We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.

We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered (which are asked to be intuitionistic).

This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

Hilbert's conference lectures during the year 1922, Neuebegründung der Mathematik. Erste Mitteilung and Die logischen Grundlagen der Mathematik (both are published in (Hilbert [1935] 1965) pp. 157-195), contain his first public presentation of an axiom system for propositional logic, or at least for a fragment of propositional logic, which is largely influenced by the study on logical woks of Frege and Russell during the previous years.The year 1922 is at the beginning of Hilbert's foundational program in its definitive form. The (...) final public presentation by Hilbert of an axiom system for propositional logic is contained in the 1934 book Grundlagen der Mathematik, I (Hilbert and Bernays [1934] 1968). Sequent .. (shrink)

We study increasing F-sequences, where F is a dilator: an increasing F-sequence is a sequence (indexed by ordinal numbers) of ordinal numbers, starting with 0 and terminating at the first step x where F(x) is reached (at every step x + 1 we use the same process as in decreasing F-sequences, cf. [2], but with "+ 1" instead of "- 1"). By induction on dilators, we shall prove that every increasing F-sequence terminates and moreover we can determine for every dilator (...) F the point where the increasing F-sequence terminates. We apply these results to inverse Goodstein sequences, i.e. increasing (1 + Id) (ω) -sequences. We show that the theorem every inverse Goodstein sequence terminates (a combinatorial theorem about ordinal numbers) is not provable in ID 1 . For a general presentation of the results stated in this paper, see [1]. We use notions and results concerning the category ON (ordinal numbers), dilators and bilators, summarized in [2, pp. 25-31]. (shrink)

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach (...) laws and Switching laws. (shrink)

We present a geometrical analysis of the principles that lay at the basis of Categorial Grammar and of the Lambek Calculus. In Abrusci it is shown that the basic properties known as Residuation laws can be characterized in the framework of Cyclic Multiplicative Linear Logic, a purely non-commutative fragment of Linear Logic. We present a summary of this result and, pursuing this line of investigation, we analyze a well-known set of categorial grammar laws: Monotonicity, Application, Expansion, Type-raising, Composition, Geach (...) laws and Switching laws. (shrink)

This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are helpful in the construction (...) of a semantic representation which is close to natural language in particular with quantified noun phrases as individual terms. We also define guidelines for the design of proof rules corresponding to generalized quantifiers. (shrink)

This paper gives an overview of the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this usual general framework represents a departure from empirical linguistic data. We briefly sketch a different idea for proof theory which is closer to the language itself than standard approaches in many aspects. We stress the importance of Hilbert’s operators—the epsilon-operator for existential and tau-operator for universal quantifications. Indeed, these operators are helpful in the construction (...) of a semantic representation which is close to natural language in particular with quantified noun phrases as individual terms. We also define guidelines for the design of proof rules corresponding to generalized quantifiers. (shrink)

This paper focuses on historic anthropological photographs, meant to depict Indigenous individuals as generic models of colonial stereotypes, and examines their later reclamation as portraits. Applying an intention-based account of portraiture, we discuss the historical context and contemporary examples of the utilisation of these images in order to address several questions. What happens when the depicted persons in colonial imagery are treated and presented as sitters, rather than model specimens? Does this change the nature of the image? If a photograph (...) was not originally intended as a portrait, can it come to function as such at a later stage? Regardless of whether they fulfill all the requirements necessary for portraiture, these colonial photographs represent a vital resource for the reclamation of Indigenous cultural heritage. As such, this paper serves as an introductory discussion into the complex issues surrounding the recategorisation, repatriation, and restitution of colonial photographic archives. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Feminist Studies 44, no. 2. © 2018 by Feminist Studies, Inc. 333 Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair Refusing to Account: Toward a Pedagogy of Tectonic Instability The increasing commoditization of knowledge and corporatization of the academy have led to a drastic restructuring of higher education, and in particular, of public institutions of learning. There is a striking similarity to the strategies enacted across institutions, each (...) governed by modes of efficiency and profitability. These moves have included a preference for larger classes, curriculum decisions that are governed by seats rather than pedagogical possibilities, an expansion of online offerings, tuition increases, and ramped-up bureaucratization, with the latter being accompanied by fewer faculty hires, a greater dependence on contingent faculty, and a swell in the ranks of senior administrative staff. This restructuring has held very specific consequences for women ’s studies programs. While larger classes are not inherently at odds with a student-centered feminist pedagogy, they do require adjustments in order to achieve similar results with our students, and they do exact greater physical and emotional labor from us as instructors. These restructuring strategies have also positioned the field in a Catch22 in that a number of issues that we have lobbied to have valued within the academy have now come into the university’s line of vision only to be redeployed as part of the university’s public relations branding agenda. There are numerous examples if we would but look: campuses that are spotted with banners portraying faculty and students of color —a visual map to the institution’s “embrace of diversity”; committees 334 Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair that are convened to review the institution’s sexual harassment policy while simultaneously refusing the involvement of women’s studies academics in the process, for whom these are scholarly and intellectual areas of study; the introduction of multicultural general education curricula, where the study of “difference” amounts to a banal presence of one or more categories of “otherness” in syllabi. This list is not exhaustive but the similarity that threads through is the commodification and the PR-ization of issues that sit at the heart of the field of women’s studies. Such cooptation notwithstanding, in this economic climate of profit maximization, small, interdisciplinary programs and departments such as women’s studies, ethnic studies, and LGBT studies have become woefully vulnerable to mergers, downsizing, and elimination.1 Our own program, now defunct, attests to this growing reality.2 So what then is the story to be told for a program that no longer exists? As alumna of Clark University’s now defunct women’s studies doctoral program, we consider the ways in which Clark, under the guidance of Cynthia Enloe, worked to move the field toward a more transnational bent. While we begin with an engagement with Clark’s specific institutional vulnerabilities, we use Clark’s commitment to a transnational praxis as our comparative point of departure to note the ways in which the importance and acuity of a transnational feminist critique have seeped away from the field. At various points in the article, we discuss how our individual trajectories emerged out of a transnational feminist sensibility. We interrogate the ways that the dominant logics of the field continue to be complicit with the very inequities and modes of representation critiqued within transnational feminist discourses. We point to the role that our scholarly pursuits play in an ongoing effort to hold the field accountable to a transnational feminist critique. Finally, 1. See Miranda Joseph, Debt to Society: Accounting for Life under Capitalism (Minneapolis, MN: University of Minnesota Press, 2014); and Chandra Talpade Mohanty, “Privatized Citizens, Corporate Academies, and Feminist Projects,” in Feminism without Borders: Decolonizing Theory, Practicing Solidarity (Durham, NC: Duke University Press, 2003). 2. The doctoral program at Clark began in 1992 and closed in 2008, graduating twenty-six PhDs and training many more who have gone on to make significant contributions at NGOs among other locations. For example, Parissara Liewkeat and Barbara Schulman have held positions with the International Labor Organization and Amnesty International, respectively. Michelle V. Rowley, Elora Halim Chowdhury, and Isis Nusair 335 we look back at our own training... (shrink)

As the need for business to address pressing social and ecological issues intensifies, so does the importance of enhancing the development of sustainable marketing. The current dominant approach to sustainable marketing is based on a Triple Bottom Line (TBL) profit‐centric worldview, which suggests that firms can simultaneously improve their financial well‐being as they reduce negative social and ecological externalities. However, whereas the scope of TBL marketing is limited to sustainability initiatives that enhance profits, there is a growing need for—and interest (...) in—developing a sustain‐centric approach to marketing that relaxes the need to maximize financial well‐being in order to optimize social and ecological well‐being. Even so, because of the dominance of the profit‐centric worldview, hallmarks of sustain‐centric marketing practices remain under‐developed and may even lend themselves to becoming inauthentically mimicked on a piecemeal basis by greenwashing profit‐centric firms. We provide an exploratory empirical study of marketing practices evident in two sustain‐centric firms and draw implications to advance theory for both sustain‐centric and profit‐centric marketing. (shrink)

The development of T cells and B cells from pluripotent hematopoietic precursors occurs through a stepwise narrowing of developmental potential that ends in lineage commitment. During this process, lineage-specific genes are activated asynchronously, and lineage-inappropriate genes, although initially expressed, are asynchronously turned off. These complex gene expression events are the outcome of the changes in expression of multiple transcription factors with partially overlapping roles in early lymphocyte and myeloid cell development. Key transcription factors promoting B-cell development and candidates for this (...) role in T-cell development are discussed in terms of their possible modes of action in fate determination. We discuss how a robust, stable, cell-type–specific gene expression pattern may be established in part by the interplay between endogenous transcription factors and signals transduced by cytokine receptors, and in part by the network of effects of particular transcription factors on each other. BioEssays 21:726–742, 1999. © 1999 John Wiley & Sons, Inc. (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

Given its non-invasive nature, there is increasing interest in the use of transcutaneous vagus nerve stimulation across basic, translational and clinical research. Contemporaneously, tVNS can be achieved by stimulating either the auricular branch or the cervical bundle of the vagus nerve, referred to as transcutaneous auricular vagus nerve stimulation and transcutaneous cervical VNS, respectively. In order to advance the field in a systematic manner, studies using these technologies need to adequately report sufficient methodological detail to enable comparison of results between (...) studies, replication of studies, as well as enhancing study participant safety. We systematically reviewed the existing tVNS literature to evaluate current reporting practices. Based on this review, and consensus among participating authors, we propose a set of minimal reporting items to guide future tVNS studies. The suggested items address specific technical aspects of the device and stimulation parameters. We also cover general recommendations including inclusion and exclusion criteria for participants, outcome parameters and the detailed reporting of side effects. Furthermore, we review strategies used to identify the optimal stimulation parameters for a given research setting and summarize ongoing developments in animal research with potential implications for the application of tVNS in humans. Finally, we discuss the potential of tVNS in future research as well as the associated challenges across several disciplines in research and clinical practice. (shrink)

In the wake of the First World War, a new form of commemoration emerged internationally, but in each case focused upon a new kind of national “hero”—the unknown soldier or warrior. The first instances appeared in France and Britain in 1920, followed by the United States in 1921, and Belgium in 1922. Other nations followed suit over the years, with the most recent WWI Unknown Soldier monument dedicated in 2004, in New Zealand. The motivational calculus of these national tombs was, (...) of course, the massive number of combatant dead whose remains could not be identified. This paper takes up the two very different arguments composed by these commemorative sites. The first argument was directed to surviving family members and was articulated most explicitly by the French as a hypothetical enthymeme “this could be your husband, your father, your brother,” etc. The second argument has been directed to national and international collectives as a constitutive proclamation of legitimated nation-state or Empire Although this argument is particularly explicit in postcolonial gestures of independence on the part of former dominions of old empires, it was evident in even the earliest cases of the tombs of the unknown. (shrink)