Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal substructural logic. (...) Soundness and completeness are proven each time. (shrink)

This comprehensive text shows how various notions of logic can be viewed as notions of universal algebra providing more advanced concepts for those who have an introductory knowledge of algebraic logic, as well as those wishing to delve into more theoretical aspects.

The challenge of giving a semantics for relevance logic in terms of worlds or situations intrigued several logicians. As a solution, Fine gave a two-sorted semantics. We overview the semantics as well as some further work of Fine in the area of relevance logic. Then we show that beyond supplying technical results such as soundness, completeness and the finite model property (fmp) for many logics, the operational–relational semantics provides footing for an informal interpretation and it naturally leads to an interpretation (...) in terms of relevance. (shrink)

The decidability of the logic of pure ticket entailment means that the problem of inhabitation of simple types by combinators over the base { B, B′, I, W } is decidable too. Type-assignment systems are often formulated as natural deduction systems. However, our decision procedure for this logic, which we presented in earlier papers, relies on two sequent calculi and it does not yield directly a combinator for a theorem of ${T_\to}$. Here we describe an algorithm to extract an inhabitant (...) from a sequent calculus proof—without translating the proof into another proof system. (shrink)

Seven lectures graced the second in the annual series at the Irish college devoted to the 13th-century saint and theologian. The topics include friendship and love, the desire for happiness as a way to God, the separated soul's natural knowledge, and truth as a good. Appended is a guide to consultat.

One recurring criticism of the best interests standard concerns its vagueness, and thus the inadequate guidance it offers to care providers. The lack of an agreed definition of ‘best interests’, together with the fact that several suggested considerations adopted in legislation or professional guidelines for doctors do not obviously apply across different groups of persons, result in decisions being made in murky waters. In response, bioethicists have attempted to specify the best interests standard, to reduce the indeterminacy surrounding medical decisions. (...) In this paper, we discuss the bioethicists’ response in relation to the state's possible role in clarifying the best interests standard. We identify and characterise two clarificatory strategies employed by bioethicists —elaborative and enumerative—and argue that the state should adopt the latter. Beyond the practical difficulties of the former strategy, a state adoption of it would inevitably be prejudicial in a pluralistic society. Given the gravity of best interests decisions, and the delicate task of respecting citizens with different understandings of best interests, only the enumerative strategy is viable. We argue that this does not commit the state to silence in providing guidance to and supporting healthcare providers, nor does it facilitate the abuse of the vulnerable. Finally, we address two methodological worries about adopting this approach at the state level. The adoption of the enumerative strategy is not defeatist in attitude, nor does it eventually collapse into (a form of) the elaborative strategy. (shrink)

In the UK, current policies and services for people with mental disorders, including those with intellectual disabilities (ID), presume that these men and women can, do, and should, make decisions for themselves. The new Mental Capacity Act (England and Wales) 2005 (MCA) sets this presumption into statute, and codifies how decisions relating to health and welfare should be made for those adults judged unable to make one or more such decisions autonomously. The MCA uses a procedural checklist to guide this (...) process of substitute decision-making. The personal experiences of providing direct support to seven men and women with ID living in residential care, however, showed that substitute decision-making took two forms, depending on the type of decision to be made. The first process, ‘strategic substitute decision-making’, paralleled the MCA’s legal and ethical framework, whilst the second process, ‘relational substitute decision-making’, was markedly different from these statutory procedures. In this setting, ‘relational substitute decision-making’ underpinned everyday personal and social interventions connected with residents’ daily living, and was situated within a framework of interpersonal and interdependent care relationships. The implications of these findings for residential services and the implementation of the MCA are discussed. (shrink)

The idea of the Internet as Gutenberg 2.0—a true revolution in disseminating information—is now a routine part of how bioethics education works. The Internet has become indispensable as a channel for sharing teaching materials and connecting learners with a central platform that houses materials to support an online or hybrid curriculum or a traditional course. A newer idea in bioethics education reflects developments in web-based medical education more broadly and draws on design principles developed for the Internet. This approach to (...) online bioethics education requires thinking about web-based learning as an engaging, potentially immersive experience, about learners' expectations concerning web-based learning, and about differences between self-directed learning and teaching to support group learning. In clinician education in bioethics, the interrelated goals of ethical reflection and practice for professionals and of continuous quality improvement in health care are supported by a focus on real-world challenges and by encouraging the habits of self-directed learning. In this paper, we describe how an international, interdisciplinary team used a web-based framework to develop a health care ethics casebook whose content, design, and pedagogy were tailored to the needs and expectations of health care professionals and other audiences in Singapore; we also explain how they used this framework to make the casebook accessible nationwide and to support cross-cultural learning. (shrink)

... END Reflections on Johannes Scottus's Place in Carolingian Eschatology BERNARD MCGINN I. Eschatology in the Ninth Century In 847, during the decade that ...

This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis, introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to (...) a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics. Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers. (shrink)

This book honors J. Michael Dunn, who was a preeminent relevance logician. Dunn's career spanned over 50 years and his research results had an impact on philosophy, mathematics and informatics. Dunn often used algebraic techniques in his research into logics such as relevance, orthomodular and substructural logics. He invented the logic R-mingle and the sequent calculus LR+; he proved crucial theorems about 2-valued first-order logic and non-classical higher-order logics - among many other results. The papers in this volume touch (...) upon topics that Dunn was concerned with. Some authors were students or colleagues of Dunn; some other authors had not met Dunn in person, but share his research interests. None of the articles published here have appeared in print before; indeed, most of the papers were written specifically for this collection. The diversity of the themes of the articles reflects the scope of Dunn's own research in logic. It will also ensure that anybody with an interest in logic - whether a student, a logician or a scholar in another field - will find reading this book a worthwhile endeavor. The editor, Katalin Bimbó was the 14th Ph.D. student of J. Michael Dunn at Indiana University in Bloomington, IN, U.S.A.; currently, she is a professor of philosophy at the University of Alberta in Canada. (shrink)

J. Michael Dunn and Gary M. Hardegree, "Algebraic Methods in Philosophical Logic", Oxford Logic Guides, no. 41, Clarendon Press, Oxford University Press, Oxford, New York, etc., 2001, pp xv + 470.

I outline a truthmaker semantics for relevanced logic.

This essay subjects to criticism the historical and philosophical attitudes to political thought found in the writings of John Dunn and Michael Oakeshott. The essay does not limit itself to criticism but attempts to elaborate what is indicated by criticism for the sake of the modern understanding of political thought. The argument is that history and philosophy as they have recently been practised suffer from limitations that can only be addressed by a recognition of something which is here called (...) theology. The significance of such a recognition is considered with regard to the history of political thought, political philosophy and finally to theology itself. The emphasis on theology makes it necessary to say that the essay is written for the benefit of historians and philosophers, not theologians. Although it is an argument for theology it is in no sense an argument from theology. Whether this is a contradictory position may require consideration elsewhere; but since the essay is a first step rather than a final step in an argument, it may gain more than it loses by such a contradiction, if there is one. (shrink)

J. Michael Dunn’s Theorem in 3-Valued Model Theory and Graham Priest’s Collapsing Lemma provide the means of constructing first-order, three-valued structures from classical models while preserving some control over the theories of the ensuing models. The present article introduces a general construction that we call a Dunn–Priest quotient, providing a more general means of constructing models for arbitrary many-valued, first-order logical systems from models of any second system. This technique not only counts Dunn’s and Priest’s techniques as special cases, (...) but also provides a generalized Collapsing Lemma for Priest’s more recent plurivalent semantics in general. We examine when and how much control may be exerted over the resulting theories in particular cases. Finally, we expand the utility of the construction by showing that taking Dunn–Priest quotients of a family of structures commutes with taking an ultraproduct of that family, increasing the versatility of the tool. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, 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, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in (...) theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects, 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, and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2. (shrink)

Telling a patient that the outcome of his illness is not good, or even hopeless, requires sensitivity and the ability to communicate with him in the setting of a hospital which is an unnatural environment divorced from family and friends. It is a task which must be taught and learned by doctors and nurses.

Uitgave ter gelegenheid van de vierhonderdste geboortedag van de Nederlandse jurist, diplomaat en schrijver Hugo de Groot (1583-1645).

This volume includes three previously untranslated transcripts of Kant's logic lectures.

A 'Kripke-style' semantics is given for combinatory logic using frames with a ternary accessibility relation, much as in the Tourley-Meyer semantics for relevance logic. We prove by algebraic means a completeness theorem for combinatory logic, by proving a representation theorem for 'combinatory posets.' A philosophical interpretation is given of the models, showing that an element of a combinatory poset can be understood simultaneously as a set of states and as a set of actions on states. This double interpretation allows for (...) one such element to be applied to another . Application turns out to be modeled the same way as 'fusion' in relevance logic.We also introduce 'dual combinators' that apply from the right. We then explore relationships to some well-known substructural logics, showing that each can be embedded into the structurally free. non-associative Lambek calculus, with the embedding taking a theorem ω to a statement of the form Γ ⊨ ω, where Γ is some fusion of the combinators needed to justify the structural assumptions of the given substructural logic. This builds on earlier ideas from Belnap and Meyer about a Gentzen system wherein structural rules are replaced with rules for introducing combinators. We develop such a system and prove a cut theorem. (shrink)

Researchers misunderstand their role in creating ethical problems when they allow dogmas to purportedly divorce scientists and scientific practices from the values that they embody. Cortina, Edwards, and Powell help us clarify and further develop our position by responding to our critique of, and alternatives to, this misleading separation. In this rebuttal, we explore how the desire to achieve the separation of facts and values is unscientific on the very terms endorsed by its advocates—this separation is refuted by empirical observation. (...) We show that positivists like Cortina and Edwards offer no rigorous theoretical or empirical justifications to substantiate their claims, let alone critique ours. Following Powell, we point to how classical pragmatism understands ‘purpose’ in scientific pursuits while also providing an alternative to the dogmas of positivism and related philosophical positions. In place of dogmatic, unscientific cries about an abstract and therefore always-unobservable ‘reality,’ we invite all organizational scholars to join us in shifting the discussion about quantitative research towards empirically grounded scientific inquiry. This makes the ethics of actual people and their practices central to quantitative research, including the thoughts, discourses, and behaviors of researchers who are always in particular places doing particular things. We propose that quantitative researchers can thus start to think about their research practices as a kind of work, rather than having the status of a kind of dogma. We conclude with some implications that this has for future research and education, including the relevance of research and research methods. (shrink)