Classical results of additive number theory lead to the undecidability of the existence of solutions for diophantine equations in given special sets of integers. Those sets which are images of polynomials are covered by a more general result in the second section. In contrast, restricting diophantine equations to images of exponential functions with natural bases leads to decidable problems, as proved in the third section.

This study examined the relationship between person–organization (PO) fit on prosocial identity (prosocial PO fit) and various employee outcomes. The results of polynomial regression analysis based on a sample of 589 hospital employees, which included medical doctors, nurses, and staff, indicate joint effects of personal and organizational prosocial identity on the development of a sense of organizational identification and on the engagement in prosocial behaviors toward colleagues, organizations, and patients. Specifically, prosocial PO fit had a curvilinear relationship with organizational (...) identification, such that organizational identification increased as organizational prosocial characteristics increased toward personal prosocial identity and then decreased when the organizational prosocial characteristics exceeded the personal prosocial identity. In addition, organizational identification and prosocial behaviors increased as both personal and organizational prosocial identity increased from low to high. (shrink)

This is an abstract of the paper to be submitted to Houston Journal of Mathematics. Our nomenclature and notation will be basically those of [3]. We shall consider algebras of type : T ! N, where T is a nonempty set, and N the set of all positive integers. By V we denote the set of all variables occurring in a polynomial symbol p. An identity p = q is called strongly non-regular if it is of the form p (...) = x for some binary polynomial symbol p, such that x; y 2 V and x =6 y. Let R denote the set of all regular identities of type . If K is a class of algebras of type , then E denotes the set of all identities satised by all algebras in K. We put R = E \ R. A variety K is called strongly non-regular if E contains some strongly non-regular identity. If is a set of identities of type , then K denotes the variety of algebras of type generated by ; E() will be the set of all identities which are consequences of . We put R() = E() \ R. We write ` e if there exists a nite proof of e starting from. (shrink)

We revisit the notion of intuitionistic equivalence and formal proof representations by adopting the view of formulas as exponential polynomials. After observing that most of the invertible proof rules of intuitionistic (minimal) propositional sequent calculi are formula (i.e., sequent) isomorphisms corresponding to the high‐school identities, we show that one can obtain a more compact variant of a proof system, consisting of non‐invertible proof rules only, and where the invertible proof rules have been replaced by a formula normalization procedure. Moreover, (...) for certain proof systems such as the G4ip sequent calculus of Vorob'ev, Hudelmaier, and Dyckhoff, it is even possible to see all of the non‐invertible proof rules as strict inequalities between exponential polynomials; a careful combinatorial treatment is given in order to establish this fact. Finally, we extend the exponential polynomial analogy to the first‐order quantifiers, showing that it gives rise to an intuitionistic hierarchy of formulas, resembling the classical arithmetical hierarchy, and the first one that classifies formulas while preserving isomorphism. (shrink)

Some simple algebraic properties, described by universally quantified disjunctions of special identities, are established. Such sentences seem to be useful for an investigation on finite algebras and its products. These considerations are exemplified by results concerning distributive lattices. By P the polynomial algebra of a finite type t is understood. P is the n-ary polynomial algebra . No notational distinction is made between an algebra and its underlying set. Similarly by the same symbol is denoted each (...) class='Hi'>polynomial and its realization in a given algebra. (shrink)

We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to \(K\) -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a (...) polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry. (shrink)

We show that arbitrary tautologies of Johansson’s minimal propositional logic are provable by “small” polynomial-size dag-like natural deductions in Prawitz’s system for minimal propositional logic. These “small” deductions arise from standard “large” tree-like inputs by horizontal dag-like compression that is obtained by merging distinct nodes labeled with identical formulas occurring in horizontal sections of deductions involved. The underlying geometric idea: if the height, h(∂), and the total number of distinct formulas, ϕ(∂), of a given tree-like deduction ∂ of a (...) minimal tautology ρ are both polynomial in the length of ρ, |ρ|, then the size of the horizontal dag-like compression ∂ᶜ is at most h(∂)×ϕ(∂), and hence polynomial in |ρ|. That minimal tautologies ρ are provable by tree-like natural deductions ∂ with |ρ|-polynomial h(∂) and ϕ(∂) follows via embedding from Hudelmaier’s result that there are analogous sequent calculus deductions of sequent ⇒ρ. The notion of dag-like provability involved is more sophisticated than Prawitz’s tree-like one and its complexity is not clear yet. Our approach nevertheless provides a convergent sequence of NP lower approximations of PSPACE-complete validity of minimal logic. (shrink)

We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function of the form x (...) cxr, c ≠ 0; in particular, this structure is polynomially bounded. Furthermore, given any definable function f:U → with U open in n, if α ε U and f is infinitely differentiable at α, then f is real analytic in a neighborhood of α. (shrink)

This paper is devoted to the algebraization of an arithmetical predicate introduced by S. Feferman. To this purpose we investigate the equational class of Boolean algebras enriched with an operation (g=rtail), which translates such predicate, and an operation τ, which translates the usual predicate Theor. We deduce from the identities of this equational class some properties of (g=rtail) and some ties between (g=rtail) and τ; among these properties, let us point out a fixed-point theorem for a sufficiently large class (...) of (g=rtail)-τ polynomials. The last part of this paper concerns the duality theory for (g=rtail)-τ algebras. (shrink)

In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of n point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial (...) wave approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions. (shrink)

Vector logic is a mathematical model of the propositional calculus in which the logical variables are represented by vectors and the logical operations by matrices. In this framework, many tautologies of classical logic are intrinsic identities between operators and, consequently, they are valid beyond the bivalued domain. The operators can be expressed as Kronecker polynomials. These polynomials allow us to show that many important tautologies of classical logic are generated from basic operators via the operations called Type I and (...) Type II products. Finally, it is described a matrix version of the Fredkin gate that extends its properties to the many-valued domain, and it is proved that the filtered Fredkin operators are second degree Kronecker polynomials that cannot be generated by Type I or Type II products. (shrink)

In 2004 Atserias, Kolaitis, and Vardi proposed $\text {OBDD}$ -based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of an identically false $\text {OBDD}$ from $\text {OBDD}$ s representing clauses of the initial formula. All $\text {OBDD}$ s in such proofs have the same order of variables. We initiate the study of $\text {OBDD}$ based proof systems that additionally contain a rule that allows changing the order in $\text {OBDD}$ s. At first we consider a proof (...) system $\text {OBDD}$ that uses the conjunction rule and the rule that allows changing the order. We exponentially separate this proof system from $\text {OBDD}$ proof system that uses only the conjunction rule. We prove exponential lower bounds on the size of $\text {OBDD}$ refutations of Tseitin formulas and the pigeonhole principle. The first lower bound was previously unknown even for $\text {OBDD}$ proofs and the second one extends the result of Tveretina et al. from $\text {OBDD}$ to $\text {OBDD}$.In 2001 Aguirre and Vardi proposed an approach to the propositional satisfiability problem based on $\text {OBDD}$ s and symbolic quantifier elimination $ algorithms). We augment these algorithms with the operation of reordering of variables and call the new scheme $\text {OBDD}$ algorithms. We notice that there exists an $\text {OBDD}$ algorithm that solves satisfiable and unsatisfiable Tseitin formulas in polynomial time, but we show that there are formulas representing systems of linear equations over $\mathbb {F}_2$ that are hard for $\text {OBDD}$ algorithms. Our hard instances are satisfiable formulas representing systems of linear equations over $\mathbb {F}_2$ that correspond to checksum matrices of error correcting codes. (shrink)

How can we think about identities in the wake of feminist critiques of identity and identity politics? Allison Weir rethinks conceptions of individual and collective identities in relation to freedom.

The paper looks into a participatory art project developed in two women’s refuges, one in Portugal and the other in England. Addressing liminality after surviving violence, the project constructs a portrait of survivors, utilising feminist pragmatist aesthetics to transfer representational agency to participants. Against a background where women who have experienced domestic violence have often been portrayed in simplistic representations of damaged beauty, the study sought to gain a deeper understanding by holding visual art workshops with participants (Portugal, England) and (...) analysing data from verbal testimonies (England). The paper contributes to a discussion of the practical issues negotiated when establishing a representational power balance between researchers and research participants. It does this by providing a critical discussion of three ethical problems emerging in relation to the project. The first concerns the dominant representation of survivors, the second the need for participants’ anonymity and the third the challenges of inequality in qualitative research. (shrink)

Hilde Lindemann Nelson focuses on the stories of groups of people--including Gypsies, mothers, nurses, and transsexuals--whose identities have been defined by those with the power to speak for them and to constrain the scope of their actions. By placing their stories side by side with narratives about the groups in question, Nelson arrives at some important insights regarding the nature of identity. She regards personal identity as consisting not only of how people view themselves but also of how others (...) view them. These perceptions combine to shape the person's field of action. If a dominant group constructs the identities of certain people through socially shared narratives that mark them as morally subnormal, those who bear the damaged identity cannot exercise their moral agency freely.Nelson identifies two kinds of damage inflicted on identities by abusive group relations: one kind deprives individuals of important social goods, and the other deprives them of self-respect. To intervene in the production of either kind of damage, Nelson develops the counterstory, a strategy of resistance that allows the identity to be narratively repaired and so restores the person to full membership in the social and moral community. By attending to the power dynamics that constrict agency, Damaged Identities, Narrative Repair augments the narrative approaches of ethicists such as Alasdair MacIntyre, Martha Nussbaum, Richard Rorty, and Charles Taylor. (shrink)

In the heated debates over identity politics, few theorists have looked carefully at the conceptualizations of identity assumed by all sides. Visible Identities fills this gap. Drawing on both philosophical sources as well as theories and empirical studies in the social sciences, Martín Alcoff makes a strong case that identities are not like special interests, nor are they doomed to oppositional politics, nor do they inevitably lead to conformism, essentialism, or reductive approaches to judging others. Identities are (...) historical formations and their political implications are open to interpretation. But identities such as race and gender also have a powerful visual and material aspect that eliminativists and social constructionists often underestimate.Visible Identities offers a careful analysis of the political and philosophical worries about identity and argues that these worries are neither supported by the empirical data nor grounded in realistic understandings of what identities are. Martín Alcoff develops a more realistic characterization of identity in general through combining phenomenological approaches to embodiment with hermeneutic concepts of the interpretive horizon. Besides addressing the general contours of social identity, Martín Alcoff develops an account of the material infrastructure of gendered identity, compares and contrasts gender identities with racialized ones, and explores the experiential aspects of racial subjectivity for both whites and non-whites. In several chapters she looks specifically at Latino identity as well, including its relationship to concepts of race, the specific forms of anti-Latino racism, and the politics of mestizo or hybrid identity. (shrink)

Rigid designators for concrete objects and for properties -- On the coherence of the distinction -- On whether the distinction assigns to rigidity the right role -- A uniform treatment of property designators as singular terms -- Rigid appliers -- Rigidity - associated arguments in support of theoretical identity statements: on their significance and the cost of its philosophical resources -- The skeptical argument impugning psychophysical identity statements: on its significance and the cost of its philosophical resources -- The skeptical (...) argument further examined: on resources, allegedly overlooked, for confirming psychological identities. (shrink)

Hermeneutical injustice is being unjustly prevented from making sense of one’s experiences, identity, or circumstances and/or communicating about them. The literature focusses almost exclusively on whether people have access to adequate conceptual resources. In this paper, we discuss a different kind of hermeneutical struggle caused by stigma. We argue that in some cases of hermeneutic injustice people have access to hermeneutical resources apt to understand their identity but reject employing these due to the stigma attached to the identity. We begin (...) with a reinterpretation of one of the cases discussed in the literature, Edmund White’s novel A Boy’s Own Story. We argue that in this case hermeneutic resources are available but are rejected due to the stigma attached to homosexuality. We then present two analogous kinds of cases: alcohol addiction and being the victim of intimate partner violence. Here, too, hermeneutic injustice occurs because of stigma attached to an identity rather than unavailability of resources. We close by suggesting that these cases may, additionally, involve the wrong of Tightlacing: by meddling with their self-conception, stigma can manipulate individuals into a view of themselves that licenses inappropriate demands on them and makes them complicit in an erasure of their identities. (shrink)

… our faults do not allow our qualities to show themselves to best effect. That is why, at the moment, Brazilians are a people of intermittent qualities and permanent faults.Mário de Andrade, Essai sur la musique brésilienne, 1928This paper sets out to discuss the use and power of music in representing social identities, concentrating on the more specific case of the Brazilian nation, which has made itself a complex and all-embracing socio-political unit in spite of the great diversity and (...) the great inequalities to be found within its borders. It is well known that what appears to be its most uniform feature, the use of a dominant language, is actually quite fragmented, due to the influence of various co-existing systems of production, cultural models and social hierarchies, which change on a daily basis. Although this diversity seems to be underwritten by daily practice and independent of debate and official encouragement, the same cannot be said of the search for national unity. It is obvious in the case of most of the action undertaken with this end in mind, that questions such as exclusion and the imbalance and arbitrariness of power have been eliminated. Besides, certain alert individuals are wary of this insistence on the construction of a nation, since the role of the old national states throughout the world seems to be disintegrating in the face of the proliferation and growing importance of social, economic and cultural relations at a supranational level. It is therefore hardly surprising that the twentieth century is considered to be a milestone in both the rise and fall of efforts to achieve Brazilian national unity. Amongst these efforts, music has played a prominent role, as I shall endeavour to show. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 209 Seiten: 149-165.

Some feminists have criticized Judith Butler's theory of performativity for providing an insufficient account of agency. In this article I first defend her against such charges by appealing to two themes central to Hans-Georg Gadamer's hermeneutics. I compare her emphasis on the sociohistorical nature of agency with Gadamer's insistence on the historical nature of knowledge, and I examine the significance Butler assigns to repetition and note its affinities with Gadamer's conception of play. In the final part of the article I (...) argue that in spite of providing an adequate account of agency, Butler's theory of performativity provides no way to allow us to evaluate performances. I show how Gadamer's account of festival, which builds on his concept of play, is useful in helping us make sense of how we might delineate true from false performances, and thus identities. (shrink)