Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...) to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.

The axiomatic presentation of modal systems and the standard formulations of natural deduction and sequent calculus for modal logic are reviewed, together with the difficulties that emerge with these approaches. Generalizations of standard proof systems are then presented. These include, among others, display calculi, hypersequents, and labelled systems, with the latter surveyed from a closer perspective.

In this paper, I advance a counterexample to the collective agency thesis.

Proofs and countermodels are the two sides of completeness proofs, but, in general, failure to find one does not automatically give the other. The limitation is encountered also for decidable non-classical logics in traditional completeness proofs based on Henkin’s method of maximal consistent sets of formulas. A method is presented that makes it possible to establish completeness in a direct way: For any given sequent either a proof in the given logical system or a countermodel in the corresponding frame class (...) is found. The method is a synthesis of a generation of calculi with internalized relational semantics, a Tait–Schütte–Takeuti style completeness proof, and procedures to finitize the countermodel construction. Finitizations for intuitionistic propositional logic are obtained through the search for a minimal derivation, through pruning of infinite branches in search trees by means of a suitable syntactic counterpart of semantic filtration, or through a proof-theoretic embedding into an appropriate provability logic. A number of examples illustrates the method, its subtleties, challenges, and present scope. (shrink)

Large portions of mathematics such as algebra and geometry can be formalized using first-order axiomatizations. In many cases it is even possible to use a very well-behaved class of first-order axioms, namely, what are called coherent or geometric implications. Such class of axioms can be translated to inference rules that can be added to a sequent calculus while preserving its structural properties. In this work, this fundamental result is extended to their infinitary generalizations as extensions of sequent calculi for both (...) classical and intuitionistic infinitary logic. As an application, a simple proof of the infinitary Barr’s theorem without the axioms of choice is shown. (shrink)

A way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive theories. All results are proved for systems in which also the rules of weakening and contraction can be eliminated. Applications include a system of predicate logic (...) with equality in which also cuts on the equality axioms are eliminated. (shrink)

In this paper, I examine the manner in which analyses of the action of single agents have been pressed into service for constructing accounts of collective action. Specifically, I argue that the best analogy to collective action is a class of individual action that Carl Ginet has called 'aggregate action.' Furthermore, once we use aggregate action as a model of collective action, then we see that existing accounts of collective action have failed to accommodate an important class of (what I (...) shall call) 'unintentional collective actions.'. (shrink)

Writers on collective action are in broad agreement that in order for a group of agents to form a collective intention, the members of that group must have beliefs about the beliefs of the other members. But in spite of the fact that this so-called "interactive knowledge" is central to virtually every account of collective intention, writers on this subject have not offered a detailed account of the nature of interactive knowledge. In this paper, we argue that such an account (...) is necessary for any adequate analysis of collective intention. Furthermore, we argue that an application of Robert Aumann's theory of interactive knowledge may be used to address several puzzling features of collective intention. CiteULike Connotea Del.icio.us What's this? (shrink)

In the current American iconoclash, certain monuments are subject to vandalism and municipal removal from their pedestals. Phrases such as “the erasure of history” and “damnatio memoriae” point to concerns that iconoclasm is an attempt to censor history or even remove certain individuals from public memory altogether. Because these phrases beckon the past, this wave of iconoclasm calls for a close examination of previous image-breaking to establish motives. Drawing first from art history, we analyze Byzantine iconoclasm and anxieties over the (...) nature of icons’ power, before contextualizing these findings within image destruction from the Paleolithic to the present day. Each comparison is suggestive of an enduring aesthetic principle: that what appears inanimate is not always inert. Next, drawing from cultural anthropology, we argue that principles of sympathetic magic are at the heart of contemporary iconoclasms, but not in the way media outlets often suggest. Instead, the fear of history’s erasure betrays a deeply rooted equivalence between the representation and the represented. In perceiving their fates as shared, sympathetic magic is seen to persist in the way humans create, interpret, and desecrate images. We conclude with the speculative realist proposition that iconoclasm can produce new, original artworks, which carries implications for the autonomy of art and its distribution between artist and artwork. (shrink)

Stakeholder management devices (SMDs) are the mechanisms through which organizations respond to stakeholder concerns. Given that SMDs serve as organizational control systems for employees and managers, this research investigates the internal rather than the external effects of a firm's SMDs. Unlike most previous research, I examined the effects of these formal structures, processes, and procedures in the aggregate, rather than focusing attention on a single type of device. The study investigates the effects of a firm's stakeholder management devices, in the (...) aggregate, on three factors that influence individual behavior in organizations: expectations, attitudes, and perceived organizational climates. Respondents were managers in 112 for-profit businesses located throughout the United States. Results suggest that a firm's stakeholder management devices affect the perceived moral climates in the firm, and affect managers' expectations about the consequences of good corporate social performance, but do not affect organization members' attitudes about corporate social responsibility. (shrink)

By presenting a case study based on the argumentative analysis of news in the press, this article introduces and discusses strategic manoeuvring with contextual frames. Drawing on the linguistic notion of frame, I introduce the concept of contextual frame to refer to the news context, that is, the background against which a certain event is presented as a piece of news. I argue that newspapers and journalists make use of contextual frames in the apparently neutral genre of news reporting to (...) propose specific interpretations of the facts at issue, which become the basis for explicit comments and editorials. To show how this works, I investigate in detail a case of newspaper coverage of a complex episode using the pragma-dialectical notion of strategic manoeuvring and the Argumentum Model of Topics to analyse argument schemes. I show that, in the use of contextual frames, there is a prominent relation between presentational devices and topical potential; contextual frames provide the implicit material premises which are at the basis of argumentations through which newspapers interpret and comment on the news. (shrink)

A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore (...) it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction. (shrink)

In this paper, we offer an analysis of ‘group intentions.’ On our proposal, group intentions should be understood as a state of equilibrium among the beliefs of the members of a group. Although the discussion in this paper is non-technical, the equilibrium concept is drawn from the formal theory of interactive epistemology due to Robert Aumann. The goal of this paper is to provide an analysis of group intentions that is informed by important work in economics and formal epistemology.

The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination.

We examined how children’s strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34 - 18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were more (...) likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems. (shrink)

Decolonial/anti-colonial Black, Indigenous and Mestiza feminist movements and scholar-activists foreground how the oft-touted apocalypse that the Covid-19 pandemic heralds is not new, nor does it signify the great rupture into chaos that those from within modernity-coloniality often claim it to be. Rather Covid-19 is preceded by and will be out-lived by the apocalyptic anti-life onto-epistemological logics that are foundational to the production of hetero-patriarchal capitalist- coloniality. However, one would commit the violence of reproduction of the epistemological logics and rationalities constitutive (...) of the current system if the story ended there. We have survived and our survival points to the urgent necessity and responsibility of social theory to listen to the story of the pandemic from a Black/Indigenous genealogy and to begin the sense-making of the Covid-19 pandemic, from prior to this particular virus, outside, against and beyond the politics of knowledge of critical social theory itself. Thus, I invite you to journey to an affirmative re-enfleshment of reason and theory-making in relation to and dialogue with Black, Indigenous, and subaltern Mestiza feminist movements in southwest Colombia and in southeast so-called Australia in the unceded lands of the Awabakal and the Worimi. I explore this through the metaphor, the materiality, the cosmology and the herstory of the mangrove swamps a knowing-being otherwise visible to the dehumanising gave of Whiteness and bring to thought three stories of a politics of knowledge of/as the Black/racialised and feminised body/flesh. To do this is to suggest that the co-creation of pathways which are life affirming and life making beyond and out of the post-Covid 19 conjuncture involves an epistemological-political project which decolonises and feminises the containments of reason and knowing being of coloniality/modernity. (shrink)

A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.

Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apartness, for sequents in which all atomic formulas appear negated. The proof extends to conservativity results for the theories of constructive order over (...) the usual theories of order. (shrink)

Charles S. Peirce held a view of human reason as creative. The objective of this article is to explore more deeply the Peircean conception of imagination, indispensable for the correct functioning of reason. The connection of reason and imagination is necessary in order to be able to interpret the world, to advance towards the truth and to direct our own actions. In this paper I will explain the principal forms in which these faculties interact, and will provide examples taken from (...) the Peircean corpus. (shrink)

A uniform calculus for linear logic is presented. The calculus has the form of a natural deduction system in sequent calculus style with general introduction and elimination rules. General elimination rules are motivated through an inversion principle, the dual form of which gives the general introduction rules. By restricting all the rules to their single-succedent versions, a uniform calculus for intuitionistic linear logic is obtained. The calculus encompasses both natural deduction and sequent calculus that are obtained as special instances from (...) the uniform calculus. Other instances give all the invertibilities and partial invertibilities for the sequent calculus rules of linear logic. The calculus is normalizing and satisfies the subformula property for normal derivations. (shrink)

Research Ethics, Volume 18, Issue 1, Page 24-38, January 2022. Are social science, cross-border research projects, where recruitment and data collection are carried out remotely, required to follow similar ethical and data-sharing procedures as ‘on-the-ground’ studies that use traditional means of recruitment and participant engagement? This article reflects on our experience of dealing with this question when we had to switch to online data collection due to the restrictions posed by the COVID-19 pandemic, such as the inability to travel or (...) work in person with local communities and collaborators. Using social media platforms and online data collection when conducting research brings many advantages, such as being able to communicate remotely but directly with gatekeepers and collaborators, and in reaching potential participants on a global scale. However, neither the guidelines and advice for conducting ethically sound internet-based research, nor the academic literature focussed on building equitable research partnerships between the Global North and the Global South, offer much information regarding the ethical concerns, or address the grey areas, posed by this type of digital and distanced transnational research. In our experience, conducting research remotely made negotiations of access very challenging due to the politics of positionality between Global North and South researchers, lack of clarity on ethical processes and perceptions of gatekeepers who we could not meet in person. We hope the reflections on, and discussion of, our experience encourage deliberation on the present ethical challenges posed by online and social-media-disseminated data collection, particularly in cross-border circumstances. (shrink)

This article analyses some of the governmental issues at stake in contemporary institutional politics in its confrontation with the challenges of digitalisation. Through notions such as algorithmic governmentality (Rouvroy and Berns), platformisation (Bratton, Stiegler), extractivism, and the affect theory (Massumi), and following a symptomatologic method, we will try to establish and discuss some key points that could be useful in order to update certain concepts regarding micro- and biopolitics (Deleuze and Guattari, Foucault), the public sphere, and the management of social (...) and individual bodies. Finally, we will try to understand how the manipulation of affects via the staging of possible catastrophic futures (Parisi) is used as a powerful neurosensory weapon, with performative effects for governing and modelling behaviours. If contemporary capitalism is capable of abstracting and extracting affects, of accumulating them and of creating value through this, which policies should we apply in this situation of uncertainty and of the manipulation of affectivity? Is there any place left for public institutions, or is the market the sole political actor left? (shrink)

The concept of solidarity is of central importance to the political sense of collective action. But it is a curious fact that solidarity is virtually unmentioned across the large and growing literature in philosophical collective action theory. Instead, we see discussions of collective action overwhelmingly focus on epistemic conditions and group-level correlates of individual action explanations such as collective intentions, collective beliefs, and so on. The aim of this paper is to elucidate the relationship between solidarity and collective action theory. (...) I will try to answer two questions: (1) What is it about the structure of accounts of collective action that seems to preclude discussions of solidarity and related concepts; and (2) How can solidarity be made to play a useful role in those accounts? (shrink)

In this article the authors challenge the hegemonic masculinity of the dominant football discourses on intra-Christian sectarianism in Scotland through a pilot study on women’s everyday experiences of sectarianism. The authors argue that dominant constructions of sectarianism often erase the standpoints of different kinds of women by minimising their roles both as agents for change and/or subjects who also reproduce sectarianism in their own right. The findings offer alternative narratives which problematise sectarianism as a white, male-only, working-class issue. This highlights (...) the need to legitimise different gendered manifestations of sectarian bigotry at the micro-social level of family and kinship networks particularly in relation to the seemingly feminised role of policing ethno-religious identities in marriage and the socialisation and upbringing of children. (shrink)

This study aims to define the ways in which the work of Fronto circulated and was used in the intellectual circles of the fourth century A.D. through the testimony offered by the letters of Symmachus. In addressing illustrious members of the senatorial aristocracy of his time, Symmachus echoes Fronto’s work several times. The examination of Symm. Ep. 3.11 to Naucellius, with special reference to the expression spectator tibi veteris monetae solus supersum in Symm. Ep. 3.11.2, allows us to evaluate how (...) Symmachus approaches the work of Fronto. The ways in which the short treatise ad M. Aurelium de orationibus is reprised lead us, further, to conclude that the lexical choices of the fourth-century letter-writer were determined by a textual variant in the text of Fronto available to him. (shrink)

Paul Ricoeur sustains in Soi-même comme un autre that the tragical conflict in Sophocle’s Antigone is only ethical. Antigone and Creon confront each other because they both have limited and partial views of good life. The aim of this brief paper is to show that Antigone's tragedy must be situated in the religions domain. Only Greek theology - the belief in a ‘cruel’ and ‘satanic’ God - gives us the ‘tools’ to understand Sophocles' complex imaginary.

Advances in molecular technologies have the potential to help remedy health inequities through earlier detection and prevention; if, however, their delivery and uptake are not more carefully considered, there is a very real risk that existing inequities in access and use will be further exacerbated. We argue this risk relates to the way that information and knowledge about the technology is both acquired and shared, or not, between health practitioners and their patients.A healthcare system can be viewed as a complex (...) social network comprising individuals with different worldviews, hierarchies, professional cultures and subcultures and personal beliefs, both for those giving and receiving care. When healthcare practitioners are not perceived as knowledge equals, they would experience informational prejudices, and the result is that knowledge dissemination across and between them would be impeded. The uptake and delivery of a new technology may be inequitable as a result. Patients would also experience informational prejudice when they are viewed as not being able to understand the information that is presented to them, and information may be withheld.Informational prejudices driven by social relations and structures have thus far been underexplored in considering equitable implementation and uptake of new molecular technologies. Every healthcare interaction represents an opportunity for experiencing informational prejudice, and with it the risk of being inappropriately informed for undertaking such screening or testing. Making knowledge acquisition and information dissemination, and experiences of informational prejudice, explicit through sociologically framed investigations would extend our understandings of equity, and offer ways to affect network relationships and structures that support equity in delivery and uptake. (shrink)

Medicine is no stranger to patience. In fact, the word ‘patient’ has an etymology stemming from the Latin word ‘patiens’, describing the one who tolerates suffering.1 In this sense, the cornerstone of medicine, the patient–physician relationship, reflects passive language, ‘to suffer’. This suffering must be understood, and should be most intimately understood by those who provide care that is beyond a patient’s reach. The case of patients and their loved ones requesting medically futile care at the end of life is (...) one where further treatment is replaced by patience and, more rarely, the patience of medical teams is replaced by futile treatment. At the heart of this debate is not only the denial of futile care but also the need for understanding the extent of patience that must be endured as a result of it. Burns and Truog2 remark on this ethical dilemma: > The best solution – although perhaps also the most difficult – is…tolerating the demands for care that we believe to be futile, and finding ways to better support the emotional needs of each other in those rare cases where we are called on to provide this care. The concept of futility in care represents medical intervention with limited, or no, chance of resulting in what is regarded as a clinically successful outcome. Since the American Medical Association’s endorsement of the lack of consensus on futile care in 1999, this integral conflict remains.3 This is a conflict of understanding. I believe this understanding can be strengthened by acknowledging the Arabic word for patience, ‘ sabr ’, along …. (shrink)

Il passo della "Retorica" (1358 a 10-21) dove è introdotta la distinzione τόποι e ἴδια è uno dei più controversi dell'opera aristotelica. Il presente lavoro propone un chiarimento della natura e del ruolo di τόποι e ἴδια nella costruzione di un'argomentazione dialettico-retorica. Tale chiarimento viene presentato attraverso un confronto tra Topici e "Retorica" che, se pur espressamente evidenziato da Aristotele stesso, sembra essere stato trascurato da quanti si sono occupati dell'esegesi di tale sezione della "Retorica".