This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is shown that Fitting’s nested calculi naturally arise from their corresponding labelled calculi—for each of the aforementioned logics—via the elimination of structural rules in labelled derivations. The translational correspondence between the two types of systems is leveraged to show that the nested calculi inherit proof-theoretic properties from their associated labelled calculi, such as (...) completeness, invertibility of rules and cut admissibility. Since labelled calculi are easily obtained via a logic’s semantics, the method presented in this paper can be seen as one whereby refined versions of labelled calculi (containing nested calculi as fragments) with favourable properties are derived directly from a logic’s semantics. (shrink)

This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic paradigms: labelled and nested sequent calculi. The formalism of labelled sequents has been successful in that cut-free calculi in possession of desirable proof-theoretic properties can be automatically generated for large classes of logics. Despite these qualities, labelled systems make use of a complicated syntax that explicitly incorporates the (...) semantics of the associated logic, and such systems typically violate the subformula property to a high degree. By contrast, nested sequent calculi employ a simpler syntax and adhere to a strict reading of the subformula property, making such systems useful in the design of automated reasoning algorithms. However, the downside of the nested sequent paradigm is that a general theory concerning the automated construction of such calculi (as in the labelled setting) is essentially absent, meaning that the construction of nested systems and the confirmation of their properties is usually done on a case-by-case basis. The refinement method connects both paradigms in a fruitful way, by transforming labelled systems into nested (or, refined labelled) systems with the properties of the former preserved throughout the transformation process. To demonstrate the method of refinement and some of its applications, we consider grammar logics, first-order intuitionistic logics, and deontic STIT logics. The introduced refined labelled calculi will be used to provide the first proof-search algorithms for deontic STIT logics. Furthermore, we employ our refined labelled calculi for grammar logics to show that every logic in the class possesses the effective Lyndon interpolation property. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...) semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we (...) show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...) a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...) and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving (...) validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

We formally introduce a novel, yet ubiquitous, category of norms: norms of instrumentality. Norms of this category describe which actions are obligatory, or prohibited, as instruments for certain purposes. We propose the Logic of Agency and Norms (LAN) that enables reasoning about actions, instrumentality, and normative principles in a multi-agent setting. Leveraging LAN , we formalize norms of instrumentality and compare them to two prevalent norm categories: norms to be and norms to do. Last, we pose principles relating the three (...) categories and evaluate their validity vis-à-vis notions of deliberative acting. On a technical note, the logic will be shown decidable via the finite model property. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

We introduce a framework that allows for the construction of sequent systems for expressive description logics extending ALC. Our framework not only covers a wide array of common description logics, but also allows for sequent systems to be obtained for extensions of description logics with special formulae that we call "role relational axioms." All sequent systems are sound, complete, and possess favorable properties such as height-preserving admissibility of common structural rules and height-preserving invertibility of rules.

We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm , Tstit and Xstit. All calculi presented possess essential structural properties such as contraction- and cut-admissibility. The labelled calculi G3Ldm and G3Tstit are shown sound and complete relative to irreflexive temporal frames. Additionally, we extend current results by showing that also Xstit can be characterized through relational frames, omitting the use of BT+AC frames.

The aim of this paper is to introduce and explain display calculi for a variety of logics. We provide a survey of key results concerning such calculi, though we focus mainly on the global cut elimination theorem. Propositional, first-order, and modal display calculi are considered and their properties detailed.

We present nested sequent systems for propositional Gödel-Dummett logic and its first-order extensions with non-constant and constant domains, built atop nested calculi for intuitionistic logics. To obtain nested systems for these Gödel-Dummett logics, we introduce a new structural rule, called the linearity rule, which (bottom-up) operates by linearising branching structure in a given nested sequent. In addition, an interesting feature of our calculi is the inclusion of reachability rules, which are special logical rules that operate by propagating data and/or checking (...) if data exists along certain paths within a nested sequent. Such rules require us to generalise our nested sequents to include signatures (i.e. finite collections of variables) in the first-order cases, thus giving rise to a generalisation of the usual nested sequent formalism. Our calculi exhibit favourable properties, admitting the height-preserving invertibility of every logical rule and the (height-preserving) admissibility of a large collection of structural and reachability rules. We prove all of our systems sound and cut-free complete, and show that syntactic cut-elimination obtains for the intuitionistic systems. We conclude the paper by discussing possible extensions and modifications, putting forth an array of structural rules that could be used to provide a sizable class of intermediate logics with cut-free nested sequent systems. (shrink)

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

What determines whether an action is right or wrong? Morality, Rules, and Consequences: A Critical Reader explores for students and researchers the relationship between consequentialist theory and moral rules. Most of the chapters focus on rule consequentialism or on the distinction between act and rule versions of consequentialism. Contributors, among them the leading philosophers in the discipline, suggest ways of assessing whether rule consequentialism could be a satisfactory moral theory. These essays, all of which are previously unpublished, provide students in (...) moral philosophy with essential material and ask key questions on just what the criteria for an adequate moral theory might be. (shrink)

Formalised knowledge systems, including universities and research institutes, are important for contemporary societies. They are, however, also arguably failing humanity when their impact is measured against the level of progress being made in stimulating the societal changes needed to address challenges like climate change. In this research we used a novel futures-oriented and participatory approach that asked what future envisioned knowledge systems might need to look like and how we might get there. Findings suggest that envisioned future systems will need (...) to be much more collaborative, open, diverse, egalitarian, and able to work with values and systemic issues. They will also need to go beyond producing knowledge about our world to generating wisdom about how to act within it. To get to envisioned systems we will need to rapidly scale methodological innovations, connect innovators, and creatively accelerate learning about working with intractable challenges. We will also need to create new funding schemes, a global knowledge commons, and challenge deeply held assumptions. To genuinely be a creative force in supporting longevity of human and non-human life on our planet, the shift in knowledge systems will probably need to be at the scale of the enlightenment and speed of the scientific and technological revolution accompanying the second World War. This will require bold and strategic action from governments, scientists, civic society and sustained transformational intent. (shrink)

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of (...) the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings. (shrink)

In a recent paper, Aidan Lyon and Mark Colyvan have proposed an explanation of the structure of the bee's honeycomb based on the mathematical Honeycomb Conjecture. This explanation has instantly become one of the standard examples in the philosophical debate on mathematical explanations of physical phenomena. In this critical note, I argue that the explanation is not scientifically adequate. The reason for this is that the explanation fails to do justice to the essentially three-dimensional structure of the bee's honeycomb.

This book offers solutions to two persistent and I believe closely related problems in epistemology. The first problem is that of drawing a principled distinction between perception and inference: what is the difference between seeing that something is the case and merely believing it on the basis of what we do see? The second problem is that of specifying which beliefs are epistemologically basic (i.e., directly, or noninferentially, justified) and which are not. I argue that what makes a belief a (...) perceptual belief, or a basic belief, is not any introspectible feature of the belief but rather the nature of the cognitive system, or "module", that is causally responsible for the belief. Thus, even zombies, who in the philosophical literature lack conscious experiences altogether, can have basic, justified, perceptual beliefs. -/- The theories of perceptual and basic beliefs developed in the monograph are embedded in a larger reliabilist epistemology. I use this theory of basic beliefs to develop a detailed reliabilist theory: Inferentialist Reliabilism, which offers a reliabilist theory of inferential justification and which solves some longstanding problems for other reliabilist views by demanding inferential support for some—but not all—beliefs. The book is an instance of a thoroughgoingly naturalistic approach to epistemology. Many of my arguments have an empirical basis, and the view that I endorse reserves a central role for the cognitive sciences—in particular, cognitive neuroscience—in filling in the details of an applied epistemological theory. (shrink)

Sense-perception—the awareness or apprehension of things by sight, hearing, touch, smell and taste—has long been a preoccupation of philosophers. One pervasive and traditional problem, sometimes called “the problem of perception”, is created by the phenomena of perceptual illusion and hallucination: if these kinds of error are possible, how can perception be what it intuitively seems to be, a direct and immediate access to reality? The present entry is about how these possibilities of error challenge the intelligibility of the phenomenon of (...) perception, and how the major theories of perception in the last century are best understood as responses to this challenge. (shrink)

Methods have been a controversial element in theories of knowledge for the last 40 years. Recent developments in theories of justification, concerning the identification and individuation of belief-forming processes, can shed new light on methods, solving some longstanding problems in the theory of knowledge. We needn’t and shouldn’t shy away from methods; rather, methods, construed as psychological processes of belief-formation, need to play a central role in any credible theory of knowledge.

Is perception cognitively penetrable, and what are the epistemological consequences if it is? I address the latter of these two questions, partly by reference to recent work by Athanassios Raftopoulos and Susanna Seigel. Against the usual, circularity, readings of cognitive penetrability, I argue that cognitive penetration can be epistemically virtuous, when---and only when---it increases the reliability of perception.

Detlef Dürr was a remarkable figure in many different ways. I recall some adventures we had with him in Abu Dhabi.

Explanation does not exist in a metaphysical vacuum. Conceptions of the structure of a phenomenon play an important role in guiding attempts to explain it, and erroneous conceptions of a phenomenon may direct investigation in misleading directions. I believe that there is a case to be made for thinking that much work on the neural underpinnings of consciousness—what is often called the neural correlates of consciousness—is driven by an erroneous conception of the structure of consciousness. The aim of this paper (...) is lay bare some connections between the explanation of consciousness and the structure of consciousness, and to argue for a conception of the structure of consciousness that is more adequate than that which currently drives much research into the neural correlates of consciousness. (shrink)

The “looks” of things are frequently invoked (a) to account for the epistemic status of perceptual beliefs and (b) to distinguish perceptual from inferential beliefs. ‘Looks’ for these purposes is normally understood in terms of a perceptual experience and its phenomenal character. Here I argue that there is also a nonexperiential sense of ‘looks’—one that relates to cognitive architecture, rather than phenomenology—and that this nonexperiential sense can do the work of (a) and (b).

Here is a template for introducing mathematical objects: “Objects are found in stages. For every stage S: (1) for any things found before S, you find at S the bland set whose members are exactly those things; (2) for anything, x, which was found before S, you find at S the result of tapping x with any magic wand (provided that the result is not itself a bland set); you find nothing else at S.” -/- This Template has rich applications, (...) it realizes John Conway’s (1976) Mathematicians’ Liberation Movement, and it generalizes a lovely idea due to Alonzo Church (1974). -/- Some parts of this Template are familiar: the bit about bland sets is just the ordinary story we tell about the cumulative iterative conception of set. But this talk of “magic wands” is new and different. Moreover, parts of the Template are left unspecified. -/- This under-specification is deliberate: we want to be able to flesh out the Template in umpteen different ways. The Main Theorem of the paper is that any loosely constructive way of fleshing out the Template is synonymous with a ZF-like theory. (shrink)

Quantum Non-Locality and Relativity is recognized as the premier philosophical study of Bell's Theorem and its implication for the relativistic account of space and time. Previous editions have been praised for the remarkable clarity of Maudlin's descriptions of both Bell's theorem and his examination of the potential conflict between the theorem and relativity. The third edition of this text has been carefully updated to reflect significant developments, including a new chapter covering important recent work in the foundations of physics. Foremost (...) among these is Roderich Tumiulka's explicit, relativistic theory that can reproduce the quantum mechanical violation of Bell's inequality. The "Free Will Theorem" of John Conway and Simon Kochen is also discussed, as is the status of locality in the Many Worlds interpretation of quantum theory. The book has also been updated to reflect recent results in information theory. The book introduces philosophers to the relevant physics and demonstrates how philosophical analysis can help to resolve some of the problems, and requires no technical background in Physics. All of the physics is presented from first principles, and as much as possible is presented pictorially"--Provided by publisher. (shrink)

Much of the intuitive appeal of evidentialism results from conflating two importantly different conceptions of evidence. This is most clear in the case of perceptual justification, where experience is able to provide evidence in one sense of the term, although not in the sense that the evidentialist requires. I argue this, in part, by relying on a reading of the Sellarsian dilemma that differs from the version standardly encountered in contemporary epistemology, one that is aimed initially at the epistemology of (...) introspection but which generalizes to theories of perceptual justification as well. (shrink)

John McDowell's contribution to philosophy has ranged across Greek philosophy, philosophy of language, philosophy of mind, metaphysics and ethics. His writings have drawn on the works of, amongst others, Aristotle, Kant, Hegel, Frege, Russell, Wittgenstein, Sellars, and Davidson. His contributions have made him one of the most widely read, discussed and challenging philosophers writing today. This book provides a careful account of the main claims that McDowell advances in a number of different areas of philosophy. The interconnections between the different (...) arguments are highlighted and Tim Thornton shows how these individual projects are unified in a post-Kantian framework that articulates the preconditions of thought and language. Thornton sets out the differing strands of McDowell's work prior to, and leading up to, their combination in the broader philosophical vision revealed in "Mind and World" and provides an interpretative and critical framework that will help shape ongoing debates surrounding McDowell's work. An underlying theme of the book is whether McDowell's therapeutic approach to philosophy, which owes much to the later Wittgenstein, is consistent with the substance of McDowell's discussion of nature that uses the vocabulary of other philosophers including, centrally, Kant. (shrink)

To what extent are cognitive capacities, especially perceptual capacities, informationally encapsulated and to what extent are they cognitively penetrable? And why does this matter? Two reasons we care about encapsulation/penetrability are: (a) encapsulation is sometimes held to be definitional of modularity, and (b) penetrability has epistemological implications independent of modularity. I argue that modularity does not require encapsulation; that modularity may have epistemological implications independently of encapsulation; and that the epistemological implications of the cognitive penetrability of perception are messier than (...) is sometimes thought. (shrink)

What does imagination do for our perception of the world? Why should reality be broken off from our imagining of it? It was not always thus, and in these essays, Tim Ingold sets out to heal the break between reality and imagination at the heart of modern thought and science. Imagining for Real joins with a lifeworld ever in creation, attending to its formative processes, corresponding with the lives of its human and nonhuman inhabitants. Building on his two previous essay (...) collections, The Perception of the Environment and Being Alive, this book rounds off the extraordinary intellectual project of one of the world's most renowned anthropologists. Offering hope in troubled times, these essays speak to coming generations in a language that surpasses disciplinary divisions. They will be essential reading not only to for anthropologists but also for students in fields ranging from art, aesthetics, architecture and archaeology to philosophy, psychology, human geography, comparative literature and theology. (shrink)

Nearly everyone agrees that perception gives us justification and knowledge, and a great number of epistemologists endorse a particular two-part view about how this happens. The view is that perceptual beliefs get their justification from perceptual experiences, and that they do so by being based on them. Despite the ubiquity of these two views, I think that neither has very much going for it; on the contrary, there’s good reason not to believe either one of them.

The choice of emphasis in kinship studies has often resulted in incompatible theoretical models of kinship that are mutually undermining and contradictory. Jones' attempts to reconcile disparate approaches to kinship using OT is useful, however; seeing kinship as a specialized system for representing genealogy may be unwarranted in the light of recent advances in mathematical approaches to kinship terminologies.

Neural organoids are laboratory-generated entities that replicate certain structural and functional features of the human brain. Most neural organoids are disembodied—completely decoupled from sensory input and motor output. As such, questions about their potential capacity for consciousness are exceptionally difficult to answer. While not disputing the need for caution regarding certain neural organoid types, this paper appeals to two broad constraints on any adequate theory of consciousness—the first involving the dependence of consciousness on embodiment; the second involving the dependence of (...) consciousness on representations—to argue that disembodied neural organoids are not plausible candidates for consciousness. (shrink)

This chapter contains sections titled: Introduction The Mathematical Theory of Probability The Philosophical Theory of Probability Conclusion References.

Today is dedicated to the remembrance of the Holy Innocents, who were victims of a state sponsored terrorist attack at the very beginning of the Christian era. We believe this is an appropriate spiritual time to review and question the moral judgement of the Catholic Bishops of the United States of America that our nation's war on the people of Afghanistan is just. We do this in a spirit of fidelity to the teachings of the Catholic Church and to the (...) charism bequeathed to us as Catholic Workers by our founders, the Servants of God Peter Maurin and Dorothy Day of New York. Our statements, questions, and conclusions may seem startling to you, they may make you uncomfortable. This is because we come to you, not as the rich and powerful, but as the weak, poor, and powerless. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

Against transmission -- For attention -- Education in the minor key -- Anthropology, art and the university.

Workplace AI is transforming labor but decisions on which AI applications are developed or implemented are made with little to no input from workers themselves. In this piece for AI & Society, I argue for nationalization as a strategy for democratizing AI.