What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically (...) impossible world, the laws of logic fail. In this paper, I provide a definition of logically impossible worlds. I then show that there is nothing strange about admitting such worlds. (shrink)

In 1947 Quine wrote one of the most important and influential articles in the twentieth century philosophy - "On What There Is". One of the aims of this article was a critique of Meinong's Theory of Object. The critique was especially focused upon nonactual possibilities, which (according to Meinong) are some kinds of nonexistent objects. In my paper I want to present Neo-Meinongian refutations of Quine's critique. In order to do this I discuss: (i) the main thesis of "On What (...) There Is" ,(ii) premises of Meinongian Theory, (iii) views of proponents and opponents of the idea of nonexistent objects, (iv) Quine's critique aimed at nonactual possibilities, (v) Terence Parsons' theory, based on the distinction between nuclear and extranucler properties, and (vi) noneism, defended by Richard Routley. I also try to give a reply to the most popular critiques aimed at both Neo-Meinongian theories. The main conclusion is that Quine's critique and his arguments against nonactual possibilities aren't dangerous for theories endorsing Meinong's Theory of Object. Contrary to what Gilbert Ryle once claimed (If Meinongianism isn't dead, nothing is), Meinongian theories are still alive and doing well. (shrink)

Richard Sylvan, a vanguard in the field of environmental philosophy published a book in 1994 with David Bennett titled The Greening of Ethics. Nearly twenty-five years later, where the environmental situation of our world is even more serious, and where some governments deny the existence and negative effects of human caused climate change, the greening of ethics is even more urgent. In this paper, I revisit Sylvan’s and Bennett’s work arguing that their approach to environmental ethics should (...) be one that is advocated. I consider the most salient features of their approach, how this translates into practice but also offer an analysis as to why some governments have reached an impasse in regard to implementing environmental policies, and why environmental ethics still remains on the margins. In the final section of this paper, I discuss what an effective practice would mean. (shrink)

According to Veritism, true belief is the sole fundamental epistemic value. Epistemologists often take Veritism to entail that all other epistemic items can only have value by standing in certain instrumental relations—namely, by tending to produce a high ratio of true to false beliefs or by being products of sources with this tendency. Yet many value theorists outside epistemology deny that all derivative value is grounded in instrumental relations to fundamental value. Veritists, I believe, can and should follow suit. After (...) setting the stage in §1, I explain in §2 why Veritism should not take an Instrumentalist form. Instrumentalist Veritism faces a generalized version of the swamping problem. But this problem undermines Instrumentalism, not Veritism: granting Instrumentalism, similar problems arise for any economical epistemic axiology. I show in §3 how Veritism can take a less narrow form and solve the swamping problem. After answering some objections in §4, I consider in §5 what some would regard as a less radical alternative solution and argue that it either fails or collapses into mine. I close in §6 by taking stock and re-evaluating the overall prospects for Veritism, suggesting that it is a highly promising epistemic axiology when divorced from Instrumentalism. (shrink)

Despite the recent backlash against epistemic consequentialism, an explicit systematic alternative has yet to emerge. This paper articulates and defends a novel alternative, Epistemic Kantianism, which rests on a requirement of respect for the truth. §1 tackles some preliminaries concerning the proper formulation of the epistemic consequentialism / non-consequentialism divide, explains where Epistemic Kantianism falls in the dialectical landscape, and shows how it can capture what seems attractive about epistemic consequentialism while yielding predictions that are harder for the latter to (...) secure in a principled way. §2 presents Epistemic Kantianism. §3 argues that it is uniquely poised to satisfy the desiderata set out in §1 on an ideal theory of epistemic justification. §4 gives three further arguments, suggesting that it (i) best explains the objective normative significance of the subject's perspective in epistemology, (ii) follows from the kind of axiology needed to solve the swamping problem together with modest assumptions about the relation between the evaluative and the deontic, and (iii) illuminates certain asymmetries in epistemic value and obligation. §5 takes stock and reassesses the score in the debate. (shrink)

This paper considers the place of reasons in the metaphysics of epistemic normativity and defends a middle ground between two popular extremes in the literature. Against members of the ‘reasons first’ movement, we argue that reasons are not the sole fundamental constituents of epistemic normativity. We suggest instead that the virtue-theoretic property of competence is the key building block. To support this approach, we note that reasons must be possessed to play a role in the analysis of central epistemically normative (...) properties, and argue that the relation of possession must be analyzed in terms of competence. But while we diverge with reasons-firsters on this score, we also distance ourselves from those who deny reasons any important role in epistemology. For we maintain that possessed reasons do help to ground deontic facts in the epistemic domain (e.g., facts about what one epistemically ought to believe, may believe, or is justified in believing). Indeed, we present an argument that the possession of sufficient epistemic reasons is necessary and sufficient for propositional justification, and that proper basing on such reasons yields doxastic justification. But since possession and proper basing are themselves grounded in competence, reasons are not the end of the explanatory road: competence enables them to do their work, putting them—and us—in the middle. (shrink)

According to a view I’ll call Epistemic Normativism, knowledge is normative in the same sense in which paradigmatically normative properties like justification are normative. This paper argues against EN in two stages and defends a positive non-normativist alternative. After clarifying the target in §1, I consider in §2 some arguments for EN from the premise that knowledge entails justification. I first raise some worries about inferring constitution from entailment. I then rehearse the reasons why some epistemologists reject the Entailment Thesis (...) and argue that a non-normativist picture provides the best explanation of all the intuitions surrounding this thesis, favorable and unfavorable. On this picture, human knowledge is a structured non-normative complex that has as one of its parts a justification-making property, analogous in role to good-making properties like pleasurableness. After giving three arguments against EN in §3 and answering an objection in §4, I turn in §5 to further develop the positive view sketched in §2. In §6, I take stock and conclude. (shrink)

It is often assumed that believing that p for a normative reason consists in nothing more than (i) believing that p for a reason and (ii) that reason’s corresponding to a normative reason to believe that p, where (i) and (ii) are independent factors. This is the Composite View. In this paper, we argue against the Composite View on extensional and theoretical grounds. We advocate an alternative that we call the Prime View. On this view, believing for a normative reason (...) is a distinctive achievement that isn’t exhausted by the mere conjunction of (i) and (ii). Its being an achievement entails that (i) and (ii) are not independent when one believes for a normative reason: minimally, (i) must hold because (ii) holds. Apart from its intrinsic interest, our discussion has important upshots for central issues in epistemology, including the analysis of doxastic justification, the epistemology of perception, and the place of competence in epistemology. (shrink)

Rationality requires us to respond to apparent normative reasons. Given the independence of appearance and reality, why think that apparent normative reasons necessarily provide real normative reasons? And if they do not, why think that mistakes of rationality are necessarily real mistakes? This paper gives a novel answer to these questions. I argue first that in the moral domain, there are objective duties of respect that we violate whenever we do what appears to violate our first-order duties. The existence of (...) these duties of respect, I argue, ensures that apparent moral reasons are exceptions to the independence of appearance and reality. I then extend these arguments to the domain of overall reason. Just as there are objective duties of respect for moral reasons that explain moral blameworthiness, so there are objective duties of respect for reasons that explain blameworthiness in the court of overall reason. The existence of these duties ensures that apparent reasons are exceptions to the independence of appearance and reality. (shrink)

This paper raises a dilemma for Skorupski’s meta-normative outlook in The Domain of Reasons and explores some escape routes, recommending a more thoroughgoing Kantianism as the best option. §1 argues that we cannot plausibly combine Skorupski’s spontaneity-based epistemology of normativity with his cognition-independent view of normative truth. §§2–4 consider whether we should keep the epistemology and revise the metaphysics, opting for constructivism. While Skorupski’s negative case for his spontaneity-based epistemology is found wanting, it is suggested that a better argument for (...) keeping the epistemology and switching to Kantian constructivism can be given from a thesis he finds appealing—viz., ‘cognitive internalism’. While this premise is not, it is argued, obviously true, the view it supports does provide a good way to undergird Skorupski’s most interesting rationale for his reasons-first approach. (shrink)

This paper is an opinionated guide to the literature on normative epistemic reasons. After making some distinctions in §1, I begin in §2 by discussing the ontology of normative epistemic reasons, assessing arguments for and against the view that they are mental states, and concluding that they are not mental states. In §3, I examine the distinction between normative epistemic reasons there are and normative epistemic reasons we possess. I offer a novel account of this distinction and argue that we (...) in fact ought to acknowledge a threefold distinction between objective, possessed, and apparent normative epistemic reasons. In §4, I discuss the question of which normative reasons for doxastic attitudes are the epistemic ones, evaluating reasons against a simple evidentialist answer. Finally, in §5, I look at the role of reasons in epistemology, considering challenges to viewing reasons as the building blocks of epistemic normativity and maintaining that the challenges recommend a novel bi-level epistemology rather than a marginalization of reasons in epistemology. (shrink)

Reasons fundamentalists maintain that we can analyze all derivative normative properties in terms of normative reasons. These theorists famously encounter the Wrong Kind of Reasons problem, since not all reasons for reactions seem relevant for reasons-based analyses. Some have argued that this problem is a general one for many theorists, and claim that this lightens the burden for reasons fundamentalists. We argue in this paper that the reverse is true: the generality of the problem makes life harder for reasons fundamentalists. (...) We do this in two stages. First, we show that reflection on the generality of the distinction between wrong-kind reasons and right-kind reasons shows that not all right-kind reasons are normative reasons. So, not only do reasons-based analyses require a distinction between right-kind reasons and wrong-kind reasons, they also need a distinction between normative right-kind reasons from nonnormative right-kind reasons. We call this the Right Kind of Reasons Problem. In the second stage of the paper, we argue that reasons fundamentalism places tight constraints on its proper solution: in particular, it forbids one from appealing to anything normative to distinguish normative RKRs from nonnormative RKRs. It hence seems that reasons fundamentalists can only appeal to natural facts to solve the problem, but it is unclear which ones can do the job. So, reflection on the generality of the distinction only multiplies the fundamentalist’s problems. We end by exploring several solutions to these problems, and recommend a form of constitutivism as the best. (shrink)

The paper is an opinionated tour of the literature on the reasons for which we hold beliefs and other doxastic attitudes, which I call ‘operative epistemic reasons’. After drawing some distinctions in §1, I begin in §2 by discussing the ontology of operative epistemic reasons, assessing arguments for and against the view that they are mental states. I recommend a pluralist non-mentalist view that takes seriously the variety of operative epistemic reasons ascriptions and allows these reasons to be both propositions (...) and truth-making facts. In §3, I turn to consider what it takes for a consideration to be an operative epistemic reason, examining three conditions – the representational, treating, and explanatory conditions – that have been proposed. I offer a novel view about the explanatory condition. In §4, I discuss the special case of inferential operative reasons and examine attempts to understand them in terms of rule-following, sketching a competence-based spinoff of dispositionalism. Finally, in §5, I consider whether there are non-inferential operative reasons, observing that one needn't countenance them to be a foundationalist but then developing a view about what they are and how they do and don't differ from inferential reasons. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Although arguments for and against competing theories of vagueness often appeal to claims about the use of vague predicates by ordinary speakers, such claims are rarely tested. An exception is Bonini et al. (1999), who report empirical results on the use of vague predicates by Italian speakers, and take the results to count in favor of epistemicism. Yet several methodological difficulties mar their experiments; we outline these problems and devise revised experiments that do not show the same results. We then (...) describe three additional empirical studies that investigate further claims in the literature on vagueness: the hypothesis that speakers confuse ‘P’ with ‘definitely P’, the relative persuasiveness of different formulations of the inductive premise of the Sorites, and the interaction of vague predicates with three different forms of negation. (shrink)

Some say the swamping problem confronts all who believe that true belief is the sole fundamental epistemic value. This, I say, is mistaken. The problem only confronts T-Monists if they grant two teleological claims: that all derived epistemic value is instrumental, and that it is the state of believing truly rather than the standard of truth in belief that is fundamentally epistemically valuable. T-Monists should reject and, and appeal to a non-teleological form of value derivation I call Fitting Response Derivation (...) that obviates swamping. Since, alas, simple reliabilists can’t apply this model to knowledge, the problem remains for them, and is local. (shrink)

This paper surveys some ways in which epistemic reasons ascriptions (or ERAs) appear to be context-sensitive, and outlines a framework for thinking about the nature of this context-sensitivity that is intimately related to ERAs' explanatory function.

A general class of labeled sequent calculi is investigated, and necessary and sufficient conditions are given for when such a calculus is sound and complete for a finite -valued logic if the labels are interpreted as sets of truth values. Furthermore, it is shown that any finite -valued logic can be given an axiomatization by such a labeled calculus using arbitrary "systems of signs," i.e., of sets of truth values, as labels. The number of labels needed is logarithmic in the (...) number of truth values, and it is shown that this bound is tight. (shrink)

Many epistemologists treat rationality and justification as the same thing. Those who don’t lack detailed accounts of the difference, leading their opponents to suspect that the distinction is an ad hoc attempt to safeguard their theories of justification. In this paper, I offer a new and detailed account of the distinction. The account is inspired by no particular views in epistemology, but rather by insights from the literature on reasons and rationality outside of epistemology. Specifically, it turns on a version (...) of the familiar distinction in meta-ethics between possessing apparent normative reasons (which may be merely apparent) and possessing objective normative reasons. The paper proceeds as follows. In §1, I discuss the history of indifference to the distinction between rationality and justification in epistemology and the striking contrast with meta-ethics. I introduced the distinction between apparent reasons and possessed objective reasons in §2 and provide a deeper basis for it in §3. I explain how the ideas extend to epistemology in §4 and explore the upshots for some central issues in §5. (shrink)

Autonomy has been central to moral and political philosophy for millenia, and has been positioned as a critical aspect of both justice and wellbeing. Research in psychology supports this position, providing empirical evidence that autonomy is critical to motivation, personal growth and psychological wellness. Responsible AI will require an understanding of, and ability to effectively design for, human autonomy (rather than just machine autonomy) if it is to genuinely benefit humanity. Yet the effects on human autonomy of digital experiences are (...) neither straightforward nor consistent, and are complicated by commercial interests and tensions around compulsive overuse. This multi-layered reality requires an analysis that is itself multidimensional and that takes into account human experience at various levels of resolution. We borrow from HCI and psychological research to apply a model (“METUX”) that identifies six distinct spheres of technology experience. We demonstrate the value of the model for understanding human autonomy in a technology ethics context at multiple levels by applying it to the real-world case study of an AI-enhanced video recommender system. In the process we argue for the following three claims: 1) There are autonomy-related consequences to algorithms representing the interests of third parties, and they are not impartial and rational extensions of the self, as is often perceived; 2) Designing for autonomy is an ethical imperative critical to the future design of responsible AI; and 3) Autonomy-support must be analysed from at least six spheres of experience in order to approriately capture contradictory and downstream effects. (shrink)

The COVID-19 pandemic prompted immense work on the investigation of the SARS-CoV-2 virus. Rapid, accurate, and consistent interpretation of generated data is thereby of fundamental concern. Ontologies––structured, controlled, vocabularies––are designed to support consistency of interpretation, and thereby to prevent the development of data silos. This paper describes how ontologies are serving this purpose in the COVID-19 research domain, by following principles of the Open Biological and Biomedical Ontology (OBO) Foundry and by reusing existing ontologies such as the Infectious Disease Ontology (...) (IDO) Core, which provides terminological content common to investigations of all infectious diseases. We report here on the development of an IDO extension, the Virus Infectious Disease Ontology (VIDO), a reference ontology covering viral infectious diseases. We motivate term and definition choices, showcase reuse of terms from existing OBO ontologies, illustrate how ontological decisions were motivated by relevant life science research, and connect VIDO to the Coronavirus Infectious Disease Ontology (CIDO). We next use terms from these ontologies to annotate selections from life science research on SARS-CoV-2, highlighting how ontologies employing a common upper-level vocabulary may be seamlessly interwoven. Finally, we outline future work, including bacteria and fungus infectious disease reference ontologies currently under development, then cite uses of VIDO and CIDO in host-pathogen data analytics, electronic health record annotation, and ontology conflict-resolution projects. (shrink)

Internalism holds that epistemic justification is determined by what is internal to the mind, not by facts about the mind-independent world. This paper introduces and defends a new kind of internalism that is rooted in rationalist ideas that have been neglected in recent epistemology, despite inspiring internalist projects in cognitive science. Ignoring rationalist insights has, I argue, damaged the prospects for internalism, by needlessly saddling internalists with empiricist burdens. Internalists can refuse these burdens by accepting a better philosophy of mind. (...) Rather than looking to 17th century rationalists, I look to Kant, and especially his idea that normativity is grounded in the constitution of agency and mind. A Kantian approach can avoid stock objections to internalism, I argue, and can also capture all the alleged benefits of externalism. The paper is structured as follows. In §2, I get back to basics and consider more ways to satisfy the core internalist template than have become standard. I draw attention to rationalist insights about how normativity could be grounded in the constitution of mind, and hypothesize that if internalism respects these insights, some problems disappear. I develop this hypothesis in §3 with a Kantian view. I further defend this view in §4. I conclude in §5 by explaining why Kantian internalism answers the latest challenges to internalism. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires that revised beliefs (...) incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent (...) in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

Tasks, tools, and techniques that we perform, use, and acquire, define the elements of expertise which we value as the hallmarks of goal-driven behavior. Somehow, the creation of tools enables us to define new tasks, or is it that the envisioning of new tasks drives us to invent new tools? Or maybe it is that new tools engender new techniques which then result in new tasks? This jumble of issues will be explored and discussed in this diverse collection of papers. (...) Individually, few of the papers are related to each other by topic or by techniques of analysis. Collectively, all focus on tasks performed using tools and discuss the techniques of tool use which enable differences in performance and expertise across individuals, societies, and (even) species. -/- . (shrink)

This report by the WHO Consultative Group on Equity and Universal Health Coverage addresses how countries can make fair progress towards the goal of universal coverage. It explains the relevant tradeoffs between different desirable ends and offers guidance on how to make these tradeoffs.

Some epistemologists and philosophers of mind hold that the non-epistemic perceptual relation of which feature-seeing and object-seeing are special cases is the foundation of perceptual knowledge. This paper argues that such relations are best understood as having only a technological role in explaining perceptual knowledge. After introducing the opposing view in §1, §2 considers why its defenders deny that some cases in which one has perceptual knowledge without the relevant acquaintance relations are counterexamples, detailing their case for lurking inferential epistemology. (...) §§3-4 suggest that this strategy fails in many other cases. While there is a computational tale that might be deemed ‘inferential’ in these cases, there is no corresponding tale in epistemic structure, not even if one rejects what Siegel (2017) calls the ‘Reckoning Model’ of inference. §5 offers a more fundamental dilemma. §6 concludes that there is only a technological role for non-epistemic perception in grounding perceptual knowledge, but allows that it might play a more-than-technological role elsewhere. (shrink)

According to ambitious responsibilism (AR), the virtues that are constitutive of epistemic responsibility should play a central and fundamental role in traditional projects like the analysis of justification and knowledge. While AR enjoyed a shining moment in the mid-1990s, it has fallen on hard times. Part of the reason is that many epistemologists—including fellow responsibilists—think it paints an unreasonably demanding picture of knowledge and justification. I agree that such worries undermine AR's existing versions. But I think the curtains have been (...) prematurely drawn on the view. My goal is to show that the objections only threaten the periphery of certain versions of AR, and to develop a version that blocks them. With this goal in mind, here is the plan. I begin in §2 by clarifying the core commitments of AR and explain how influential responsibilists have added to these commitments in optional ways. In §3, I rehearse the standard objections to AR, explaining why they only impugn the add-ons. I turn in §4 to develop a version I call Kantian Responsibilism (KR). KR is a two-level view consisting of (i) a high-level analysis of epistemic normativity in responsibilist terms, and (ii) a first-order account of the conditions under which these terms apply. According to KR's first tier, epistemically virtuous thought is thought that manifests respect for truth; because I hold that manifesting certain reasons-sensitive dispositions is necessary and sufficient for respecting truth, KR's second tier takes epistemic virtues to coincide substantively with reasons-sensitive dispositions. After unpacking KR in §4, I show in §5 how it answers the objections to AR. I close in §6 by making some broader points about KR's virtues, especially when compared with reliabilist views. (shrink)

We present a new understanding of Christ’s real presence in the Eucharist on the model of Stump’s account of God’s omnipresence and Green and Quan’s account of experiencing God in Scripture. On this understanding, Christ is derivatively, rather than fundamentally, located in the consecrated bread and wine, such that Christ is present to the believer through the consecrated bread and wine, thereby making available to the believer a second-person experience of Christ, where the consecrated bread and wine are the way (...) in which she shares attention with him. The consecrated bread and wine are then, in a sense, icons of Christ. (shrink)

What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.

Whilst media and political rhetoric in Britain is sceptical and often outright damning of the (presumed) morals and behaviours of the White marginalized poor, our aim is to explore the conditions under which successful communities are nevertheless built. Specifically, we examine the features of community and stress its importance both for belonging and bonding around shared norms and practices and for fostering the necessary bridging essential for interacting and cooperating with others. In considering what it means to foster a community (...) that acts as a breakwater against the tides of stigma or disadvantage, we pay special attention to what we will call enabling conditions – essential features that communities either can or should be able to provide or that exist independent of communities and are indispensable for accessing opportunities in the wider society. We detail the dynamics of White poverty and exclusion before turning our attention to possible responses to these challenges. In searching for viable responses to stigma and disadvantage, we compare some different typologies of community presently available to the White poor in Britain and examine whether these are sufficient to satisfy the enabling conditions associated with more robust forms of group membership. (shrink)

La cobertura universal de salud está en el centro de la acción actual para fortalecer los sistemas de salud y mejorar el nivel y la distribución de la salud y los servicios de salud. Este documento es el informe fi nal del Grupo Consultivo de la OMS sobre la Equidad y Cobertura Universal de Salud. Aquí se abordan los temas clave de la justicia (fairness) y la equidad que surgen en el camino hacia la cobertura universal de salud. Por lo (...) tanto, el informe es pertinente para cada agente que infl uye en ese camino y en particular para los gobiernos, ya que se encargan de supervisar y guiar el progreso hacia la cobertura universal de salud. (shrink)

Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, focussing (...) primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert’s consistency program. Similar efforts continue, but have been (...) expanded by the development of sophisticated methods to study the properties of such systems using proof and model theory. In parallel with this evolution of logical formalisms as tools for articulating mathematical theories (broadly speaking), much progress has been made in the quest for a mechanization of logical inference and the investigation of its theoretical limits, culminating recently in the development of new foundational frameworks for mathematics with sophisticated computer-assisted proof systems. In addition, logical formalisms developed by logicians in mathematical and philosophical contexts have proved immensely useful in describing theories and systems of interest to computer scientists, and to some degree, vice versa. Three examples of the influence of logic in computer science are automated reasoning, computer verification, and type systems for programming languages. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...) logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)