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 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)

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)

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)

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)

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)

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)

Academic dishonesty is a persistent problem in the American educational system. The present investigation examined how reports of academic cheating related to students' emphasis on their moral identities and their sensitivity to social evaluation. Seventy college students at a large southeastern university completed a battery of surveys. Symptoms of social anxiety were positively correlated with recall of academic cheating. Additionally, relative to students who placed less importance on their moral identities, students who placed more importance on their moral (...) identities recalled significantly fewer instances of cheating. In summary, these findings suggest that students are less likely to cheat on their school work when they place greater emphasis on their moral identity and are less sensitive to social evaluation. Practical interventions to rampant cheating in American schools are discussed. (shrink)

This essay outlines one way to conceptualise the relation between cultural identity, collective memory, and artifacts. It starts by characterising the notion of cultural identity as our membership to cultural groups and briefly explores the relation between cultural and narrative identity (section 2). Next, it presents how human memory is conceptualised on an individual and collective level (section 3) and then distinguishes between small-scale and large-scale collective memory (section 4). Having described cultural identity and collective memory, it argues that cultural (...) identity is materialised in the environment when we retrieve and construct collective memories by integrating information from our biological memory with information in artifacts or in other people’s embodied brains (section 5). This essay ends with analysing how materialised cultural identities are constructed by using a niche construction approach from evolutionary biology (section 6). (shrink)

Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar (...) model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article. (shrink)

This essay outlines one way to conceptualise the relation between cultural identity, collective memory, and artifacts. It starts by characterising the notion of cultural identity as our membership to cultural groups and briefly explores the relation between cultural and narrative identity (section 2). Next, it presents how human memory is conceptualised on an individual and collective level (section 3) and then distinguishes between small-scale and large-scale collective memory (section 4). Having described cultural identity and collective memory, it argues that cultural (...) identity is materialised in the environment when we retrieve and construct collective memories by integrating information from our biological memory with information in artifacts or in other people’s embodied brains (section 5). This essay ends with analysing how materialised cultural identities are constructed by using a niche construction approach from evolutionary biology (section 6). (shrink)

Trans studies constitute part of the coming-to-voice of transpeople, long the theorized and researched objects of sexology, psychiatry, and feminist theory. Sandy Stone’s pioneering, “The Empire Strikes Back: A Posttranssexual Manifesto” sought the end of monolithic medical and feminist accounts of transsexuality to reveal a multiplicity of trans-authored narratives. My goal is a better understanding of what it is for transpeople to come to this polyvocality. I argue that trans politics ought to proceed with the principle that transpeople have first-person (...) authority (FPA) over their own gender, and I clarify what this means. (shrink)

_Cultures and Identities in Transition_ returns to the roots of analytical psychology, offering a thematic approach which looks at personal and cultural identities in relation to Jung’s own identity and the identities of contemporary Jungians. The book begins with two clinical studies, representing a meeting point between the traditional praxis of Jungian analysis, on the one side, and the current zeitgeist, world events and collective anxieties as impacting on persons in therapy, on the other. An international range (...) of expert contributors go on to discuss topics including: issues of national and personal identity – looking back to a shared history and forward to novel applications of Jungian ideas. Jung’s cross-disciplinary dialogues with Victor White. what the designation "Jungian" actually means. Based on papers given at the joint IAAP and IAJS conference held in Zurich in 2008, this book will be essential reading for all Jungians. (shrink)

Kant has long been taxed with an inability to explain the detailed normative content of our lives by making universalizability the sole arbiter of our values. Korsgaard addresses one form of this critique by defending a Kantian theory amended by a seemingly attractive conception of practical identities. Identities are dependent on the contingent circumstances of each person's world. Hence, obligations issuing from them differ from Kantian moral obligations in not applying to all persons. Still, Korsgaard takes Kantian autonomy (...) to mean the normativity of all obligations is rooted in universalizability. The wealth of values informing our lives is thus said to be accommodated within a Kantian framework.After briefly explaining Korsgaard’s understanding of practical identities and their role in her reformation of Kant's moral philosophy, I argue that she gives an inadequate explanation of how the obligations that arise from a person’s practical identities derive their authority from the person's will. I then consider how her position might be developed to meet this objection in accordance with her allegiance to “constructivism” and I argue that the epistemic commitments of people’s actual identities makes it unlikely that such a development could preserve Kantian autonomy as she interprets it. (shrink)

Kant has long been taxed with an inability to explain the detailed normative content of our lives by making universalizability the sole arbiter of our values. Korsgaard addresses one form of this critique by defending a Kantian theory amended by a seemingly attractive conception of practical identities. Identities are dependent on the contingent circumstances of each person's world. Hence, obligations issuing from them differ from Kantian moral obligations in not applying to all persons. Still, Korsgaard takes Kantian autonomy (...) to mean the normativity of all obligations is rooted in universalizability. The wealth of values informing our lives is thus said to be accommodated within a Kantian framework.After briefly explaining Korsgaard's understanding of practical identities and their role in her reformation of Kant's moral philosophy, I argue that she gives an inadequate explanation of how the obligations that arise from a person's practical identities derive their authority from the person's will. I then consider how her position might be developed to meet this objection in accordance with her allegiance to “constructivism” and I argue that the epistemic commitments of people's actual identities makes it unlikely that such a development could preserve Kantian autonomy as she interprets it. (shrink)

The article by Liudmyla Fylypovych «Religious Identities in Ukraine: formulation of the problem» is devoted to the problem of religious identities, which were activated in modern Ukraine in connection with radical political and civilizational challenges-shifts, and therefore they require deep study.

A popular stance amongst philosophers is one according to which, in Lewis’ words, “identity is utterly simple and unproblematic”. Building from Lewis’ famous passage on the matter, we reconstruct, and then criticize, an argument to the conclusion that identities cannot be grounded. With the help of relatively uncontroversial assumption concerning identity facts, we show that not all identities are equi-fundamental, and, on the contrary, some appear to be provided potential grounding bases using two-level identity criteria. Further potential grounding (...) bases for identities are presented. Identity might be utterly simple and unproblematic, but this is not sufficient to conclude that identities are ungrounded, or fundamental. (shrink)

Journal of Political Philosophy, Volume 30, Issue 3, Page 273-297, September 2022.

Obtaining community consent before conducting genetic research seems to be a way of ensuring that a whole community is not harmed against its wishes—that all Jews, or all African Americans, or all Hutterites are not forced to learn things about themselves they would rather not know, or are not forced into identities they would rather not have. Unfortunately, there are insurmountable problems both in identifying the right representatives of the community and in obtaining their consent.

In this conceptual paper, we draw on social identity theory as a means to bridge individuals’ memberships in social groups with value creation in stakeholder networks defined by a socio-economic issue. To address recent calls for microfoundations of stakeholder theory, we introduce a reconceptualization of stakeholders as social groups to examine how value is defined and interpreted in intergroup processes embedded in an issue-based stakeholder network. We establish a theoretical model of value creation that links individuals’ identification with stakeholder groups (...) to intergroup trust, co-operation, and value creation. Specifically, we argue that the salience of preexisting social identities causes harmful tensions in stakeholder relationships that negatively impact value creation. We then propose that the development of a more inclusive stakeholder identity overcomes these negative intergroup consequences in multistakeholder settings. We discuss the impact on value creation of four stakeholder identity representations based on the salience of specific and superordinate stakeholder groups. The paper concludes with implications of our theoretical model for both research and practice related to value creation in issue-based stakeholder networks. (shrink)

As a consequence of recent changes, health research policies in the United States mandate the inclusion of women and members of racial and ethnic minority groups as experimental subjects in biomedical research. This article analyzes debates that underlie these policies and that concern the medical management of bodies, groups, identities and differences. Much of the uncertainty surrounding these new policies reflects the fact that researchers, physicians, policy makers and health advocates have adopted competing, and often murky, understandings of the (...) nature of sex, gender, racial and ethnic differences, and of the relation of the biological to the social in the manifestation of bodily illness. (shrink)

So-called identity theories that postulate the identity of mental phenomena with brain states are usually associated with materialistic ontology. However, the historical picture of the actual attempts at spelling out the mind–brain identities is more complex. In the eighteenth century such identities were most enthusiastically proposed by dualists , whereas non-reductionistic materialists such as Diderot tried to get along without them. In the nineteenth century physiologists such as Broca, Charcot and Wernicke, who postulated discrete and localizable neural correlates (...) for ideas and mental images, ended up, despite their professed materialism, defending theories that resembled Cartesian schemes and the theories of their eighteenth-century dualistic predecessors. Some problems resulting from the use of these theoretical models postulating local and discrete traces, images or representations in the brain in the context of materialist ontology are obviously related to their dualistic origins and to the fact that they are necessarily bound up with dualistic presuppositions. In the context of the criticism of the nineteenth-century memory trace paradigm it is, however, important to bear in mind that functional localization as such is not dependent on the notion of localizable representations. Nor are materialist theories of the mind necessarily dependent on postulating specific type–type identities between the mental and the physiological. (shrink)

In this article I propose to explore the meanings, mechanisms and issues at stake in the reconstitution of identities which can now be seen taking place in the countries of the post-communist space. We shall consider this space not as a thing in itself, but in terms of its old and new interactions with the countries of western Europe, in order to understand the phenomena of reconstructed identities in general, in the context of their relationship to the period (...) of globalisation in which we now find ourselves. (shrink)

In this paper, I argue that whether, how, and to what extent an experience is transformative is often highly contingent. I then further argue that sometimes social conditions are a major factor in whether a certain type of experience is often or typically transformative. Sometimes social conditions make it easy for a type of experience to be transformative, and sometimes they make it hard for a type of experience to be transformative. This, I claim, can sometimes be a matter of (...) social justice: social conditions can make transformativeness too easy or too hard, in a way that harms people. (shrink)