Constitutivism argues that the source of the categorical force of the norms of rationality and morality lies in the constitutive features of agency. A systematic failure to be guided by these norms would amount to a loss or lack of agency. Since we cannot but be agents, we cannot but be unconditionally guided by these norms. The constitutivist strategy has been challenged by David Enoch. He argues that our participation in agency is optional and thus cannot be a source of (...) categorical demands. In this paper, I defend the viability of constitutivism by showing that agency is indeed a special ‘inescapable’ enterprise. Agency has the largest jurisdiction, and it is closed under rational assessment. This inescapability does not exempt constitutivism from raising the question whether agents have reason to be agents, but this question has to be taken up within agency. If this question is answered affirmatively, then—I argue—the criteria of practical correctness are self-ratifying in a non-circular way. This is sufficient to show the viability of the constitutivist strategy. Whether agents have conclusive reasons to be agents, however, is a matter to be addressed in the terms of particular versions of constitutivism. (shrink)

According to Jim Pryor’s dogmatism, if you have an experience as if P, you acquire immediate prima facie justification for believing P. Pryor contends that dogmatism validates Moore’s infamous proof of a material world. Against Pryor, I argue that if dogmatism is true, Moore’s proof turns out to be non-transmissive of justification according to one of the senses of non-transmissivity defined by Crispin Wright. This type of non-transmissivity doesn’t deprive dogmatism of its apparent antisceptical bite.

It is often argued that future-directed decisions are effective at shaping our future conduct because they give rise, at the time of action, to a decisive reason to act as originally decided. In this paper, I argue that standard accounts of decision-based reasons are unsatisfactory. For they focus either on tie-breaking scenarios or cases of self-directed distal manipulation. I argue that future-directed decisions are better understood as tools for the non-manipulative, intrapersonal division of deliberative labor over time. A future-directed decision (...) to ϕ gives rise to a defeasible exclusionary reason to ϕ. This reason is grounded on the default authority that is normally granted to one’s prior self as an “expert” deliberator. I argue that this kind of exclusionary reason is the only one that can account for the effectiveness of future-directed decisions at shaping our diachronic agency without violating our autonomy over time. (shrink)

In this paper, I argue against the popular philosophical thesis---aka the ‘own action condition’---that an agent can only intend one’s own actions. I argue that the own action condition does not hold for any executive attitude, intentions included. The proper object of intentions is propositional rather than agential (‘I intend that so-and-so be the case’ rather than ‘I intend to do such-and-such’). I show that, although there are some essential de se components in intending, they do not restrict the content (...) of intentions to one’s own actions. I then discuss the special way in which one’s own actions can figure in the content of one’s intentions, which shows that the distinction between intending and acting is less stark than it appears at first. This is a conclusion that many defenders of the own action condition might find appealing but which, I argue, is better supported by rejecting the own action condition. (shrink)

In this paper I investigate whether there are genuine and irreducible pressures of diachronic rationality grounded on the structure of the subject rather than on substantive considerations, such as pragmatic ones. I argue that structural pressures of diachronic rationality have a limited scope. The most important pressure only tells against arbitrary interference with the mechanisms for the retention of attitudes over time. I then argue that in the practical case, a substantial account in terms of the agent's temporal identity appears (...) more promising than a purely structural one, but in the end it still leaves many questions about diachronic practical rationality underdetermined. (shrink)

This chapter discusses the structure of our temporally extended agency. We do not have the power to act directly at a distance, so any of our temporally extended projects must be sustained over its temporal unfolding by momentary actions. We need both the capacity to organize these momentary steps in light of a synoptic overview of the extended activity as a whole and to sustain our motivation to continue to pursue the extended activity. Hence, the distinctive mode in which we (...) act over time is that of ’planning agency,’ which requires a form of temporal identification that goes beyond mere psychological continuity. I then discuss the differences in internal structure between merely continuous and integrated activities, and between telic and atelic ones. I provide a taxonomy of the different kinds of temporal goods and values and how these structures might bear on the risk of crisis of meaning in our temporal existence. I then touch briefly on the issue of how our mortality might make a difference to the structure of what we find valuable and how it relates to the temporal features of our agency. In the closing section, I discuss the effects of the moving temporal location of the agent (with her local executive powers) relative to her extended pursuits, including the asymmetries generated by the distinction between past and future stages of the activity and the moving horizon of what the agent can anticipate and (indirectly) control. (shrink)

In this chapter we argue that Robert Hare's psychopathy checklist revised (PCL-R) offers a construct of psychopathy that is valid enough for philosophical investigations of the moral and legal responsibility of psychopathic offenders.

What can the philosophy of agency learn from Nguyen’s book on games? The most important lesson concerns, to use Nguyen’s terms, the ‘layered’ structure of our agency and the ‘fluidity’ requ...

In this paper, I will discuss the various ways in which intentions can be said to be conditional, with particular attention to the internal conditions on the intentions’ content. I will first consider what it takes to carry out a conditional intention. I will then discuss how the distinctive norms of intention apply to conditional intentions and whether conditional intentions are a weaker sort of commitments than the unconditional ones. This discussion will lead to the idea of what I call (...) the ‘deep structure’ of intentions. Roughly, this is the idea that the conditional nature of our intentions is only partially made explicit in the expressions we use to communicate our intentions and in the explicit form of our thinking about and reasoning with them. Most conditions that qualify our intentions are part of a deep functional structure that can be evinced by observing the actual psychological functioning of intentions and by considering the rational requirements that they engage. I will argue that the deep structure of intentions is characteristically conditional. Genuinely unconditional intentions are only limiting instances of conditional intentions and their contribution to agency can only be understood in light of this fact. I will conclude by showing that the characteristic conditional structure of intentions is intimately related to distinctive features of human agency, especially to its unity over time. (shrink)

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse (...) fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. (shrink)

The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to (...) establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics. (shrink)

Experiences like pains, pleasures, and emotions have affective phenomenal character: they feel pleasant or unpleasant. Imperativism proposes to explain affective phenomenal character by appeal to imperative content, a kind of intentional content that directs rather than describes. We argue that imperativism is on the right track, but has been developed in the wrong way. There are two varieties of imperativism on the market: first-order and higher-order. We show that neither is successful, and offer in their place a new theory: reflexive (...) imperativism. Our proposal is that an experience P feels pleasant in virtue of being constituted by a Command with reflexive imperative content, while an experience U feels unpleasant in virtue of being constituted by a Command with reflexive imperative content : More of P!Less of U! If you need a slogan: experiences have affective phenomenal character in virtue of commanding us Get more of me! Get less of me! (shrink)

Timothy Smiley’s wonderful paper ‘Rejection’ (1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection – recently advanced by Julien Murzi and Ole Hjortland (2009) – to one of Smiley’s key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues discussed in (...) Smiley’s paper. (shrink)

According to Jim Pryor’s dogmatism, when you have an experience with content p, you often have prima facie justification for believing p that doesn’t rest on your independent justification for believing any proposition. Although dogmatism has an intuitive appeal and seems to have an antisceptical bite, it has been targeted by various objections. This paper principally aims to answer the objections by Roger White according to which dogmatism is inconsistent with the Bayesian account of how evidence affects our rational credences. (...) If this were true, the rational acceptability of dogmatism would be seriously questionable. I respond that these objections don’t get off the ground because they assume that our experiences and our introspective beliefs that we have experiences have the same evidential force, whereas the dogmatist is uncommitted to this assumption. I also consider the question whether dogmatism has an antisceptical bite. I suggest that the answer turns on whether or not the Bayesian can determine the priors of hypotheses and conjectures on the grounds of their extra-empirical virtues. If the Bayesian can do so, the thesis that dogmatism has an antisceptical bite is probably false. (shrink)

In this paper, I discuss Ludwig's systematic and illuminating account of conditional intentions, with particular reference to my own view (presented in "Conditional Intentions", Noûs, 2009). In contrast to Ludwig, I argue that we should prefer a formal characterization of conditional intentions rather than a more substantial one in terms of reasons for action (although the conditions that qualify an intention bear on the reasonableness and justifiability of the intention). I then defend a partially different taxonomy of the conditions that (...) might qualify an intention and discuss how the difference bears on the application of the rational pressures of intention. I go on to acknowledge that Ludwig is correct on insisting on the centrality of the *epistemic* element in the antecedent of conditional intentions. But I argue that even when a condition has been settled (that is, when the agent has ascertained that it holds), the intention remains genuinely conditional. In my view, conditions that have been settled are not just part of the background of planning: they continue to qualify the content of the intention (although they come to play a different role when settled). I then discuss how the settling of a condition does not interrupt the *continuity* of the content and structure of the intention---in contrast to Ludwig's account, where the conditional intention appears to give rise, when the conditions are taken as settled, to a distinct *unconditional* intention. I close by discussing the serious concern that my way of characterizing conditional intentions threatens to swallow most intentions, given that it is unlikely that we have intentions that do not rest on our accepting the obtaining of relevant conditions. (shrink)

The purpose of this paper is to explore the connection between change and the B-theory of time, sometimes also called the Scientific view of time, according to which reality is a four-dimensional spacetime manifold, where past, present and future things equally exist, and the present time and non-present times are metaphysically the same. I argue in favour of a novel response to the much-vexed question of whether there is change on the B-theory or not. In fact, B-theorists are often said (...) to hold a ‘static’ view of time. But this far from being innocent label: if the B-theory of time presents a model of temporal reality that is static, then there is no change on the B-theory. From this, one can reasonably think as follows: of course, there is change, so the B-theory must be false. What I plan to do in this paper is to argue that in some sense there is change on the B-theory, but in some other sense, there is no change on the B-theory. To do so, I present three instances of change: Existential Change, namely the view that things change with respect to their existence over time; Qualitative Change, the view that things change with respect to how they are over time; Propositional Change, namely the view that things (i.e. propositions) change with respect to truth value over time. I argue that while there is a reading of these three instances of change that is true on the B-theory, and so there is change on the B-theory in this sense, there is a B-theoretical reading of each of them that is not true on the B-theory, and therefore there is no change on the B-theory in this other sense. (shrink)

First collected in Italy in 1985, _Art's Claim to Truth_ is considered by many philosophers to be one of Gianni Vattimo's most important works. Newly revised for English readers, the book begins with a challenge to Plato, Aristotle, Kant, and Hegel, who viewed art as a metaphysical aspect of reality rather than a futuristic anticipation of it. Following Martin Heidegger's interpretation of the history of philosophy, Vattimo outlines the existential ontological conditions of aesthetics, paying particular attention to the works of (...) Kandinsky, which reaffirm the ontological implications of art. Vattimo then builds on Hans-Georg Gadamer's theory of aesthetics and provides an alternative to a rationalistic-positivistic criticism of art. This is the heart of Vattimo's argument, and with it he demonstrates how hermeneutical philosophy reaffirms art's ontological status and makes clear the importance of hermeneutics for aesthetic studies. In the book's final section, Vattimo articulates the consequences of reclaiming the ontological status of aesthetics without its metaphysical implications, holding Aristotle's concept of beauty responsible for the dissolution of metaphysics itself. In its direct engagement with the works of Gadamer, Heidegger, and Luigi Pareyson, _Art's Claim to Truth_ offers a better understanding of the work of Vattimo and a deeper knowledge of ontology, hermeneutics, and the philosophical examination of truth. (shrink)

Some Presentists—according to whom everything is present—identify instants of time with propositions of a certain kind. However, the view that times are propositions seems to be at odds with Presentism: if there are times then there are past times, and therefore things that are past; but how could there be things that are past if everything is present? In this paper, we describe the Presentist view that times are propositions ; we set out the argument that Presentism is incompatible with (...) the view that times are propositions ; and then we describe three possible responses to that argument on behalf of Presentists who identify times with propositions. We argue that each of these responses comes with significant costs. Finally, we describe a fourth possible response—according to which times are irreducibly higher-order entities—which appears to avoid the costs of the other three. We also describe and respond to two objections to the higher-order strategy. (shrink)

In this paper, I discuss whether there are genuinely *diachronic* constraints of practical rationality, that is, pressures on combinations of practical attitudes over time, which are not reducible to mere synchronic rational pressures. Michael Bratman has recently argued that there is at least one such diachronic rational constraint that governs the stability of intentions over time. *Pace* Bratman, I argue that there are no genuinely diachronic constraints on intentions that meet the stringent desiderata set by him. But I show that (...) there are at least two synchronic rational constraints with distinctive and important, although only indirect, diachronic dimensions. Neither of them, however, supports the practical conservatism in the face of normative underdetermination that, according to Bratman, is part and parcel of the diachronic rationality of intention stability. (shrink)

In this paper, we develop an impure somatic theory of emotion, according to which emotions are constituted by the integration of bodily perceptions with representations of external objects, events, or states of affairs. We put forward our theory by contrasting it with Prinz's pure somatic theory, according to which emotions are entirely constituted by bodily perceptions. After illustrating Prinz's theory and discussing the evidence in its favor, we show that it is beset by serious problems—i.e., it gets the neural correlates (...) of emotion wrong, it isn't able to distinguish emotions from bodily perceptions that aren't emotions, it cannot account for emotions being directed towards particular objects, and it mischaracterizes emotion phenomenology. We argue that our theory accounts for the empirical evidence considered by Prinz and solves the problems faced by his theory. In particular, we maintain that our theory gives a unified and principled account of the relation between emotions and bodily perceptions, the intentionality of emotions, and emotion phenomenology. (shrink)

In this paper we focus on transmission and failure of transmission of warrant. We identify three individually necessary and jointly sufficient conditions for transmission of warrant, and we show that their satisfaction grounds a number of interesting epistemic phenomena that have not been sufficiently appreciated in the literature. We then scrutinise Wright’s analysis of transmission failure and improve on extant readings of it. Nonetheless, we present a Bayesian counterexample that shows that Wright’s analysis is partially incoherent with our analysis of (...) warrant transmission and prima facie defective. We conclude exploring three alternative lines of reply: developing a more satisfactory account of transmission failure, which we outline; dismissing the Bayesian counterexample by rejecting some of its assumptions; reinterpreting Wright’s analysis to make it immune to the counterexample. (shrink)

Moral constitutivism purports to explain moral normativity by appeal to the nature of either agency or rational powers. Ambitious constitutivism aspires to ground the categorical authority of morality and to derive the content of the basic moral norms while avoiding the problems of moral realism. As a general strategy, moral constitutivism faces three serious challenges. First, the shmagency challenge. The worry is that the authority of the norms derived from the nature of agency is only conditional on having a reason (...) to be an agent rather than some other kind of subject, a shmagent or an alienated agent. Constitutivists usually reply by appealing to the inescapability of agency. Second, there is a worry that agency is too thin a basis for the derivation of the substantive content of moral norms. Finally, there is the worry that constitutivism might be unable to make room for bad actions. The entry considers possible responses by moral constitutivism to these concerns and whether, if these responses are unsatisfactory, moral constitutivism might still have some explanatory power but of a less ambitious sort. (shrink)

This paper introduces the Monstrous Conclusion, according to which, for any population, there is a better population consisting of just one individual (the Monster). The Monstrous Conclusion is deeply counterintuitive. I defend a version of Prioritarianism as a particularly promising population axiology that does not imply the Monstrous Conclusion. According to this version of Prioritarianism, which I call Asymptotic Prioritarianism, there is diminishing marginal moral importance of individual welfare that can get close to, but never quite reach, some upper limit. (...) I argue that Asymptotic Prioritarianism faces a theoretical cost, that I call the Absolute Priority Principle. However, the Absolute Priority Principle is an extreme version of what I call the Trade-off Condition, an already noteworthy problem facing other (more widely endorsed) versions of Prioritarianism. I conclude that it is better for a theory to imply the Absolute Priority Principle and avoid the Monstrous Conclusion than to imply the Monstrous Conclusion and the Trade-off Condition. The potential for Asymptotic Prioritarianism is substantial. (shrink)

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

The Schön misconduct case has been widely publicized in the media and has sparked intense discussions within and outside the scientific community about general issues of science ethics. This paper analyses the Report of the official Committee charged with the investigation in order to show that what at first seems to be a quite uncontroversial case, turns out to be an accumulation of many interesting and non-trivial questions (of both ethical and philosophical interest). In particular, the paper intends to show (...) that daily scientific practices are structurally permeated by chronic problems; this has serious consequences for how practicing scientists assess their work in general, and scientific misconduct in particular. A philosophical approach is proposed that sees scientific method and scientific ethics as inextricably interwoven. Furthermore, the paper intends to show that the definition of co-authorship that the members of the Committee use, although perhaps clear in theory, proves highly problematic in practice and raises more questions that it answers. A final plea is made for a more self-reflecting attitude of scientists as far as the moral and methodological profile of science is concerned as a key element for improving not only their scientific achievements, but also their assessment of problematic cases. (shrink)

There are two standard conceptions of the functioning of and rationale for the diachronic will, i.e., for an agent's capacity to settle on her future conduct in advance. According to the pragmatic-instrumentalist view, the diachronic will benefits us by increasing the long-term satisfaction of our rational preferences. According to the cognitive view, it benefits us by satisfying our standing desire for self-knowledge and self-understanding. Contrary to these views, I argue for a constitutive view of the diachronic will: the rationale for (...) it is that it makes possible to engage in activities with a radically novel temporal structure, activities that are not merely continuous over time, but temporally integrated and unified. These activities are essential to our form of life and to our existence as temporally unified agents. The instrumental and cognitive benefits, if any, are merely secondary to the ontological ones. (shrink)

The discussion of whether psychopaths are morally responsible for their behaviour has long taken place in philosophy. In recent years this has moved into scientific and psychiatric investigation. Responsibility and Psychopathy discusses this subject from both the philosophical and scientific disciplines, as well as a legal perspective.

In [9] we have considered a wide class of "well-behaved" reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [9] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions).

This paper offers an overview of the ways agents might extend over time and the characteristic structure of extended human agency. Agency can extend in two distinct but combinable modes: the ontological, which gives rise to simple continuous agents; and the conceptual, which gives rise to agents who conceive of and care about distal times, and have minimal planning abilities. Our extended form of agency combines both. But we are still limited by the temporal locality in the operation of our (...) psychological and executive powers. To account for this locality, I introduce the notion of 'temporal selves,' as the loci of immediacy in the agent's determination of their psychology, conduct, and practical standpoint. I argue that the passage of time generates, by itself, the threat of temporal alienation from distant temporal selves. A genuinely extended agency requires temporal identification: the sharing, by separate temporal selves, of a temporally extended and integrated practical standpoint. This temporal identification cannot be produced simply by temporal identity as continuity. What is required is temporal identity in the mode of unity and integration. This identity does not precede temporal identification but is co-constituted with it. I offer a preliminary account of the structure of the units of integration for agents who aspire to persist in the mode of unity and integration. I close with a cautionary note: the complex structure of integration, although familiar in everyday life, is often missed by standard philosophical accounts, which tend to focus on simple models of extended agency. (shrink)

A common feature of all versions of constitutivism is the “simple constitutivist move” to the effect that engagement in any enterprise requires respecting the constitutive standards of the enterpri...

Human mental workload is arguably the most invoked multidimensional construct in Human Factors and Ergonomics, getting momentum also in Neuroscience and Neuroergonomics. Uncertainties exist in its characterization, motivating the design and development of computational models, thus recently and actively receiving support from the discipline of Computer Science. However, its role in human performance prediction is assured. This work is aimed at providing a synthesis of the current state of the art in human mental workload assessment through considerations, definitions, measurement techniques (...) as well as applications, Findings suggest that, despite an increasing number of associated research works, a single, reliable and generally applicable framework for mental workload research does not yet appear fully established. One reason for this gap is the existence of a wide swath of operational definitions, built upon different theoretical assumptions which are rarely examined collectively. A second reason is that the three main classes of measures, which are self-report, task performance, and physiological indices, have been used in isolation or in pairs, but more rarely in conjunction all together. Multiple definitions complement each another and we propose a novel inclusive definition of mental workload to support the next generation of empirical-based research. Similarly, by comprehensively employing physiological, task-performance, and self-report measures, more robust assessments of mental workload can be achieved. (shrink)

In this paper we aim to offer a balanced argument to motivate (re)thinking about the mental illness clause within the insanity defence. This is the clause that states that mental illness should have a relevant causal or explanatory role for the presence of the incapacities or limited capacities that are covered by this defence. We offer three main considerations showing the important legal and epistemological roles that the mental illness clause plays in the evaluation of legal responsibility. Although we acknowledge (...) that these advantages could be preserved without having this clause explicitly stated in the law, we resist proposals that deny the importance of mental illness in exculpation. We argue, thus, that any attempt at removing the mental illness clause from legal formulations of the insanity defence should offer alternative ways of keeping in place these advantages. (shrink)

The aim of this paper is to address the semantic issue of the nature of the representation I and of the transcendental designation, i.e., the self-referential apparatus involved in transcendental apperception. The I think, the bare or empty representation I, is the representational vehicle of the concept of transcendental subject; as such, it is a simple representation. The awareness of oneself as thinking is only expressed by the I: the intellectual representation which performs a referential function of the spontaneity of (...) a thinking subject. To begin with, what exactly does Kant mean when he states that I is a simple and empty representation? Secondly, can the features of the representation I and the correlative transcendental designation explain the indexical nature of the I? Thirdly, do the Kantian considerations on indexicality anticipate any of the semantic elements or, if nothing else, the spirit of the direct reference theory? (shrink)

We present a natural deduction system for dual-intuitionistic logic. Its distinctive feature is that it is a single-premise multiple-conclusions system. Its relationships with the natural deduction systems for intuitionistic and classical logic are discussed.

The non-well-founded set theories described by Aczel (1988) have received attention from category theorists and computer scientists, but have been largely ignored by philosophers. At the root of this neglect might lie the impression that these theories do not embody a conception of set, but are rather of mere technical interest. This paper attempts to dispel this impression. I present a conception of set which may be taken as lying behind a non-well-founded set theory. I argue that the axiom AFA (...) is justified on the conception, which provides, contra Rieger (Mind 109:241–253, 2000), a rationale for restricting attention to the system based on this axiom. By making use of formal and informal considerations, I then make a case that most of the other axioms of this system are also justified on the conception. I conclude by commenting on the significance of the conception for the debate about the justification of the Axiom of Foundation. (shrink)

The Stone-Weierstrass Theorem for compact Hausdorff spaces is a basic result of functional analysis with far-reaching consequences. We introduce an equational logic ⊨Δ associated with an infinitary variety Δ and show that the Stone-Weierstrass Theorem is a consequence of the Beth definability property of ⊨Δ, stating that every implicit definition can be made explicit. Further, we define an infinitary propositional logic ⊢Δ by means of a Hilbert-style calculus and prove a strong completeness result whereby the semantic notion of consequence associated (...) with ⊢Δ coincides with ⊨Δ. (shrink)