We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes...

We compute the domination monoid in the theory of dense meet‐trees. In order to show that this monoid is well‐defined, we prove weak binarity of and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.

The paper explores the logical strength of Isbell's zig‐zag theorem using the framework of reverse mathematics. Working in, we show that is equivalent to Isbell's zig‐zag theorem for countable monoids: If B is a monoid extension of A, then is dominated by A if and only if b has a zig‐zag over A. Our proof of Isbell's zig‐zag theorem avoids use of strong comprehension axioms common in traditional proofs. We also analyze the strength of theorems concerning binary relations.

What exactly is the human element separating humans from animals and machines? The common answers that immediately come to mind—like art, empathy, or technology—fall apart under close inspection. Dominic Pettman argues that it is a mistake to define such rigid distinctions in the first place, and the most decisive “human error” may be the ingrained impulse to understand ourselves primarily in contrast to our other worldly companions. In _Human Error_, Pettman describes the three sides of the cybernetic triangle—human, animal, and (...) machine—as a rubric for understanding key figures, texts, and sites where our species-being is either reinforced or challenged by our relationship to our own narcissistic technologies. Consequently, species-being has become a matter of _specious_-being, in which the idea of humanity is not only a case of mistaken identity but indeed the mistake of identity. _Human Error_ boldly insists on the necessity of relinquishing our anthropomorphism but also on the extreme difficulty of doing so, given how deeply this attitude is bound with all our other most cherished beliefs about forms of life. (shrink)

In _ Psychiatry in the Scientific Image, _Dominic Murphy looks at psychiatry from the viewpoint of analytic philosophy of science, considering three issues: how we should conceive of, classify, and explain mental illness. If someone is said to have a mental illness, what about it is mental? What makes it an illness? How might we explain and classify it? A system of psychiatric classification settles these questions by distinguishing the mental illnesses and showing how they stand in relation to one (...) another. This book explores the philosophical issues raised by the project of explaining and classifying mental illness. Murphy argues that the current literature on mental illness -- exemplified by the Diagnostic and Statistical Manual of Mental Disorders -- is an impediment to research; it lacks a coherent concept of the mental and a satisfactory account of disorder, and yields too much authority to commonsense thought about the mind. He argues that the explanation of mental illness should meet the standards of good explanatory practice in the cognitive neurosciences, and that the classification of mental disorders should group symptoms into conditions based on the causal structure of the normal mind. (shrink)

[David Charles] Aristotle, it appears, sometimes identifies well-being with one activity, sometimes with several, including ethical virtue. I argue that this appearance is misleading. In the Nicomachean Ethics, intellectual contemplation is the central case of human well-being, but is not identical with it. Ethically virtuous activity is included in human well-being because it is an analogue of intellectual contemplation. This structure allows Aristotle to hold that while ethically virtuous activity is valuable in its own right, the best life available for (...) humans is centred around, but not wholly constituted by, intellectual contemplation. /// [Dominic Scott] In Nicomachean Ethics X 7-8, Aristotle distinguishes two kinds of eudaimonia, primary and secondary. The first corresponds to contemplation, the second to activity in accordance with moral virtue and practical reason. My task in this paper is to elucidate this distinction. Like Charles, I interpret it as one between paradigm and derivative cases; unlike him, I explain it in terms of similarity, not analogy. Furthermore, once the underlying nature of the distinction is understood, we can reconcile the claim that paradigm eudaimonia consists just in contemplation with a passage in the first book requiring eudaimonia to involve all intrinsic goods. (shrink)

For centuries, philosophers have identified beauty with what brings pleasure. Dominic McIver Lopes challenges this interpretation by offering an entirely new theory of beauty - that beauty engages us in action, in concert with others, in the context of social networks - and sheds light on why aesthetic engagement is crucial for quality of life.

Les Arts et les Images se veut une introduction aux principaux terrains d’investigation de Dominic McIver Lopes, philosophe canadien contemporain, figure incontournable de l’esthétique et de la philosophie de l’art en langue anglaise au cours des vingt dernières années. Il ouvre une réflexion sur les méthodes employées en esthétique et philosophie de l’art aujourd’hui, qu’on soit un philosophe dit « analytique » ou bien « continental », Lopes cherchant à penser le lien entre les deux traditions. -/- À travers leur (...) textes respectifs, Laure Blanc-Benon, Jacques Morizot et Frédéric Pouillaude instaurent un dialogue avec Dominic McIver Lopes, sur plusieurs de ses livres : Understanding Pictures (1996), ouvrage de référence sur la question philosophique des images et de la représentation, Beyond Art (2014), livre qui traite de la question classique au XXe siècle de la définition de l’œuvre d’art, et Four Arts of Photography (2016) dans lequel Dominic Lopes met en avant une nouvelle philosophie de la photographie. À ce dialogue s’ajoutent trois textes de Lopes inédits en français, portant sur la méthode de l’esthétique et de la philosophie de l’art et également sur la question de la beauté et de la valeur esthétique. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way (...) of handling duality. (shrink)

Using the example of recent attempts to engineer the concept of conspiracy theory, I argue that philosophers should be far more circumspect in their approach to conceptual engineering than we have been – in particular, that we should pay much closer attention to the history behind and context that surrounds our target concept in order to determine whether it is a site of what I have elsewhere called ‘conceptual domination’. If it is, we may well have good reason to (...) avoid engineering. In their recent ‘What is a Conspiracy Theory?’, M. Giulia Napolitano and Kevin Reuter argue that the disagreement between generalists and particularists in the literature on conspiracy theories is best characterized as a set of dueling conceptual engineering projects. While I agree with their turn to this metaphilosophical literature, I give a very different account of its applicability. Particularists, on my account, are better read as aiming to diagnose the ways in which many discussions of the concept of conspiracy theories are a form of conceptual domination, where this broader context should then prompt us to abandon or block any concept of conspiracy theory that treats its referents as inherently defective. Broader metaphilosophical lessons are drawn. (shrink)

Why me? -- Sticks and stones -- Hammer of God -- God is great -- The problem of atheists -- Guardian angels -- Nations under God -- God knows.

Dominic Scott compares the Republic and Nicomachean Ethics from a methodological perspective. He argues that Plato and Aristotle distinguish similar levels of argument in the defence of justice, and that they both follow the same approach: Plato because he thinks it will suffice, Aristotle because he thinks there is no need to go beyond it.

There is not one but many ways to picture the world--Australian "x-ray" pictures, cubish collages, Amerindian split-style figures, and pictures in two-point perspective each draw attention to different features of what they represent. Understanding Pictures argues that this diversity is the central fact with which a theory of figurative pictures must reckon. Lopes advances the theory that identifying pictures' subjects is akin to recognizing objects whose appearances have changed over time. He develops a schema for categorizing the different ways pictures (...) represent--the different kinds of meaning they have--and argues that that depiction's epistemic value lies in its representational diversity. He also offers a novel account of the phenomenology of pictorial experience, comparing pictures to visual prostheses like mirrors and binoculars. (shrink)

Certain representations are bound in special ways to our sensory capacities; consider, for instance, pictures, sound recordings, and the various forms of mental sensory imagery. What do these representations have in common, and what makes them different from representations of other kinds? Dominic Gregory employs novel ideas on perceptual states and sensory perspectives to explain the special nature of the contents of distinctively sensory representations. The book contains extensive discussions of e.g. perceptual imagination, pictorial representation, and memories.

What is computer art? Do the concepts we usually employ to talk about art, such as ‘meaning’, ‘form’ or ‘expression’ apply to computer art? _A Philosophy of Computer Art_ is the first book to explore these questions. Dominic Lopes argues that computer art challenges some of the basic tenets of traditional ways of thinking about and making art and that to understand computer art we need to place particular emphasis on terms such as ‘interactivity’ and ‘user’. Drawing on a wealth (...) of examples he also explains how the roles of the computer artist and computer art user distinguishes them from makers and spectators of traditional art forms and argues that computer art allows us to understand better the role of technology as an art medium. (shrink)

Images have power - for good or ill. They may challenge us to see things anew and, in widening our experience, profoundly change who we are. The change can be ugly, as with propaganda, or enriching, as with many works of art. Sight and Sensibility explores the impact of images on what we know, how we see, and the moral assessments we make. Dominic Lopes shows how these are part of, not separate from, the aesthetic appeal of images. His book (...) will be essential reading for anyone working in aesthetics and art theory, and for all those intrigued by the power of images to affect our lives. '...tightly focused and carefully argued... an exceptionally interesting contribution to the philosophy of art: it contains subtle, concise, and convincing discussions of a number of difficult concepts and contentious doctrines... lucid and meticulous'. (shrink)

Is it ethical for doctors or courts to prevent patients from making choices that will cause significant harm to themselves in the future? According to an important liberal principle the only justification for infringing the liberty of an individual is to prevent harm to others; harm to the self does not suffice.In this paper, I explore Derek Parfit’s arguments that blur the sharp line between harm to self and others. I analyse cases of treatment refusal by capacitous patients and describe (...) different forms of paternalism arising from a reductionist view of personal identity. I outline an Identity Relative Paternalistic Intervention Principle for determining when we should disallow refusal of treatment where the harm will be accrued by a future self, and consider objections including vagueness and non-identity.Identity relative paternalism does not always justify intervention to prevent harm to future selves. However, there is a stronger ethical case for doing so than is often recognised. (shrink)

This paper argues that social media companies’ power to regulate communication in the public sphere illustrates a novel type of domination. The idea is that, since social media companies can partially dictate the terms of citizens’ political participation in the public sphere, they can arbitrarily interfere with the choices individuals make qua citizens. I contend that social media companies dominate citizens in two different ways. First, I focus on the cases in which social media companies exercise direct control over (...) political speech. They exercise quasi-public power over citizens because their regulation of speech on social media platforms implies the capacity to arbitrarily interfere with citizens’ democratic contestation in the political system. Second, companies’ algorithmic governance entails the capacity to interfere with citizens’ choices about what mode of discursive engagement they endorse in their relationships with fellow citizens. By raising the cost of deliberative engagement, companies narrow citizens’ choice menu. (shrink)

In recent years, there has been a wide-ranging debate about the neo-republican principle of non-domination. Neo-republicans argue that domination is a capacity for one to intentionally use arbitrary power to interfere in someone’s life. Critics of neo-republicanism argue that this definition of freedom as non-domination precludes a structural analysis of domination, which would explain and critique the ways in which societies produce structural domination unintentionally. The article focuses on capitalism’s labor process and its labor markets. (...) It argues that critics are correct to think that the neo-republican principle of non-domination has an insufficient scope, but that an alternative account of structural domination should still support the neo-republican idea that agency must be involved. Otherwise, we might simply fail to explain the social processes that reproduce structural domination. What is needed is to explain how the labor process creates incentives for agents to intentionally produce structures that have unintended, yet dominating effects, and in turn, how the intentions of agents are conditioned by their social positions. Domination is thus agential and structural. (shrink)

This book offers a bold new approach to the philosophy of art. General theories of art don't work: they can't deal with problem cases. Instead of trying to define art, we should accept that a work of art is nothing but a work in one of the arts. Lopes's buck passing theory works well for the avant garde, illuminating its radical provocations.

The paper examines the relationships between the contents of imaginative episodes and the mental images that often play a central role within them. It considers, for example, whether the presence of mental imagery is required for a mental episode to count as an imagining.

In early 2020, a number of countries developed and published intensive care triage guidelines for the pandemic. Several of those guidelines, especially in the UK, encouraged the explicit assessment...

This article proposes a Social Determinants of Health framework as a counter to the prominence of bio-determinist tropes in understandings of the relationship between concussion and later life neurodegenerative conditions in athletic populations. It is argued that debates about concussion (or repetitive head impacts) causing CTE have been particularly influenced by broader social trends towards neuro-essentialism. This paradigm reduces complex social behaviour to brain matter and continues to dominate the field despite the recent diversification of evidence from autopsy-based studies of (...) neuropathology to epidemiological studies comparing recorded causes of death among former elite athletes. In contrast, this article explores the ‘causes of causes’ of neurodegenerative conditions. It outlines the ways in which the distinct dynamics of: a) employment, b) education, income and wealth, c) health systems and services, and d) social environment and public safety relate to the specific occupational conditions of elite sport and likely negatively shape health outcomes of athletic populations. The article concludes by arguing that to more effectively address these particular health harms we must move beyond narrow, mono-causal models and evoke a cultural change that extends beyond making rule changes and adjusting psychological attitudes and behavioural norms, to redress the social structural parameters of elite sports participation. The continuation of narrower, neuro-centric and reductionist paradigms obscures the causes of the causes of neurodegenerative decline and limits the scope for change. (shrink)

Interpreters of Hume on causation consider that an advantage of the ‘quasi-realist’ reading is that it does not commit him to scepticism or to an error theory about causal reasoning. It is unique to quasi-realism that it maintains this positive epistemic result together with a rejection of metaphysical realism about causation: the quasi-realist supplies an appropriate semantic theory in order to justify the practice of talking ‘as if’ there were causal powers in the world. In this paper, I problematise the (...) quasi-realist reading of Hume on causation by showing how quasi-realism does not speak to inductive scepticism. I also offer evidence that Hume takes inductive scepticism to result from his theory of causation, and that his scepticism is tied to his rejection of metaphysical causal realism. (shrink)

On 24 July 2017, the long-running, deeply tragic and emotionally fraught case of Charlie Gard reached its sad conclusion. Following further medical assessment of the infant, Charlie’s parents and doctors finally reached agreement that continuing medical treatment was not in Charlie’s best interests. Life support was subsequently withdrawn and Charlie died on 28 July 2017.Box 1 ### Case summary and timeline21–23 Charlie Gard was born at full term, apparently healthy, in August 2016. At a few weeks of age his parents (...) noticed early signs of muscle weakness. At 2 months of age, he was admitted to Great Ormond Street Hospital with poor feeding, failure to thrive and respiratory failure. He was admitted to intensive care, where investigations led to the diagnosis of a rare severe mitochondrial disorder – infantile onset encephalomyopathic mitochondrial DNA depletion syndrome. The specific genetic form of MDDS in Charlie Gard had previously been reported in approximately 15 infants, with typical clinical features including early onset, rapid progression and death in infancy.24 By that point, Charlie was paralysed and unable to breathe without respiratory support. He was found to have congenital deafness, and his heart, liver and kidneys were affected by the disorder. Doctors felt that Charlie’s prognosis was extremely poor. In early 2017, Charlie’s parents identified an experimental treatment, previously used in a different form of MDDS, which they hoped might benefit Charlie. In mouse models of a myopathic form of MDDS, early supplementation with deoxypryrimidine nucleosides apparently bypasses the genetic defect and leads to a reduction in the biochemical defect and in the severity of the clinical phenotype.25 26 Doctors at GOSH initially planned to use nucleoside treatment in Charlie, but in January he developed evidence of electrical seizures, and clinicians became convinced that treatment, both continued intensive care and the requested …. (shrink)

The COVID-19 coronavirus pandemic raises a host of challenging ethical questions at every level of society. However, some of the most acute questions relate to decision making in intensive care. The problem is that a small but significant proportion of patients develop severe viral pneumonitis and respiratory failure. It now seems likely that the number of critically ill patients will overwhelm the capacity of intensive care units within many health systems, including the National Health Service in the UK. The experience (...) of Northern Italy—a couple of weeks ahead of the UK, suggests that it will simply not be possible to provide mechanical ventilation to every patient who might need it. When the crunch comes, the unpalatable question facing clinicians is which patient to save. There are some obvious strategies to avoid or reduce the problem—through measures to increase intensive care capacity, and via society-level interventions to reduce the spread of the virus. These are vitally important, but unfortunately they are unlikely to prevent the problem of demand outstripping supply from occurring. What, then, should clinicians do? How should they allocate the scarce resource of intensive care—particularly over the coming weeks as the crisis escalates? There are different values at stake in triage decisions, but at a basic level the key values are those of benefit and …. (shrink)

Williamson has argued against scepticism concerning our metaphysically modal knowledge, by arguing that standard patterns of suppositional reasoning to counterfactual conclusions provide reliable sources of correct ascriptions of possibility and necessity. The paper argues that, while Williamson’s claims relating to necessity may well be right, he has not provided adequate reasons for thinking that the familiar modes of counterfactual reasoning to which he points generalise to provide a decent route to ascriptions of possibility. The paper also explores another path to (...) ascriptions of possibility that may be extracted from Williamson’s ideas, before briefly considering the general status of counterfactual reasoning in relation to our knowledge of possibilities. (shrink)

Questions about learning and discovery have fascinated philosophers from Plato onwards. Does the mind bring innate resources of its own to the process of learning or does it rely wholly upon experience? Plato was the first philosopher to give an innatist response to this question and in doing so was to provoke the other major philosophers of ancient Greece to give their own rival explanations of learning. This book examines these theories of learning in relation to each other. It presents (...) an entirely different interpretation of the theory of recollection which also changes the way we understand the development of ancient philosophy after Plato. The final section of the book compares ancient theories of learning with the seventeenth-century debate about innate ideas, and finds that the relation between the two periods is far more interesting and complete than is usually supposed. (shrink)

Ethical analyses, professional guidelines and legal decisions support the equivalence thesis for life-sustaining treatment: if it is ethical to withhold treatment, it would be ethical to withdraw the same treatment. In this paper we explore reasons why the majority of medical professionals disagree with the conclusions of ethical analysis. Resource allocation is considered by clinicians to be a legitimate reason to withhold but not to withdraw intensive care treatment. We analyse five arguments in favour of non-equivalence, and find only relatively (...) weak reasons to restrict rationing to withholding treatment. On the contrary, resource allocation provides a strong argument in favour of equivalence: non-equivalence causes preventable death in critically ill patients. We outline two proposals for increasing equivalence in practice: (1) reduction of the mortality threshold for treatment withdrawal, (2) time-limited trials of intensive care. These strategies would help to move practice towards more rational treatment limitation decisions. (shrink)

Theories of domination are primarily attempts to understand the value of justice, freedom, and equality by examining cases where they are absent. Such theories seek to clarify and systematize our judgments about what it is to be weak against uncontrolled strength, i.e., about what it is to be vulnerable, degraded, and defenseless against unrestrained power. -/- Much contemporary disagreement about domination involves competing answers to three questions: (1) Who, or what, can dominate? (2) Is it possible to dominate (...) merely by having power with a certain structure, or is domination an exercise or an abuse of power? (3) Exercised or unexercised, what kind of power is domination? The remainder of this entry will address each of these questions in turn, then conclude with a survey of how the idea of domination has been used in recent applied ethical theory. It will become clear as we examine competing answers to these three questions that different theorists have very different ideas of why, exactly, we need a theory of domination. There may be wide agreement that we need the idea of domination to make sense of unjust power relations, but unjust power relations are wildly varied, and theorists of domination disagree not only about which varieties most need to be understood, but about how theorizing domination helps us to understand them. (shrink)

Limiting dangerous climate change is now widely believed to require negative emissions, a prospect some believe to be unjust and unacceptably risky. While NETs are not risk-free, I argue tha...

This chapter begins by sketching an account of morally responsible agency and the general conditions under which it may fail. We discuss how far individuals with psychiatric diagnoses may be exempt from morally responsible agency in the way that infants are, with examples drawn from a sample of diagnoses intended to make dierent issues salient. We further discuss a recent proposal that clinicians may hold patients responsible without blaming them for their acts. We also consider cognitively impaired subjects in the (...) light of related issues in moral and political theory, asking whether they have been unjustly excluded from liberal conceptions of political community due to their presumed lack of agency. (shrink)

Vagueness, Logic and Ontology explores various responses to the philosophical problems generated by vagueness and its associated paradox - the sorites paradox. Hyde argues that the theoretical space in which vagueness is sometimes ontologically grounded and modelled by a truth-functional logic affords a coherent response to the problems posed by vagueness. Showing how the concept of vagueness can be applied to the world, Hyde's ontological account proposes a substantial revision of orthodox semantics, metaphysics and logic. This book will be of (...) particular interest to readers in philosophy, linguistics, cognitive science and geographic information systems. (shrink)

Care of the critically ill newborn includes support for the birth mother/parents with regular updates around the clinical condition of the baby, and involvement in discussions around complex decision-making issues. Discussions around continuation or discontinuation of life-sustaining are challenging even in the most straightforward of cases, but what happens when the birth mother is critically unwell? Such cases can lead to uncertainty around who should assume the parental role for these difficult discussions. In this round table discussion, we explore the (...) ethical, moral and legal uncertainties raised by coincident severe maternal and neonatal illness in the context of surrogacy. (shrink)

Ethical discussions about medical treatment for seriously ill babies or children often focus on the ‘value of life’ or on ‘quality of life’ and what that might mean. In this paper, I look at the other side of the coin—on the value of death, and on the quality of dying. In particular, I examine whether there is such a thing as a good way to die, for an infant or an adult, and what that means for medical care. To do (...) that, I call on philosophy and on personal experience. However, I will also make reference to art, poetry and music. That is partly because the topic of mortality has long been reflected on by artists as well as philosophers and ethicists. It is also because, as we will see, there may be some useful parallels to draw. (shrink)

Who should decide how a machine will decide what to do when it is driving a car, performing a medical procedure, or, more generally, when it is facing any kind of morally laden decision? More and more, machines are making complex decisions with a considerable level of autonomy. We should be much more preoccupied by this problem than we currently are. After a series of preliminary remarks, this paper will go over four possible answers to the question raised above. First, (...) we may claim that it is the maker of a machine that gets to decide how it will behave in morally laden scenarios. Second, we may claim that the users of a machine should decide. Third, that decision may have to be made collectively or, fourth, by other machines built for this special purpose. The paper argues that each of these approaches suffers from its own shortcomings, and it concludes by showing, among other things, which approaches should be emphasized for different types of machines, situations, and/or morally laden decisions. (shrink)

One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...) recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics. (shrink)

This article offers a prolegomenon for an African feminist philosophy. The prompt for this as an interrogation of Oluwole’s claim that an African feminist philosophy cannot develop until identifiable African worldviews that guide the relationship between men and women have been established. She argues that until there is general agreement about the nature of African philosophy itself, African feminist philosophy will remain impoverished. I critique this claim, unpacking Oluwole’s argument, and examine the contested nature of both African and Western philosophy. (...) Drawing from the work of Mignolo and decolonial thinking, I then argue for the possibility of “epistemic disobedience” concerning the emergence of an African feminist philosophy. Engaging with precolonial African examples which disrupt modern normative gender assumptions and looking at the project of decoloniality, I issue a call for an African feminist philosophy unfettered by the falsely universal claims of modernity/coloniality. My call is for an African feminist philosophy from African loci of enunciation, rooted in the epistemes and experiences of African women. (shrink)

You have a complex and detailed aesthetic life. You make aesthetic decisions every day. You wake up, shower, and dress. When you decide what to wear, you think about how it feels and fits. You have aesthetic feelings and reactions every day. The sunset swings into view as you turn a corner and you think, “That’s beautiful.” A wave of calm and pleasure wash over you. You take a bite of cake and you think, “Wow, that’s sweet.” Maybe too sweet. (...) Almost everything you do has an aesthetic dimension—from the way you make your bed, prepare your coffee, and tie your shoes, to the way you speak to others and edit photos to post on social media. You have a complex and detailed aesthetic life that you orchestrate every day through your aesthetic decisions, reactions, feelings, and actions. But why live this way? What exactly is aesthetic life and why, if at all, does it matter? In Aesthetic Life and Why It Matters, three philosophers present their different answers to this question and discuss the many challenging and fascinating philosophical issues that arise in our aesthetic lives. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way (...) of handling duality. (shrink)

Each Girard quantale provides a support for a semantics for linear propositional formulas. Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group. In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.