The most common way of proving decidability in propositional modal logic is to shew that the system in question has the finite model property. This is not however the only way. Gabbay in [4] proves the decidability of many modal systems using Rabin's result in [8] on the decidability of the second-order theory of successor functions. In particular [4, pp. 258-265] he is able to prove the decidability of a system which lacks the finite model property. Gabbay's system (...) is however complete, in the sense of being characterized by a class of frames, and the question arises whether there is a decidable modal logic which is not complete. Since no incomplete modal logic has the finite model property [9, p. 33], any proof of decidability must employ some such method as Gabbay's. In this paper I use the Gabbay/Rabin technique to prove the decidability of a finitely axiomatized normal modal propositional logic which is not characterized by any class of frames. I am grateful to the referee for suggesting improvements in substance and presentation.The terminology I am using is standard in modal logic. By aframeis understood a pair 〈W, R〉 in whichWis a class (of “possible worlds”) andR⊆W2. To avoid confusion in what follows, a frame will henceforth be referred to as aKripkeframe. By contrast, ageneral frameis a pair 〈,Π〉 in whichis a Kripke frame andΠis a collection of subsets ofWclosed under the Boolean operations and satisfying the condition that ifAis inΠthen so isR−1“A. A model on a frame (of either kind) is obtained by adding a functionVwhich assigns sets of worlds to propositional variables. In the case of a general frame we require thatV(p) ∈Π. (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)

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)

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)

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)

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)

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments (...) made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration. (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)

The book offers a proposal on how to define truth in all its complexity, without reductionism, showing at the same time which questions a theory of truth has to answer and which questions, although related to truth, do not belong within the scope of such a theory. Just like any other theory, a theory of truth has its structure and limits. The semantic core of the position is that truth-ascriptions are pro-forms, i.e. natural language propositional variables. The book also offers (...) an explanation of the syntactic behaviour of truth-terms, and the pragmatic roles of truth-acts. The theory of truth we present is a technical proposal, relatively uncontaminated by radical philosophical discussion. It makes indeed philosophical points, but it is intended to be a conceptual analysis, as neutral as possible, of the aspects that may serve as a point of departure for more philosophically-laden destinations. Like the Fregean account of quantifiers, which is prior to and, to a large extent, independent of the metaphysical debate about existence and its forms, or the Kaplanian view on demonstratives, that is neutral regarding the debate about individuals and the possibilities we have to actually “reach” them in a referring act, we intend our proposal about truth to be a sophisticated and explicative setting that helps to situate other debates about truth accurately, far from the distorted and sometimes strongly ideological discussions that have turned the topic into a paradigm of philosophical impasse. (shrink)

Adverbial modification is probably one of the least understood areas of linguistics. The essays in this volume all address the problem of how to give an analysis of adverbial modifiers within truth-conditional semantics. Chapters I-VI provide analyses of particular modifiers within a possible worlds framework, and were written between 1974 and 1981. Original publication details of these chapters may be found on p. vi. Of these, all but Chapter I make essential use of the idea that the time reference involved (...) in tensed sentences should be a time interval rather than a single instant. The final chapter (Chapter VII) was written especially for this volume and investigates the question of how the 'situation semantics' recently devised by Jon Barwise and John Perry, as a rival to possible-worlds semantics, might deal with adverbs. In addition I have included an appendix to Chapter III and an introduction which links all the chapters together. (shrink)

Semantic Indexicality shows how a simple syntax can be combined with a propositional language at the level of logical analysis. It is the adoption of such a base language which has not been attempted before, and it is this which constitutes the originality of the book. Cresswell's simple and direct style makes this book accessible to a wider audience than the somewhat specialized subject matter might initially suggest.

Over a longer period than I sometimes care to contemplate I have worked on possible-worlds semantics. The earliest work was in modal logic, to which I keep returning, but a sabbatical in 1970 took me to UCLA, there to discover the work of Richard Montague in applying possible-worlds semantics to natural lan guage. My own version of this appeared in Cresswell (1973) and was followed up in a number of articles, most of which were collected in Cresswell (1985b). A central (...) problem for possible worlds semantics is how to accommodate propositional attitudes. This problem was addressed in Cresswell (1985a), and the three books mentioned so far represent a reasonably complete picture of my positive views on formal semantics. I have regarded the presentation of a positive view as more important than the criticism of alternatives, although the works referred to do contain many passages in which I have tried to defend my own views against those of others. But such criticism is important in that a crucial element in establishing the content of a theory is that we be able to evaluate it in relation to its com petitors. It is for that reason that I have collected in this volume a number of articles in which I attempt to defend the positive semantical picture I favour against objections and competing theories. (shrink)

This article discusses the argument we cannot have knowledge of abstract entities because they are not part of the causal order. The claim of this article is that the argument fails because of equivocation. Assume that the “causal order” is concerned with contingent facts involving time and space. Even if the existence of abstract entities is not contingent and does not involve time or space it does not follow that no truths about abstract entities are contingent or involve time or (...) space. I argue that it is the latter which is required to obtain the desired conclusion. (shrink)

The use of coercive measures in the care for the addicted has changed over the past 20 years. Laws that have adopted the “dangerousness” criterion in order to secure patients’ rights to non-intervention are increasingly subjected to critique as many authors plead for wider dangerousness criteria. One of the most salient moral issues at stake is whether addicts who are at risk of causing danger to themselves should be involuntarily admitted and/or treated. In this article, it is argued that the (...) dilemma between coercion on the one hand and abandonment on the other cannot be analysed without differentiated perspectives on the key notions that are used in these debates. The ambiguity these notions carry within care practice indicates that the conflict between the prevention of danger and respect for autonomy is not as sharp as the legal systems seem to imply. Some coercive measures need not be interpreted as an infringement of autonomy—rather, they should be interpreted as a way to provide good care. (shrink)

We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist candidate can win (...) the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.  2003 Elsevier Inc. All rights reserved. (shrink)

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

When people hear the name of Cardinal Newman, one of the first associations they make is to his Idea of a University. However, it is rarely known that his first love was Catholic education at the elementary and secondary levels, so that the Oratory School he founded has been described as the “apple of his eye.” Interestingly, Pope Francis is the first pontiff in modern history, at least, to have taught high school (chemistry and Latin) and who has reflected extensively (...) on his own personal experiences of being raised by the Salesian Fathers in Argentina. Both Newman and Francis would regard Catholic elementary and secondary schools as essential to producing what Newman repeatedly referred to as “an educated laity” – equally essential for what St. John Paul II dubbed “the new evangelization.”. (shrink)

The Venerable John Henry Cardinal Newman seemingly had the “Midas touch” in reverse. Oxford, Littlemore, Dublin were all sites of failures; the “Achilli Affair” was a humiliation; the quarrel with Faber was an embarrassment. Nonetheless, most people today think of Newman as a rousing success story. Why? Newman serves as an object lesson in living the Paschal Mystery, whereby each moment of crisis can be transformed into a moment of grace.