By operations on models we show how to relate completeness with respect to permissivenominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction. The results are of interest in their own right, (...) but also, we factor the mathematics so as to maximise the chances that it could be used off-the-shelf for other nominal reasoning systems too. Models with infinite support can be easier to work with, so it is useful to have a semi-automatic theorem to transfer results from classes of infinitely-supported nominal models to the more restricted class of models with finite support. In conclusion, we consider different permissive-nominal syntaxes and nominal models and discuss how they relate to the results proved here. (shrink)

We are used to the idea that computers operate on numbers, yet another kind of data is equally important: the syntax of formal languages, with variables, binding, and alpha-equivalence. The original application of nominal techniques, and the one with greatest prominence in this paper, is to reasoning on formal syntax with variables and binding. Variables can be modelled in many ways: for instance as numbers (since we usually take countably many of them); as links (since they may `point' to a (...) binding site in the term, where they are bound); or as functions (since they often, though not always, represent `an unknown'). None of these models is perfect. In every case for the models above, problems arise when trying to use them as a basis for a fully formal mechanical treatment of formal language. The problems are practical—but their underlying cause may be mathematical. The issue is not whether formal syntax exists, since clearly it does, so much as what kind of mathematical structure it is. To illustrate this point by a parody, logical derivations can be modelled using a Gödel encoding (i.e., injected into the natural numbers). It would be false to conclude from this that proof-theory is a branch of number theory and can be understood in terms of, say, Peano's axioms. Similarly, as it turns out, it is false to conclude from the fact that variables can be encoded e.g., as numbers, that the theory of syntax-with-binding can be understood in terms of the theory of syntax-without-binding, plus the theory of numbers (or, taking this to a logical extreme, purely in terms of the theory of numbers). It cannot; something else is going on. What that something else is, has not yet been fully understood. In nominal techniques, variables are an instance of names, and names are data. We model names using urelemente with properties that, pleasingly enough, turn out to have been investigated by Fraenkel and Mostowski in the first half of the 20th century for a completely different purpose than modelling formal language. What makes this model really interesting is that it gives names distinctive properties which can be related to useful logic and programming principles for formal syntax. Since the initial publications, advances in the mathematics and presentation have been introduced piecemeal in the literature. This paper provides in a single accessible document an updated development of the foundations of nominal techniques. This gives the reader easy access to updated results and new proofs which they would otherwise have to search across two or more papers to find, and full proofs that in other publications may have been elided. We also include some new material not appearing elsewhere. (shrink)

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; it is not always possible to ‘α-convert a bound variable symbol’ or to ‘quotient by α-equivalence’; the notion of unifier is not based just on substitution.Permissive nominal terms closely resemble nominal terms but they recover these properties, and in (...) particular the ‘always fresh’ and ‘always rename’ properties. In the permissive world, freshness contexts are elided, equality is fixed, and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of unification based on substitution plus extra freshness conditions.We prove that expressivity is not lost moving to the permissive case and provide an injection of nominal terms unification problems and their solutions into permissive nominal terms problems and their solutions.We investigate the relation between permissive nominal unification and higher-order pattern unification. We show how to translate permissive nominal unification problems and solutions in a sound, complete, and optimal manner, in suitable senses which we make formal. (shrink)

In this paper we make some observations about Natural Deduction derivations [Prawitz, 1965, van Dalen, 1986, Bell and Machover, 1977]. We assume the reader is familiar with it and with proof-theory in general. Our development will be simple, even simple-minded, and concrete. However, it will also be evident that general ideas motivate our examples, and we think both our specific examples and the ideas behind them are interesting and may be useful to some readers. In a sentence, the bare technical (...) content of this paper is: Extending natural deduction with global well-formedness conditions can neatly and cheaply capture classical and intermediate logics. The interest here is in the ‘neatly’ and ‘cheaply’. By ‘neatly’ we mean ‘preserving proof-normalisation’,1 and ‘maintaining the subformula property’, and by ‘cheaply’ we mean ‘preserving the formal structure of deductions’ (so that a deduction in the original system is still, formally, a deduction in the extended system, and in particular it requires no extra effort to write just because it is in the extended system). To illustrate what we have in mind consider intuitionistic first-order logic (FOL) [van Dalen, 1986] as a paradigmatic example of a formal notion of deduction. A natural deduction derivation (or deduction) is an inductively defined tree structure where each node contains an instance of a formula. A deduction is valid when each successive node follows from its predecessors in accordance with some predetermined inference rules. A particular attraction of Natural Deduction is its clean and economical presentation. Here for example are deduction (fragments) proving A ∧ B from A and B, and ∀x. (P (x) ∧ Q(x)) from ∀x. P (x) and ∀x. Q(x): ∀x. P (x) (∀E). (shrink)

Interpolation has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact that common logical formalisms often lack uniform interpolants, we (...) advocate the need for developing general methods to engineer a specification logic so that some critical uniform interpolants become available. (shrink)

Stone-walling dialogues are exercises in structured non-cooperation. It is true that dialogue participants need to cooperate with one another and in ways sufficient to make possible the very dialogue they are now having. Beyond that there is room for non-cooperation on a scale that gives great offence to what we call the Goody Two-Shoes Model of argument. In this paper, we argue that non-cooperation dialogues have perfectly legitimate objectives and that in relation to those objectives they need not be considered (...) at all subpar to conversations that brim with sunny amity.Two categories of stone-walling non-cooperation dialogues are here examined. They are called MindClosed and NoEngage. They are exemplified by the following cases:1. Hostile Police Interrogation2. Judicial Cross-Examination3. Department Store Complaints Management4. Lakatosian Science5. Gödel's First Incompleteness Proof. (shrink)

Provision of adequate nutrition to elderly patients who develop dysphagia after a stroke can be quite challenging, often leading to the placement of a percutaneous entero‐gastrostomy (PEG) tube for nutritional support. This hypothetical case describes the additional challenge of cross‐cultural belief that leads a daughter to provide oral feeding to her mother, an act that the medical team believes is dangerous and the daughter sees as salubrious. In this case, what is the proper balance between patient safety and deference to (...) cultural traditions and norms? Where are the limits? Two commentaries offer insights for conflict resolution, including recommending that the medical team seek to understand the cultural motivations of the family, balancing safety and respect for cultural norms. The second commentary also disagrees with the team's presumption that the daughter's feeding of her mother is a greater threat to the patient than the PEG tube feeding is. (shrink)

The purpose of this paper is to communicate some developments in what we call the new logic. In a nutshell the new logic is a model of the behaviour of a logical agent. By these lights, logical theory has two principal tasks. The first is an account of what a logical agent is. The second is a description of how this behaviour is to be modelled. Before getting on with these tasks we offer a disclaimer and a warning. The disclaimer (...) is that although the new logic is significantly different from it, we have no inclination to see the new logic as a rival of mathematical logic. We do not advocate the displacement of, e.g. model theory, but rather its supplementation or adaptation. The warning is that, whereas mathematical logic must eschew psychologism, the new logic cannot do without it. The fuller story of the new logic must eschew psychologism, the new logic cannot do without it. The fuller story of the new logic is part of our book, The Reach of Abduction, scheduled to appear in 2001 or early 2002. (shrink)

This volume constitutes the proceedings of the First International Conference on Temporal Logic (ICTL '94), held at Bonn, Germany in July 1994. Since its conception as a discipline thirty years ago, temporal logic is studied by many researchers of numerous backgrounds; presently it is in a stage of accelerated dynamic growth. This book, as the proceedings of the first international conference particularly dedicated to temporal logic, gives a thorough state-of-the-art report on all aspects of temporal logic research relevant for computer (...) science and AI. It contains 27 technical contributions carefully selected for presentation at ICTL '94 as well as three surveys and position papers. (shrink)

Derrida is typically taken to be the thinker most antithetical to Hegel, and deconstruction to be the philosophical antithesis to Hegel’s systematic rationality. While I do not dispute the accuracy of this perception, I argue in this paper that it does not offer an adequate or a complete picture. Specifically, much about Derrida and about deconstruction is more similar to Hegel than is typically realized. I argue that Derrida’s deconstruction shares a great affinity to the method of Hegel’s Phenomenology of (...) Spirit, so much so that we could identify and articulate a latent Hegelianism in Derrida’s approach. I begin with a description of Derrida’s own project, then offer something of an apologia for his work. Finally, I describe Hegel’s method of exposition [Darstellung] and compare it to deconstruction, pointing out the fundamental similarities between the two thinkers. (shrink)

Patients from religious minorities can face unique challenges reconciling their beliefs with the values that undergird Western Medical Ethics. This paper explores homologies between approaches of Orthodox Judaism and Islam to medical ethics, and how these religions’ moral codes differ from the prevailing ethos in medicine. Through analysis of religious and biomedical literature, this work examines how Jewish and Muslim religious observances affect decisions about genetic counseling, reproductive health, pediatric medicine, mental health, and end-of-life decisions. These traditions embrace a theocentric (...) rather than an autonomy-based ethics. Central to this conception is the view that life and the body are gifts from God rather than the individual and the primacy of community norms. These insights can help clinicians provide care that aligns Muslim and Jewish patients’ health goals with their religious beliefs and cultural values. Finally, dialogue in a medical context between these faith traditions provides an opportunity for rapprochement amidst geopolitical turmoil. (shrink)

Levinas and other contemporary thinkers have claimed that the philosophy of "the other" provides a devastating critique of systematic rationality as such and of Hegel as a paradigm case thereof.The critique links an ethical moment and socio-political issues to a thorough-going critique of Hegelian metaphysics and the dialectical method. I articulate the meaning of alterity as a critique of Hegel through Levinas and Marx, and then discuss possible Hegelian responses to this criticism. I conclude that this critique of Hegel pertains (...) to the character of his final synthesis rather than to questions of difference and identity, and challenge the interpretation of Hegelian closure as the realization of eschatology. (shrink)

When the COVID-19 surge hit New York City hospitals, the Division of Medical Ethics at Weill Cornell Medical College, and our affiliated ethics consultation services, faced waves of ethical issues sweeping forward with intensity and urgency. In this article, we describe our experience over an eight-week period (16 March through 10 May 2020), and describe three types of services: clinical ethics consultation (CEC); service practice communications/interventions (SPCI); and organizational ethics advisement (OEA). We tell this narrative through the prism of time, (...) describing the evolution of ethical issues and trends as the pandemic unfolded. We delineate three phases: anticipation and preparation, crisis management, and reflection and adjustment. The first phase focused predominantly on ways to address impending resource shortages and to plan for remote ethics consultation, and CECs focused on code status discussions with surrogates. The second phase was characterized by the dramatic convergence of a rapid increase in the number of critically ill patients, a growing scarcity of resources, and the reassignment/ redeployment of staff outside their specialty areas. The third phase was characterized by the recognition that while the worst of the crisis was waning, its medium- and long-term consequences continued to pose immense challenges. We note that there were times during the crisis that serving in the role of clinical ethics consultant created a sense of dis-ease as novel as the coronavirus itself. In retrospect we learned that our activities far exceeded the familiar terrain of clinical ethics consultation and extended into other spheres of organizational life in novel ways that were unanticipated before this pandemic. To that end, we defined and categorized a middle level of ethics consultation, which we have termed service practice communication intervention (SPCI). This is an underappreciated dimension of the work that ethics consult services are capable of in times of crisis. We believe that the pandemic has revealed the many enduring ways that ethics consultation services can more robustly contribute to the ethical life of their institutions moving forward. (shrink)

In Capital as Organic Unity, Mark E. Meaney argues “that the doctrinal content of Marx’s Grundrisse is indebted for its logical form to Hegel’s exposition of logical categories as found in the Wissenschaft der Logik”. Meaney builds upon an important work by Hiroshi Uchida which had already explored Marx’s debt in the Grundrisse to Hegel’s Logic. But beyond Uchida’s claims, Meaney maps the entire structure of the Grundrisse onto the parallel movements of Hegel’s larger Science of Logic. Meany’s text contains (...) seven chapters. Besides the introduction and conclusion, one chapter discusses money as being, two discuss capital as essence or the essence of capital, and two more discuss the concept of capital in its objective, conceptual completeness. Capital is for Marx a concrete manifestation of Hegel’s objectification of the concept. (shrink)

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...) to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in the nodes of (...) a network. The suitable semantics for such networks is Kripke semantics. We also introduce a new key concept of usability of an argument. This is the beginning of a continuing research for adding contents to the nodes of an argumentation network. This research will allow us to address notions like ?what does it exactly mean for a node to attack another? or ?what does it mean for a network to be consistent? or ?can we give proper proof rules to manipulate networks?, and more. (shrink)

A 47-year-old woman with a history of anxiety disorder is admitted to the hospital for shortness of breath. On the third day of hospitalization, she asks her physician for a copy of all documents pertaining to her care. What expectation should she have for full disclosure? Are there limits on her access to her medical records and do her physician's concerns about professional privilege matter?The virtues of transparency in medicine have been well described. As proponents of transparency, we favor patient (...) access to their medical records, but we are increasingly troubled by the ease and extent of disclosure in current practice as technology advances and... (shrink)

Numerous social, economic and academic pressures can have a negative impact on representations of biomedical research. We review several of the forces playing an increasingly pernicious role in how health and science information is interpreted, shared and used, drawing discussions towards the role of narrative. In turn, we explore how aspects of narrative are used in different social contexts and communication environments, and present creative responses that may help counter the negative trends. As traditional methods of communication have in many (...) ways failed the public, changes in approach are required, including the creative use of narratives. (shrink)

This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, J. M. Dunn and G. Hardegree's Algebraic Methods in (...) Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control. (shrink)

We motivate and introduce a new method of abduction, Matrix Abduction, and apply it to modelling the use of non-deductive inferences in the Talmud such as Analogy and the rule of Argumentum A Fortiori. Given a matrix $${\mathbb {A}}$$ with entries in {0, 1}, we allow for one or more blank squares in the matrix, say a i,j =?. The method allows us to decide whether to declare a i,j = 0 or a i,j = 1 or a i,j =? (...) undecided. This algorithmic method is then applied to modelling several legal and practical reasoning situations including the Talmudic rule of Kal-Vachomer. We add an Appendix showing that this new rule of Matrix Abduction, arising from the Talmud, can also be applied to the analysis of paradoxes in voting and judgement aggregation. In fact we have here a general method for executing non-deductive inferences. (shrink)

Résumé éditeur : This book tells two intertwined stories, centered on twentieth-century moral philosophers Elizabeth Anscombe, Mary Midgley, Philippa Foot, and Iris Murdoch. The first is the story of four friends who came up to Oxford together just before WWII. It is the story of their lives, loves, and intellectual preoccupations; it is a story about women trying to find a place in a man's world of academic philosophy. The second story is about these friends' shared philosophical project and (...) their unintentional creation of a school of thought that challenged the dominant way of doing ethics. That dominant school of thought envisioned the world as empty, value-free matter, on which humans impose meaning. This outlook treated statements such as “this is good” as mere expressions of feeling or preference, reflecting no objective standards. It emphasized human freedom and demanded an unflinching recognition of the value-free world. The four friends diagnosed this moral philosophy as an impoverishing intellectual fad. This style of thought, they believed, obscured the realities of human nature and left people without the resources to make difficult moral choices or to confront evil. As an alternative, the women proposed a naturalistic ethics, reviving a line of thought running through Plato, Aristotle, and Aquinas, and enriched by modern biologists like Jane Goodall and Charles Darwin. The women proposed that there are, in fact, moral truths, based in facts about the distinctive nature of the human animal and what that animal needs to thrive.". (shrink)