighter, unless outstanding conjectures in complexity theory are resolved at the same time. (shrink)

This paper describes an application of linear logic programming to the frame problem. This treatment has both practical and conceptual advantages over standard treatments: it is computationally efficient, and this efficiency arises because linear logic respects the identity, or otherwise, of situations.

While every endpointed interval I in a linear order J is, considered as a linear order in its own right, trivially Muchnik‐reducible to J itself, this fails for Medvedev‐reductions. We construct an extreme example of this: a linear order in which no endpointed interval is Medvedev‐reducible to any other, even allowing parameters, except when the two intervals have finite difference. We also construct a scattered linear order which has many endpointed intervals Medvedev‐incomparable to itself; the only (...) other known construction of such a linear order yields an ordinal of extremely high complexity, whereas this construction produces a low‐level‐arithmetic example. Additionally, the constructions here are “coarse” in the sense that they lift to other uniform reducibility notions in place of Medvedev reducibility itself. (shrink)

We study an extension of Stackelberg’s model in which many firms can produce at many different times. Demand is affine, while cost is linear. In this setting, we investigate whether Stackelberg’s results in a two-firm game are robust when the number of firms increases. We show that firms may not need to anticipate further entries, leaders might earn less than in the simultaneous game, and, whatever its cost and its time of entry, the firm’s entry always improves welfare.

Utilization of renewable energies in association with energy storage is increased in different applications such as electrical vehicles, electric boats, and smart grids. A robust controller strategy plays a significant role to optimally utilize the energy resources available in a power system. In this paper, a suitable controller for the energy resources of an EB which consists of a 5 kW solar power plant, 5 kW fuel cell, and 2 kW battery package is designed based on the linear parameter (...) varying controller design approach. Initially, all component dynamics are augmented, and by exploiting the sector-nonlinearity approach, the LPV representation is derived. Then, the LPV control method determines the suitable gains of the states’ feedbacks to provide the required pulse commands of the boost converters of the energy resources to regulate the DC-link voltage and supply the power of EB loads. Comparing with the state-of-the-art nonlinear control methods, the developed control approach assures the stability of the overall system, as it considers all component dynamics in the design procedure. The real-time simulation results demonstrate the performance of the designed controller in the creation of a constant DC-link voltage. (shrink)

Slaman and Wehner have constructed structures which distinguish the computable Turing degree 0 from the noncomputable degrees, in the sense that the spectrum of each structure consists precisely of the noncomputable degrees. Downey has asked if this can be done for an ordinary type of structure such as a linear order. We show that there exists a linear order whose spectrum includes every noncomputable Δ 0 2 degree, but not 0. Since our argument requires the technique of permitting (...) below a Δ 0 2 set, we include a detailed explanation of the mechanics and intuition behind this type of permitting. (shrink)

We consider finite multisets over some set of urelements equipped only with additive union [uplus ] and show that the {[otimes], -0}-Horn fragment of Intuitionistic Linear Logic has a sound and complete interpretation in them by interpreting [otimes] as [uplus ]. The linear implication is interpreted by ordered pairs of multisets expressing replacement. The operator ! is also defined in an asymptotic way. Soundness, completeness and partial completeness results are proved for the {×, -0, !}-Horn fragment as well.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

In response to recent suggestions that the phenomena of consciousness may be related to those described by quantum theory, it is argued that distinctive features of brain activity are more typical of nonlinear classical dynamics than of quantum dynamics, which is a linear theory. Thus natural scientists should turn to hierarchies of nonlinear classical systems rather than quantum theory for explanations of the brain's mysterious behaviour.

The aim of this paper is to give one kind of internal proportional systems with general representation and without closure and finiteness assumptions. First, we introduce the notions of internal proportional system and of general representation. Second, we briefly review the existing results which motivate our generalization. Third, we present the new systems, characterized by the fact that the linear order induced by the comparison weak order ≥ at the level of equivalence classes is also a weIl order. We (...) prove the corresponding representation theorem and make some comments on strong limitations of uniqueness; we present in an informal way a positive result, restricted uniqueness for what we call connected objects. We conclude with some final remarks on the property that characterizes these systems and on three possible empirical applications. (shrink)

The present paper introduces and studies the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋn of n-linear weakly Heyting algebras. It corresponds to the algebraic semantic of the strict implication fragment of the normal modal logic K with a generalization of the axiom that defines the linear intuitionistic logic or Dummett logic. Special attention is given to the variety [MATHEMATICAL SCRIPT CAPITAL W]ℋ2 that generalizes the linear Heyting algebras studied in [10] and [12], and the linear Basic algebras introduced (...) in [2]. (shrink)

Linear mixed-effects models (LMMs) are increasingly being used for data analysis in cognitive neuroscience and experimental psychology, where within-participant designs are common. The current article provides an introductory review of the use of LMMs for within-participant data analysis and describes a free, simple, graphical user interface (LMMgui). LMMgui uses the package lme4 (Bates et al., 2014a, b ) in the statistical environment R (R Core Team).

We show that the maximal linear extension theorem for well partial orders is equivalent over RCA0 to ATR0. Analogously, the maximal chain theorem for well partial orders is equivalent to ATR0 over RCA0.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

Ethical attitudes and behaviour are complex. This complexity extends to the influencers operating at different levels both outside and within the organisation, and in different combinations for different individuals. There is hence a growing need to understand the proximal and distal influencers of ethical attitudes, and how these operate in concert at the individual, organisational, and societal levels. Few studies have attempted to combine these main research streams and systematically examine their combined impact. The minority of studies that have taken (...) a combined approach have often done so using conventional statistical and analytical techniques which imply linearity between variables—a situation that rarely exists in business settings and is likely to lead to simplistic or even erroneous conclusions. Applying a fuzzy-set qualitative comparative analysis approach, this paper reports on the mutual and simultaneous influence of individual demographic factors, as well as proximal and distal factors stemming from within and outside the work environment to understand individuals’ ethical views within the workplace. The multiple configurations that emerged reveal the complex nature of influencers of ethical attitudes, and reinforce the view that “one size does not fit all”. We discuss these implications together with managerial recommendations and future research directions. (shrink)