We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.

We prove that all semisimple varieties of FL ew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL ew-algebras follows. It matches exactly a natural classification of logics over FL ew proposed by H. Ono.

In this paper, we show that all semisimple varieties of bounded weak-commutative residuated lattices with an S4-like modal operator are discriminator varieties. We also give a characterization of discriminator and EDPC varieties of bounded weak-commutative residuated lattices with an S4-like modal operator follows.

Anyone who has ever worked with a variety \ of algebras with a reduct in the variety of bounded distributive lattices will know a restricted Priestley duality when they meet one—but until now there has been no abstract definition. Here we provide one. After deriving some basic properties of a restricted Priestley dual category \ of such a variety, we give a characterisation, in terms of \, of finitely generated discriminator subvarieties of \. As an application of our characterisation, (...) we give a new proof of Sankappanavar’s characterisation of finitely generated discriminator varieties of distributive double p-algebras. A substantial portion of the paper is devoted to the application of our results to Cornish algebras. A Cornish algebra is a bounded distributive lattice equipped with a family of unary operations each of which is either an endomorphism or a dual endomorphism of the bounded lattice. They are a natural generalisation of Ockham algebras, which have been extensively studied. We give an external necessary-and-sufficient condition and an easily applied, completely internal, sufficient condition for a finite set of finite Cornish algebras to share a common ternary discriminator term and so generate a discriminator variety. Our results give a characterisation of discriminator varieties of Ockham algebras as a special case, thereby yielding Davey, Nguyen and Pitkethly’s characterisation of quasi-primal Ockham algebras. (shrink)

This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [ 48 ] and [ 50 ] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary expansion (...) of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH . We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH . Finally, we apply these results to give bases for “small” subvarieties of BDQDSH , DQSSH , and DblSH. (shrink)

In this paper I show that a variety of Cartesian Conceptions of the mental are unworkable. In particular, I offer a much weaker conception of limited discrimination than the one advanced by Williamson (2000) and show that this weaker conception, together with some plausible background assumptions, is not only able to undermine the claim that our core mental states are luminous (roughly: if one is in such a state then one is in a position to know that one is) but (...) also the claim that introspection is infallible with respect to our core mental states (where a belief that C obtains is infallible just in case if one believes that C obtains then C obtains). The upshot is a broader and much more powerful case against the Cartesian conception of the mental than has been advanced hitherto. (shrink)

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

A discriminator logic is the 1 -assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator (...) logic S can be presented as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work. (shrink)

In this paper we pursue the study of the variety of m -generalized Łukasiewicz algebras of order n which was initiated in [1]. This variety contains the variety of Łukasiewicz algebras of order n . Given , we establish an isomorphism from its congruence lattice to the lattice of Stone filters of a certain Łukasiewicz algebra of order n and for each congruence on A we find a description via the corresponding Stone filter. We characterize the principal congruences on A (...) via Stone filters. In doing so, we obtain a polynomial equation which defines the principal congruences on the algebras of . After showing that for m > 1 and n > 2, the variety of Łukasiewicz algebras of order n is a proper subvariety of , we prove that is a finitely generated discriminator variety and point out some consequences of this strong property, one of which is congruence permutability. (shrink)

The paper has two parts preceded by quite comprehensive preliminaries.In the first part it is shown that a subvariety of the variety ${\cal T}$ of all tense algebras is discriminator if and only if it is semisimple. The variety ${\cal T}$ turns out to be the join of an increasing chain of varieties ${\cal D}_n$, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term (...) conditions. In the case of tense algebras, the varieties ${\cal D}_n$ can be further characterised by certain natural conditions on Kripke frames.In the second part it is shown that the lattice of subvarieties of ${\cal D}_0$ has two atoms, the lattice of subvarieties of ${\cal D}_1$ has countably many atoms, and for $n>1$, the lattice of subvarieties of ${\cal D}_n$ has continuum atoms. The proof of the second of the above statements involves a rather detailed description of zero-generated simple algebras in ${\cal D}_1$.Almost all the arguments are cast in algebraic form, but both parts begin with an outline describing their contents from the dual point of view of tense logics. (shrink)

The ability to represent same-different relations is an important condition for abstract thought. However, there is mixed evidence for when this ability develops, both ontogenetically and phylogenetically. Apparent success in relational reasoning may be evidence for genuine conceptual understanding or may be the result of low-level, perceptual strategies. We introduce a method to discriminate these possibilities by pitting two conditions that are perceptually matched but conceptually different: in a "fused" condition, same and different objects are joined, creating single objects that (...) have the same perceptual features as the two object pairs in the "relational" condition. However, the "fused" objects do not provide evidence for the relation 'same.' Using this method with human toddlers in a causal relational reasoning task provides evidence for genuine conceptual understanding. This novel technique offers a simple manipulation that may be applied to a variety of existing match-to-sample procedures used to assess same-different reasoning to include in future research with non-human animals across species, as well as human infants. (shrink)

Social Justice is a concept familiar to most Indians but one whose meaning is not always understood as it signifies a variety of government strategies designed to enhance opportunities for underprivileged groups. By tracing the trajectory of social justice from the colonial period to the present, this book examines how it informs ideas, practices and debates on discrimination and disadvantage today. After outlining the historical context for reservations for scheduled castes and scheduled tribes that began under British colonial rule, the (...) book examines the legal and moral strands of demands raised by newer groups since 1990. In addition the book shows how the development of quota policies has been significantly influenced by the nature and operation of democracy in India. It describes the recent proliferation of quota demands for reservations in higher education, private sector and for women and religious minorities in legislative assemblies. The book goes on to argue that while proliferation of demands address unequal incidence of poverty, deprivation and inequalities across social groups and communities, care has to be taken to ensure that existing justifications for quotas for discriminated groups due to caste hierarchies are not undermined. Providing a rich historical background to the subject, the book is a useful contribution to the study on the evolution of multiple conceptions of social justice in contemporary India. (shrink)

Research on gender inequality has posited the importance of gender discrimination for women’s experiences at work. Previous studies have suggested that gender stereotyping and organizational factors may contribute to discrimination. Yet it is not well understood how these elements connect to foster gender discrimination in everyday workplaces. This work contributes to our understanding of these relationships by analyzing 219 discrimination narratives constructed from sex discrimination cases brought before the Ohio Civil Rights Commission. By looking across a variety of actual work (...) settings, the analysis sheds light on the cultural underpinnings and structural contexts in which discriminatory actions occur. The analyses reveal how gender stereotyping combines in predictable ways with sex composition of workplaces and organizational policies, often through interactional dynamics of discretionary policy usage, to result in discrimination. The findings suggest the importance of cultural, structural, and interactional influences on gender discrimination. (shrink)

The renewed interest in the issue of black reparations, both in the public sphere and among scholars, is a welcome development because the racial injustices of the past continue to shape American society by disadvantaging African Americans in a variety of ways. Attention to the past and how it has shaped present-day inequality seems essential both to understanding our predicament and to justifying policies that would address and undermine racial inequality. Given this, any argument for policies designed to pursue racial (...) justice must be, at least in part, backward-looking, justifi ed partly as compensation for the effects of the wrongs of the past. However, some arguments about black reparations, both pro and con, are focused too far in the past. An unspoken assumption of much of the debate about black reparations is that these would be reparations for slavery. This, we argue, is a mistake. Racial inequality in the United States today may, ultimately, be based on slavery, but it is also based on the failure of the country to take effective steps since slavery to undermine the structural racial inequality that slavery put in place. From the latter part of the nineteenth century through the fi rst half of the twentieth century, the Jim Crow system continued to keep Blacks “in their place,” and even during and after the civil rights era no policies were adopted to dismantle the racial hierarchy that already existed. An important part of the story of racial inequality today is the history of housing and lending discrimination in the second half of the twentieth century (McCarthy 2002; 2004). Home equity, for many Americans, is a very important source of wealth, and the decades after World War II were ones of rapid home equity growth. They were the decades that saw the creation of a large, mostly suburban, middle class. But the middle class that was created was also mostly White, and this was due largely to government policies that (in many cases intentionally) excluded Blacks from the opportunities to get into the home market and benefi t from home equity growth. In this paper we argue that recent housing and lending discrimination constitutes an important basis for black reparations.. (shrink)

A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters (...) and use this to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom. (shrink)

In this paper, we have two goals. First, we argue for a blueprint for hermeneutical injustice that allows us to schematize existing and discover new varieties of hermeneutical injustices. The underlying insight is that Fricker provides both a general concept of hermeneutical injustice and a specific conception thereof. By distinguishing between the general concept and its specific conceptions, we gain a fruitful tool to detect such injustices in our everyday lives. Second, we use this blueprint to provide a further (...) example of hermeneutical injustice that draws our attention to yet another distinction: Some hermeneutical injustices result from a lack or distortion in the collective conceptual resource and some are due to problems in the application of existing concepts. We argue that to combat hermeneutical injustices, we have to make sure not only that individuals have accurate concepts at their disposal but that they have the capabilities to use these concepts adequately. (shrink)

Niebuhr's definitions of "Christ" and "culture" set up a problematic dualism that leads to a misrepresentation of the Christ-against-culture type. The paper proposes that instead of Niebuhr's "idealized" Christ, an embodied Christology locates Christ within culture. The tension, then, is not between Christ and culture, but between different cultural visions. A cultural vision with Christ as norm provides a discriminating ethic of normative practices to engage culture. Many scholars have recognized that Niebuhr not only develops a descriptive typology in Christ (...) and Culture, he also argues that the fifth type, Christ-the-transformer-of-culture, is the most adequate position. Almost everyone identifies with this type. Why is that? The problem is that the variety of meanings of "transformation" is not illuminated by Niebuhr's typology. An alternative typology is proposed which addresses these two problems: a richer development of three types that Niebuhr lumps together in his Christ-against-culture type; and the development of a typology to show that there are four different ways to understand what the church has meant by Christ-the-transformer-of-culture. (shrink)

People may be subjected to discrimination from a variety of sources in the workplace. In this study of mental health workers, we contrast four potential perpetrators of discrimination (managers, co-workers, patients, and visitors) to investigate whether the negative impact of discrimination on victims’ well-being will vary in strength depending on the relative power of the perpetrator. We further explore whether the negative impact of discrimination is at least partly explained by its effects on people’s sense of organizational justice, and whether (...) the strength of mediation varies according to the source of discrimination. Using survey data from 1,733 UK mental health workers, a structural equation model was designed to test these hypotheses following a bootstrap approach. Discrimination from all sources was related to well-being, with that from managers having the strongest effects. The results support an explanation of the effect of discrimination on well-being in terms of organizational justice perceptions for discrimination from managers and from visitors, but less so for discrimination from co-workers or from patients. The study highlights the importance of differentiating amongst sources of discrimination at work and the salience of organizational justice perceptions in explaining the effects of discrimination from some sources. (shrink)

In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed.

Many legal, social, and medical theorists and practitioners, as well as lay people, seem to be concerned with the harmfulness of discriminative practices. However, the philosophical literature on the moral wrongness of discrimination, with a few exceptions, does not focus on harm. In this paper, I examine, and improve, a recent account of wrongful discrimination, which divides into a definition of group discrimination, and a characterisation of its moral wrong-making feature in terms of harm. The resulting account analyses the wrongness (...) of discrimination in terms of intrapersonal comparisons of the discriminatee’s actual, and relevantly counterfactual, well-being levels. I show that the account faces problems from counterfactuals, which can be traced back specifically to the orthodox - comparative, counterfactual, welfarist - concept of harm. I argue that non-counterfactual and non-comparative harm concepts face problems of their own, and don’t fit easily with our best understanding of discrimination; hence they are unsuitable to replace the orthodox concept here. I then propose a non-orthodox - comparative, counterfactual, hybrid - concept of harm, which relies on counterfactual comparisons of ways of being treated. I suggest how such a concept can help us handle the problems from counterfactuals, at least for my account of discrimination. I also show that there are similar proposals in other harm-related debates. An upshot of the paper is thus to corroborate the case for a non-orthodox, hybrid concept of harm, which seems better able to fulfil its functional roles in a variety of contexts. (shrink)

This paper attempts to clarify the relations between trust, agency and latent forms of discrimination. Its main argument is in social philosophy, and it articulates considerations from moral psychology and the philosophy of language. The aim is to provide a better insight into the deflated level of trustworthiness that members of stigmatized categories are credited with. Identity prejudice determining low levels of credibility for its victims has received substantial philosophical attention in the wake of the epistemic injustice literature. Instead of (...) the standard cognitive concept of trust usually brought in, I apply a moral (or agential) account of trust (drawing on Domenicucci and Holton 2017) to discriminatory issues. We can fail to trust the trustworthy (Jones 2013) in a variety of ways. When it comes to the members of discriminated categories, I argue in the first part, this happens because they are refused a necessary condition of trust: a presumption of agency. This presumption of agency, prima facie attributed to human adults, is precisely what goes wrong for the members of stigmatized groups. Not recognised as individual agents, but as mere quasi-agents, the discriminatees cannot be trusted: their trustworthiness actually becomes unthinkable. The very possibility to give reasons for or against out-group members’ trustworthiness is thus dismissed. Articulating documentality and feminist philosophy of language, the second part shows that members of stigmatized categories have their conduct described and recorded through a non-agential grammar. Once widespread and socially dominant, non-agential descriptions of their action give the discriminatees a peculiar moral status that jeopardizes the very possibility of their being recognised as trustworthy. (shrink)

In this paper, I argue that instead of primarily paying attention to the nature of implicit attitudes that are taken to cause implicit discrimination, we should investigate how discrimination can be implicit in itself. I propose to characterize implicit discrimination as unintentional discrimination: the person responds to facts unintentionally and often unconsciously which are, given their end, irrelevant and imply unfair treatment. The result is a unified account of implicit bias that allows for the different ways in which it can (...) display itself and can be explained. Furthermore, the view can account for the central characteristics of implicit bias: (1) that it is, for a variety of reasons, difficult to control, (2) that we are not necessarily unconscious of implicit bias but not properly conscious either, and (3) that we can unintentionally discriminate regardless of whether we claim to care about fairness. (shrink)

This paper uses evidence from laboratory experiments to identify a variety of tribalisms. This is important because some tribalisms encourage zerosum thinking and others do not; and some are not developed by Buchanan. This, in turn, supplies new insights into Buchanan’s project of identifying the kinds of environment that encourage his sense of moral progress. In particular, current levels of inequality become a significant barrier to moral progress not only because they create an economic form of tribalist zero-sum thinking but (...) they also undermine the scope for positive-sum. (shrink)

Abstract What do we mean to say when we call some person a good business manager? And where do the criteria flow from by which we judge people good business managers? I answer these questions by drawing on von Wright's distinction between several varieties of goodness. We can then discriminate between instrumental, technical and moral senses of the expression ?to be a good business manager?. The first two senses presume that business managers have a characteristic task or that they (...) engage in typical activities. It is natural to specify this task and these activities by appealing to goods and to the good of a business. These goods may then be identified as goods for people. Insofar as the welfare of people is of moral value, we obtain a morally loaded account of business management. I argue against this account and plead for a more sober understanding of economic goods and of the good of a business. The latter can be understood in analogy to the good of an individual person, but is largely determined by the goals of the founders and owners. Economic goods are things that are wanted by some people and thus exchanged on markets. If this is so, then there is no direct conceptual path from instrumentally or technically good business managers to morality even though there are certain affinities. To conclude, I trace the consequences for our understanding of business ethics. (shrink)

How should we respond to individuals with disabilities? What does it mean to be disabled? Over fifty million Americans, from neonates to the fragile elderly, are disabled. Some people say they have the right to full social participation, while others repudiate such claims as delusive or dangerous. In this compelling book, three experts in ethics, medicine, and the law address pressing disability questions in bioethics and public policy. Anita Silvers, David Wasserman, and Mary B. Mahowald test important theories of justice (...) by bringing them to bear on subjects of concern in a wide variety of disciplines dealing with disability. They do so in the light of recent advances in feminist, minority, and cultural studies, and of the groundbreaking Americans with Disabilities Act. (shrink)

Normative political theorists working in the field of linguistic justice generally believe that participation in democratic life in linguistically diverse societies requires a shared lingua franca (e.g., Patten 2009; Van Parijs 2011). Even when a shared lingua franca is present, however, there is likely to be a variety of ways in which people speak it, due to variations in accent, pitch, register, and lexicon. This paper examines the implications of intra‐linguistic diversity for democracy and political representation. More specifically, by drawing (...) on Andrew Rehfeld's (2010) work and on relevant sociolinguistics research, the paper argues that widespread unconscious linguistic prejudice constitutes a constraint on some citizens' right to run for political office that is incompatible with democratic equality. The argument is illustrated via a number of examples concerning Australian politicians. (shrink)

In the future systems of ambient intelligence will include decision support systems that will automate the process of discrimination among people that seek entry into environments and to engage in search of the opportunities that are available there. This article argues that these systems must be subject to active and continuous assessment and regulation because of the ways in which they are likely to contribute to economic and social inequality. This regulatory constraint must involve limitations on the collection and use (...) of information about individuals and groups. The article explores a variety of rationales or justifications for establishing these limits. It emphasizes the unintended consequences that flow from the use of these systems as the most compelling rationale. (shrink)

Gender discrimination and sexual harassment of female police officers by their male counterparts remain areas of liability where police departments appeared to have failed to effectively confront the nagging issues. However, the appreciable level of research conducted on these issues in the global North has not been matched by the South, where issues bordering on sexual violence have cultural underpinnings. Drawing from the case of the Nigeria Police Force, feminist analysis was used to explore the lived reality of 43 female (...) officers in a qualitative study. Participants expressed distress in abiding by structural discriminatory regulations against female officers which include non-admittance of married women into the force, forbidding unmarried officers from getting pregnant, and a stipulated minimum of three-year work period before a female officer can marry. Findings also indicated that participants suffer a variety of sexual harassment, intimidation, and, violence from their male colleagues, while they feel constrained in reporting their victimization. Important policy and practical implications requiring the Nigerian police to address hegemonic masculinity and promote gender equality were provided. (shrink)

Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, (...) etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean. (shrink)

Mandik (2012)understands color-consciousness conceptualism to be the view that one deploys in a conscious qualitative state concepts for every color consciously discriminated by that state. Some argue that the experimental evidence that we can consciously discriminate barely distinct hues that are presented together but cannot do so when those hues are presented in short succession suggests that we can consciously discriminate colors that we do not conceptualize. Mandik maintains, however, that this evidence is consistent with our deploying a variety of (...) nondemonstrative concepts for those colors and so does not pose a threat to conceptualism. But even if Mandik has shown that we deploy such concepts in these experimental conditions, there are cases of conscious states that discriminate colors but do not involve concepts of those colors. Mandik’s arguments sustain only a theory in the vicinity of conceptualism: The view that we possess concepts for every color we can discriminate consciously, but need not deploy those concepts in every conscious act of color discrimination. (shrink)

The current WSN is vulnerable to a variety of malicious attacks, resulting in the decline of its comprehensive performance. Multihop routing involves a number of safety and privacy issues. Problems such as snooping, sinkhole, manipulation, cloning, wormhole, spoofing, and so on affect the integrity, availability, and confidentiality of the WSNs. Therefore, this paper mainly studies the mathematical modeling of WSN multiattack behavior discrimination based on the incidence matrix. The WSN node model is used to collect relevant data and mark and (...) map the disguised data, so as to determine the characteristics of multiattack behavior and establish the WSN multiattack behavior discrimination model based on the incidence matrix. The experimental results show that the designed multiattack behavior discrimination model can distinguish the attack type according to the characteristics, has high recognition ability, can spend a short time to effectively distinguish the attack behavior, has a low false positive rate, and can effectively improve the antiattack ability of the WSN. (shrink)

ABSTRACTThe idea of “church autonomy” has risen to prominence in law and religion discourse in recent years. Defenders argue that church autonomy is essential to protecting religious freedom, while critics argue that it permits great harm. This heated dispute often obscures the fact that religious group autonomy is not all-or-nothing. Religious organizations can enjoy some autonomy without being free from all legal oversight. This article thus seeks to make progress in the debate by providing a taxonomy of kinds of judicial (...) examination of religious organizations’ decisions—focusing on employment decisions—and normatively assessing each kind. I argue that religious groups should enjoy protection from certain kinds of examination, but other kinds are justifiable, and even required. My argument supports an approach similar to that seen in some recent European Court of Human Rights decisions, rather than the less discriminating approach of U.S. courts. (shrink)

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local (...) deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open. (shrink)

A \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!}$$\end{document}-sentence is a sentence of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall x_{1}\cdots x_{n}\exists!y_{1}\cdots y_{m}O(\overline{x},\overline{y})}$$\end{document}, where O is a quantifier-free formula, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\exists!}$$\end{document} stands for “there exist unique”. We prove that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is (up to isomorphism) a finite class of finite models then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is axiomatizable by a set of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!}$$\end{document}-sentences if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is closed under isomorphic images, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} has the intersection property, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is closed under fixed-point submodels. This result is employed to characterize the subclasses of finitely generated discriminator varieties axiomatizable by sentences of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\forall\exists!\bigwedge p=q}$$\end{document}. (shrink)

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...) Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. (shrink)

\ of monadic m-generalized Łukasiewicz algebras of order n -algebras), namely a generalization of monadic n-valued Łukasiewicz algebras. In this article, we determine the congruences and we characterized the subdirectly irreducible \-algebras. From this last result we proved that \ is a discriminator variety and as a consequence we characterized the principal congruences. In the last part of this paper we find an immersion of these algebras in a functional algebra and we proved that in the finite case they (...) are isomorphic. This last result allows to show a new functional representation for monadic n-valued Łukasiewicz algebras. Finally, we define the notions of \-algebra of fractions and maximal algebra of fractions and we prove the existence of a maximal \-algebra of fractions for an \-algebra. (shrink)

We investigate expansions of Heyting algebras in possession of a unary term describing the filters that correspond to congruences. Hasimoto proved that Heyting algebras equipped with finitely many normal operators have such a term, generalising a standard construction on finite-type boolean algebras with operators. We utilise Hasimoto’s technique, extending the existence condition to a larger class of EHAs and some classes of double-Heyting algebras. Such a term allows us to characterise varieties with equationally definable principal congruences using a single (...) equation. Moreover, in the presence of a dual pseudocomplement operation, discriminator varieties are characterised by a pair of equations. We also prove that a variety of dually pseudocomplemented EHAs with a normal filter term is semisimple if and only if it is a discriminator variety. This generalises two known results, one by Kowalski and Kracht for finite-type varieties of BAOs, and the other by the present author for dually pseudocomplemented Heyting algebras without additional operations. (shrink)

We investigate expansions of Heyting algebras in possession of a unary term describing the filters that correspond to congruences. Hasimoto proved that Heyting algebras equipped with finitely many normal operators have such a term, generalising a standard construction on finite-type boolean algebras with operators. We utilise Hasimoto’s technique, extending the existence condition to a larger class of EHAs and some classes of double-Heyting algebras. Such a term allows us to characterise varieties with equationally definable principal congruences using a single (...) equation. Moreover, in the presence of a dual pseudocomplement operation, discriminator varieties are characterised by a pair of equations. We also prove that a variety of dually pseudocomplemented EHAs with a normal filter term is semisimple if and only if it is a discriminator variety. This generalises two known results, one by Kowalski and Kracht for finite-type varieties of BAOs, and the other by the present author for dually pseudocomplemented Heyting algebras without additional operations. (shrink)

Combating homophobia, racism, sexism, and other forms of discrimination and violence in our society requires more than just focusing on the overt acts of prejudiced and abusive individuals. The very intelligibility of such acts, in fact, depends upon a background of shared beliefs, attitudes, and behaviors that together form the context of social practices in which these acts come to have the meaning they do. This book, inspired by Wittgenstein as well as feminist and critical race theory, shines a critical (...) light on this background in order to show that we all share more responsibility for the persistence of oppressive social practices than we commonly suppose—or than traditional moral theories that connect responsibility just with the actions, rights, and liberties of individuals would lead us to believe. First sketching a nonessentialist view of rationality, and emphasizing the role of power relations, Peg O’Connor then examines in subsequent chapters the relationship between a variety of "foreground" actions and "background" practices: burnings of African American churches, hate speech, child sexual abuse, coming out as a gay or lesbian teenager, and racial integration of public and private spaces. These examples serve to illuminate when our "language games" reinforce oppression and when they allow possibilities for resistance. Attending to the background, O’Connor argues, can give us insight into ways of transforming the nature and meaning of foreground actions. (shrink)

The origins of agriculture lie in the distant past, approximately 12 000 years ago, when hunter-gatherers of the Palaeolithic embraced sedentism at the dawn of the Neolithic. The variety of life history transitions emanating from this unique phenomenon have had an enormous impact on the biodiversity of the planet, while subjecting humanity to a variety of life-changing physical and social challenges right up to the present. The ever-present consequences of the Agricultural Revolution continue to demand our attention, yet frustrate our (...) efforts, on a seemingly perpetual basis, to effectively manage the outcomes. Here we review the origins and lasting after-effects of the Agricultural Revolution and its impact on the human condition, with reference to sedentism, nutrition, health issues, disease, gender discrimination as well as mythmaking and religion. Contribution: Our aim is to engage a wider audience with respect to the causes and consequences of the Agricultural Revolution. We discuss a broad spectrum of relevant phenomena implicated in this epochal event and consequently underline that the Agricultural Revolution precipitated not only major changes to the ecology of the planet, but also and most importantly to the social and cultural well-being of humanity. (shrink)

We argue that Anthropocentrism – the kind of speciesism that privilegies the human species – is morally unacceptable. We distinguish and criticize three varieties of Anthropocentrism: unqualified, qualified empirical and qualified non-empirical. Firstly, unqualified Anthropocentrism is dismissed because it is grounded on a moral principle which implies that discriminations like racism and sexism are justified. Secondly, qualified empirical Anthropocentrism falls victim to the marginal cases argument, an argument that shows that properties which allegedly attribute moral status to every human (...) and to no animal, ultimately, if they exclude every animal, they also exclude some humans. Lastly, qualified non-empirical Anthropocentrism is rejected due to implausible consequences about which individuals have moral status. After rejecting Anthropocentrism, we consider a generalization of the marginal cases argument against all forms of speciesism. We show that only a species entirely comprised of essentially moral individuals would be unaffected by this argument. However, the possibility of such a species has limited practical import. Contrarily, Anthropocentrism’s moral unacceptability requires profound changes in the way humans relate with animals. (shrink)

For a variety of reasons, it's difficult to determine, with any accuracy, the number of trans and gender nonbinary folks living in the United States.1 Data are difficult to obtain since neither the U.S. Census Bureau nor the Centers for Disease Control and Prevention survey people's gender identity. But even if they did, responses would likely be unreliable. Many members of these two groups are hesitant to answer such questions for fear of their safety, resulting discrimination, or because they disagree (...) on the definition of what it means to be transgender. It's also difficult to obtain accurate numbers on these groups since most medical forms still rely on a two-sex system of... (shrink)

Addressing a myriad of complex social, economic and political issues in the South African context requires that we draw from a variety of voices. This postcolonial reflection draws on the work of Vuyani Vellem’s African spirituality to highlight how it can help Africans conceptualise race epistemologically. The contribution emerged out of an article presented at a conference themed ‘unthinking West. The article employed the concepts of liminality and threshold to discuss the ambivalence encountered by Vuyani Vellem and highlights how his (...) theological convictions still present unsettling ideological aftershocks within the unjust structures of society.Contribution: This contribution is a black liberation theological reflection, which laments how Vellem did not live to witness the full realisation of his dreams regarding the liberation of the black masses. The article identifies racial discrimination and misconceptions on African spirituality as some examples of the ‘unsettling aftershocks’ regarding challenges, which Vellem confronted within the unjust structures of South African society. (shrink)

Cultural accounts of scientific ideas and practices have increasingly come to be welcomed as a corrective to previous—and still widely held—theories of scientific knowledge and practices as universal. The editors caution, however, against the temptation to overgeneralize the work of culture, and to lapse into a kind of essentialism that flattens the range and variety of scientific work. The book refers to this tendency as culturalism. The contributors to the volume model a new path where historicized and cultural accounts of (...) scientific practice retain their specificity and complexity without falling into the traps of culturalism. They examine, among other issues, the potential of using notions of culture to study behavior in financial markets; the ideology, organization, and practice of earthquake monitoring and prediction during China's Cultural Revolution; the history of quadratic equations in China; and how studying the "glass ceiling" and employment discrimination became accepted in the social sciences. Demonstrating the need to understand the work of culture as a fluid and dynamic process that directly both shapes and is shaped by scientific practice, Cultures without Culturalism makes an important intervention in science studies. Contributors. Bruno Belhoste, Karine Chemla, Caroline Ehrhardt, Fa-ti Fan,Kenji Ito, Evelyn Fox Keller, Guillaume Lachenal, Donald MacKenzie, Mary S. Morgan, Nancy J. Nersessian, David Rabouin, Hans-Jörg Rheinberger, Claude Rosental, Koen Vermeir. (shrink)

In vowel discrimination, commonly found discrimination patterns are directional asymmetries where discrimination is faster if differing vowels are presented in a certain sequence compared to the reversed sequence. Different models of speech sound processing try to account for these asymmetries based on either phonetic or phonological properties. In this study, we tested and compared two of those often-discussed models, namely the Featurally Underspecified Lexicon model and the Natural Referent Vowel framework. While most studies presented isolated vowels, we investigated a large (...) stimulus set of German vowels in a more naturalistic setting within minimal pairs. We conducted an mismatch negativity study in a passive and a reaction time study in an active oddball paradigm. In both data sets, we found directional asymmetries that can be explained by either phonological or phonetic theories. While behaviorally, the vowel discrimination was based on phonological properties, both tested models failed to explain the found neural patterns comprehensively. Therefore, we additionally examined the influence of a variety of articulatory, acoustical, and lexical factors but also the influence of factors beyond the well-known in depth via multiple regression analyses. The analyses revealed that the perceptual factor of perceived loudness has a greater impact than considered in the literature and should be taken stronger into consideration when analyzing preattentive natural vowel processing. (shrink)