Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally broad (...) scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers. (shrink)

In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the (...) announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs . The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras . Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL. (shrink)

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to (...) game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com. (shrink)

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC and (...) its associated analytic calculus. These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations. (shrink)

Graph-based frames have been introduced as a logical framework which internalises an inherent boundary to knowability (referred to as ‘informational entropy’), due, e.g. to perceptual, evidential or linguistic limits. They also support the interpretation of lattice-based (modal) logics as hyper-constructive logics of evidential reasoning. Conceptually, the present paper proposes graph-based frames as a formal framework suitable for generalising Pawlak's rough set theory to a setting in which inherent limits to knowability exist and need to be considered. Technically, the present paper (...) establishes systematic connections between the first-order correspondents of Sahlqvist modal reduction principles on Kripke frames, and on the more general relational environments of graph-based and polarity-based frames. This work is part of a research line aiming at: (a) comparing and inter-relating the various (first-order) conditions corresponding to a given (modal) axiom in different relational semantics; (b) recognising when first-order sentences in the frame-correspondence languages of different relational structures encode the same ‘modal content’; (c) meaningfully transferring relational properties across different semantic contexts. The present paper develops these results for the graph-based semantics, polarity-based semantics, and all Sahlqvist modal reduction principles. As an application, we study well known modal axioms in rough set theory (such as those corresponding to seriality, reflexivity, and transitivity) on graph-based frames and show that, although these axioms correspond to different first-order conditions on graph-based frames, their intuitive meaning is retained. This allows us to introduce the notion of hyperconstructivist approximation spaces as the subclass of graph-based frames defined by the first-order conditions corresponding to the same modal axioms defining classical generalised approximation spaces, and to transfer the properties and the intuitive understanding of different approximation spaces to the more general framework of graph-based frames. The approach presented in this paper provides a base for systematically comparing and connecting various formal frameworks in rough set theory, and for the transfer of insights across different frameworks. (shrink)

We introduce a new and general notion of canonical extension for algebras in the algebraic counterpart of any finitary and congruential logic . This definition is logic-based rather than purely order-theoretic and is in general different from the definition of canonical extensions for monotone poset expansions, but the two definitions agree whenever the algebras in are based on lattices. As a case study on logics purely based on implication, we prove that the varieties of Hilbert and Tarski algebras are canonical (...) in this new sense. (shrink)

In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.

In this paper we introduce canonical extensions of partially ordered sets and monotone maps and a corresponding discrete duality. We then use these to give a uniform treatment of completeness of relational semantics for various substructural logics with implication as the residual(s) of fusion.

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.

In the present article, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The display approach is suitable to modularly chart the space of dynamic epistemic logics on weaker-than-classical propositional base. The presence of types endows the language of the Dynamic Calculus with additional expressivity, allows for a smooth proof-theoretic treatment, and paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly (...) beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag–Moss–Solecki's dynamic epistemic logic, and enjoys Belnap-style cut elimination. (shrink)

The present article provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems that have been successfully applied to diverse scientific disciplines, but the proof-theoretic treatment of which presents many difficulties. After an illustration of the proof-theoretic semantic principles most relevant to the treatment of logical connectives, we turn to illustrating the main features of display calculi, (...) a proof-theoretic paradigm that has been successfully employed to give a proof-theoretic semantic account of modal and substructural logics. Then, we review some of the most significant proposals of proof systems for dynamic epistemic logics, and we critically reflect on them in the light of the previously introduced proof-theoretic semantic principles. The contributions of the present article include a generalization of Belnap's cut-elimination metatheorem for display calculi, and a revised version of the display-style calculus D.EAK. We verify that the revised version satisfies the previously mentioned proof-theoretic semantic principles, and show that it enjoys cut-elimination as a consequence of the generalized metatheorem. (shrink)

We-thinking theories allow groups to deliberate as agents. They have been introduced into the economic domain for both theoretical and empirical reasons. Among the few scholars who have proposed formal approaches to illustrate how we-thinking arises, Bacharach offers one of the most developed theories from the game theoretic point of view. He presents a number of intuitions, not always mutually consistent and not fully developed. In this article, I propose a way to complete Bacharach’s theory, generalizing the interdependence hypothesis and (...) building on his intuition about vacillation. It is a simple model of vacillation between the I and we-modes of reasoning, as a way in which we-thinking can come to mind in the face of a decision problem. The vacillation model makes we-reasoning more easily usable in game theory. (shrink)

It is a common opinion that chance events cannot be understood in causal terms. Conversely, according to a causal view of chance, intersections between independent causal chains originate accidental events, called “coincidences”. Firstly, this book explores this causal conception of chance and tries to shed new light on it. Such a view has been defended by authors like Antoine Augustine Cournot and Jacques Monod. Second, a relevant alternative is provided by those accounts that, instead of acknowledging an intersection among causal (...) lines, claim to track coincidences back to some common cause. Third, starting from Herbert Hart and Anthony Honoré’s view of coincidences (Causation in the Law. Clarendon Press, Oxford, 1959). This book provides a more detailed account of coincidences, according to which coincidental events are hybrids constituted by ontic (physical) components, which is the intersection between independent causal chains, plus epistemic aspects, including but not limited to, access to information, expectations, relevance, significance, desires, which in turn are psychological aspects. -/- The main target of the present work is to show that the epistemic aspects of coincidences are, together with the independence between the intersecting causal chains, a constitutive part of coincidental phenomena. This book aims to introduce and discuss recent work in psychology concerning one’s judgment about coincidences; this data offers further materials and reasons to reflect upon our understanding of coincidences and to refine our hybrid conception. (shrink)

We associate a canonical unital involutive quantale to a topological groupoid. When the groupoid is also étale, this association is compatible with but independent from the theory of localic étale groupoids and their quantales [9] of P. Resende. As a motivating example, we describe the connection between the quantale and the C*-algebra that both classify Penrose tilings, which was left as an open problem in [5].

The exponential rise in transgender self-identification invites consideration of what constitutes an ethical response to transgender individuals’ claims about how best to promote their well-being. In this paper, we argue that ‘accepting’ a claim to medical transitioning in order to promote well-being would be in the person’s best interests iff at the point of request the individual is correct in their self-diagnosis as transgender (i.e., the distress felt to reside in the body does not result from another psychological and/or societal (...) problem) such that the medical interventions they are seeking will help them to realise their preferences. If we cannot assume this—and we suggest that we have reasonable grounds to question an unqualified acceptance in some cases—then ‘acceptance’ potentially works against best interests. We propose a distinction between ‘acceptance’ and respectful, in-depth exploration of an individual’s claims about what promotes their well-being. We discuss the ethical relevance of the unconscious mind to considerations of autonomy and consent in working with transgender individuals. An inquisitive stance, we suggest, supports autonomous choice about how to realise an embodied form that sustains well-being by allowing the individual to consider both conscious and unconscious factors shaping wishes and values, hence choices. (shrink)

In this chapter I show that idealizing assumptions can obscure conversational dynamics because they neglect power differentials that are crucial enablers of the successful performance of some speech acts (see, Sbisà, 2020). I examine how silencing is promoted by conversational norms that would defeasibly entitle linguistic agents to presume that silence indicates acceptance. I focus on Goldberg’s (2020) discussion of these phenomena. Goldberg argues in support of a norm of no silent rejections claiming that silencing is partly the result of (...) the misapplication of this norm. He further defends the view that the norm itself is part of the solution to the problem of silencing. In the chapter I argue that Goldberg is mistaken on these points. Instead, drawing inspiration from Sbisà (2020), I argue that norms of no silent rejection are temporarily enacted by means of speech acts that function as exercitive assertions. (shrink)

Logical metonymy resolution (begin a book begin reading a book or begin writing a book) has traditionally been explained either through complex lexical entries (qualia structures) or through the integration of the implicit event via post-lexical access to world knowledge. We propose that recent work within the words-as-cues paradigm can provide a more dynamic model of logical metonymy, accounting for early and dynamic integration of complex event information depending on previous contextual cues (agent and patient). We first present a self-paced (...) reading experiment on German subordinate sentences, where metonymic sentences and their paraphrased version differ only in the presence or absence of the clause-final target verb (Der Konditor begann die Glasur Der Konditor begann, die Glasur aufzutragen/The baker began the icing The baker began spreading the icing). Longer reading times at the target verb position in a high-typicality condition (baker + icing spread ) compared to a low-typicality (but still plausible) condition (child + icing spread) suggest that we make use of knowledge activated by lexical cues to build expectations about events. The early and dynamic integration of event knowledge in metonymy interpretation is bolstered by further evidence from a second experiment using the probe recognition paradigm. Presenting covert events as probes following a high-typicality or a low-typicality metonymic sentence (Der Konditor begann die Glasur AUFTRAGEN/The baker began the icing SPREAD), we obtain an analogous effect of typicality at 100 ms interstimulus interval. (shrink)

Combining philosophy and literature, this book considers distraction not as an imperfection, but as a mental state with political and aesthetic potential.

After more than three centuries, Molyneux's question continues to challenge our understanding of cognition and perceptual systems. Locke, the original recipient of the question, approached it as a theoretical exercise relevant to long-standing philosophical issues, such as nativism, the possibility of common sensibles, and the empiricism-rationalism debate. However, philosophers were quick to adopt the experimentalist's stance as soon as they became aware of recoveries from congenital blindness through ophtalmic surgery. Such recoveries were widely reported to support empiricist positions, suggesting that (...) the question had found its empirical answer. Contrary to this common view, we argue that studies of patients recovering from early blindness through surgery cannot provide an answer. In fact, because of the very nature of such ophtalmological interventions it is impossible to test the question in the empirical conditions outlined by Molyneux. Thus we propose that Molyneux's question be treated as an early thought experiment of a specific kind. Although thought experiments of this kind cannot be turned into actual experimental conditions, they provide a conceptual restructuring of theories. Such restructuring in turn leads to new predictions that can then be tested by normal experiments. In accord with this interpretation, we show that Molyneux's question can be analyzed into a hierarchy of specific questions about vision in its phenomenal and sensory-motor components. Some of these questions do lead to actual experimental conditions that could be studied empirically. (shrink)

After more than three centuries, Molyneux's question continues to challenge our understanding of cognition and perceptual systems. Locke, the original recipient of the question, approached it as a theoretical exercise relevant to long-standing philosophical issues, such as nativism, the possibility of common sensibles, and the empiricism-rationalism debate. However, philosophers were quick to adopt the experimentalist's stance as soon as they became aware of recoveries from congenital blindness through ophtalmic surgery. Such recoveries were widely reported to support empiricist positions, suggesting that (...) the question had found its empirical answer. Contrary to this common view, we argue that studies of patients recovering from early blindness through surgery cannot provide an answer. In fact, because of the very nature of such ophtalmological interventions it is impossible to test the question in the empirical conditions outlined by Molyneux. Thus we propose that Molyneux's question be treated as an early thought experiment of a specific kind. Although thought experiments of this kind cannot be turned into actual experimental conditions, they provide a conceptual restructuring of theories. Such restructuring in turn leads to new predictions that can then be tested by “normal” experiments. In accord with this interpretation, we show that Molyneux's question can be analyzed into a hierarchy of specific questions about vision in its phenomenal and sensory-motor components. Some of these questions do lead to actual experimental conditions that could be studied empirically. (shrink)

We show unintended consequences of quota regulations to get women on boards. Board members may have different characteristics, and even among women, there are variations. We assume that the characteristics of the board members have an influence on their contributions to boards, to businesses as well as to society. In this paper, we argue that different types of societal pressure to get women on boards have an influence on the social capital characteristics of the women getting multiple board memberships. The (...) paper is drawing on institutional theory and social capital theory, and we distinguish between mimetic, normative, and coercive types of pressure. Through a cluster analysis of 58 Italian “golden skirts”, we show that different types of societal pressure may lead to differences in social capital characteristics. The study has implications for the ongoing international debate about women and diversity on boards, and we propose developing a pressure theory for getting women on boards. (shrink)