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Non-Tarskian interpretations of many-valued logics have been widely explored in the logic literature. The development of non-tarskian conceptions of logical consequence set the theoretical foundations for rediscovering well-known (Tarskian) many-valued logics. One may find in distinct authors many novel interpretations of many-valued systems. They are produced through a type of procedure which consists in altering the semantic structure of Tarskian many-valued logics in order to output a non-Tarskian interpretation of these logics. Through this type of transformation the paper explores a uniform way of transforming finitely many-valued Tarskian logics into their non-Tarskian interpretation. Some general properties of carrying out this type of procedure are studied, namely the dualities between these logics and the conditions under which negation-explosive and negation-complete Tarskian logics become non-explosive.

In this article, I will explore how the underlying research values of ‘openness’ and ‘mutual responsiveness’, which are central to open science practices, can be integrated into a new ethos of science. Firstly, I will revisit Robert Merton's early contribution to this issue, examining whether the ethos of science should be understood as a set of norms for scientists to practice ‘good’ science or as a set of research values as a functional requirement of the scientific system to produce knowledge, irrespective of individual adherence to these norms. Secondly, I will analyse the recent codification of scientific practice in terms of ‘scientific integrity’, a framework that Merton did not pursue. Based on this analysis, and illustrated on the case of COVID-19 as a case in which the institution of science was challenged to deliver urgently on societal desirable outcomes, I will argue that promoting open science and its core norms of collaboration and openness requires broader governance of the institution of science in its relationship with society at large, rather than relying solely on self-governance within the scientific community through a new ethos of science. This conclusion has implications for re-evaluating research assessments, suggesting that the evaluation of the scientific system should take precedence over evaluating individual researchers, and that incentives should be provided to encourage specific research behaviour rather than solely focusing on individual research outputs.

The core insight of this thoughtful and provocative article is that science has become engineering and must be re-governed appropriately. Science today is as much artefact constructing as it is knowledge-producing. Certified knowledge is found through certified construction; science has become technoscience. As such, received practices of and models for governance need re-examining. It is not possible here to address the full range of insights and questions that René von Schomberg’s challenging paper puts on the table. His argument is clearly the outgrowth of years of critical reflection in the science policy trenches of the European Commission. I would wager that there’s no one who has thought longer, harder, and at greater depth about these issues. I will concentrate my comments on the question concerning engineering.

Von Schomberg’s call to place mutual responsiveness – which I understand as the ability of researchers and the research system as a whole to foster meaningful exchanges and learn from novel experiences, no matter where those originate – at the core of Open Science and related efforts to reform the scientific landscape is both timely and significant. Widespread sharing is not enough to guarantee responsible and inclusive research, nor are vague appeals to improve research culture, whatever it is that such culture may turn out to include (Leonelli, 2023). Rather, emphasis needs to be placed on the conditions under which sharing materials, methods and insights – and debating the goals and directions towards which these may be put to use – may improve research exchange, communication and scrutiny, resulting in scientific outputs that are both reliable and socially responsive. Hence von Schomberg’s focus on the interplay between institutional and behavioural features of science and his plea for a reform in governance structures, such as initiated by COARA, are very well-taken. He is, however, too quick to dismiss the importance of some degree of autonomy for those involved in creating knowledge. To show why this matters, I here briefly discuss two of von Schomberg’s additional claims: (1) his focus on ‘knowledge actors’ as the protagonists of research efforts; and (2) his critique of the effectiveness of self-governance efforts by researchers.

Von Schomberg offers a compelling examination of key open science principles and their potential role in fostering responsible research and innovation (RRI). Utilizing Merton's Ethos of Science framework, the paper constructs a series of arguments supporting a central thesis: “the transition towards open science is vital to facilitate RRI.” This transition necessitates significant institutional reforms within the scientific community and adjustments to incentive structures that promote the adoption of open and mutually responsive practices. The manuscript reframes the discourse surrounding responsibility and responsiveness in light of the evolving landscape of open science, shifting the focus from normative commitments to actionable frameworks in research and open science practices. Overall, the position paper strives to bridge the gap between idealised models of scientific communities based on RRI principles and the reality of actual scientific endeavour (Anderson et al., 2007; Politi, 2021, 2024). However, it is important to acknowledge certain omissions that could enrich the analysis. Firstly, a more comprehensive examination of the profound crisis facing science amidst the increasing marketisation and commodification of academia and research would provide valuable context beyond discussions of system failures related to productivity and reproducibility. Secondly, a more nuanced and critical approach to conceptualising open science would enrich the discussion, considering its multifaceted nature and potential pitfalls. Thirdly, the validity of the Mertonian framework and its selective analysis of values, particularly its exclusive focus on the norm of communism. Lastly, a deeper exploration of the challenges and promises inherent in the pursuit of responsible Open Science within ongoing institutional processes.

It is hard to disagree with the thrust of René von Schomberg’s position paper. It is driven by the worry that current conceptions of “open science” are all too impoverished – that they need to be complemented by the social practice of “mutual responsiveness”. In terms of political theory or notions of democracy, on the one hand, in terms of socially relevant research practice, on the other hand, only an ambitious commitment to open science will be robust enough to make a difference and contribute to the solution of pressing problems. In contrast, it is paying lip service only to the ideal of openness when “open science” becomes reduced to “open access publishing” or data storage rituals. As von Schomberg shows, this might actually deepen disparities and redundancies within dysfunctional science.

René von Schomberg’s article (von Schomberg, 2024) makes an invigorating case for the co-responsibility of societal actors to give direction to the pursuit of science. In this reply, I wish to endorse his position as a much-needed reconceptualisation in the face of societal challenges and internal scientific developments. At the same time, I urge that there remain theoretical and practical intricacies in attempting to steer science.

Personal comment on the responses to “Towards a New Ethos of Science or a Reform of the Institution of Science? Merton Revisited and the Prospects of Institutionalizing the Research Values of Openness and Mutual Responsiveness” by René von Schomberg.

We address the problem of combining intuitionistic and S4 modal logic in a non-collapsing way inspired by the recent works in combining intuitionistic and classical logic. The combined language includes the shared constructors of both logics namely conjunction, disjunction and falsum as well as the intuitionistic implication, the classical implication and the necessity modality. We present a Gentzen calculus for the combined logic defined over a Gentzen calculus for the host S4 modal logic. The semantics is provided by Kripke structures. The calculus is proved to be sound and complete with respect to this semantics. We also show that the combined logic is a conservative extension of each component. Finally we establish that the Gentzen calculus for the combined logic enjoys cut elimination.

We introduce the notion of positive strong amalgamation property and we investigate some universal forms and properties of this notion. Considering the close relationship between the amalgamation property and the notion of complete theories, we explore the fundamental properties of positively complete theories, and we illustrate the behaviour of this notion by bringing changes to the language of the theory through the groups theory.

Abstract It is often argued that constitution and causation are different kinds of dependence relations. Some have argued for a distinction between constitutive explanation of causal capacities that explain what a system would do in specific situations from causal or etiological explanations that explain why an event such as a change in the property of a system happened. In what follows we argue against the claim that causation and constitution are always distinct metaphysical relations. This paper develops a temporal account of constitution. We call this species of constitution, diachronic constitution. We show how diachronic constitution is a consequence of a common type of causation in the empirical sciences: continuous reciprocal causation, a variety of causal production instantiated in complex dynamical systems. Hence, this paper seeks to establish that constitution does not only resemble causation in certain respects. We argue for the stronger claim that constitution can be analysed in terms of causation understood as production of change. Temporalizing the constitution relation is neither as remarkable nor as problematic as it might initially seem. The idea of diachronic constitution will appear almost inevitable in the context of complex dynamical systems, given local interactions between microscale and macroscale states in such systems.

One of Pavel Tichý’s celebrated observations was that definite descriptions do not denote individuals but individual offices. In our paper, we compare Tichý’s concept of individual offices to the concept proposed by Arthur N. Prior, who differentiated between the strong and the weak "the". The aim of our paper is to point out parallels and differences. The differences stem in particular from their different approaches to contingency given by their accepted ontology. In addition, we would like to enrich Tichý’s analysis of individual offices by including certain features of Prior’s concept. The proposed outline might provide a challenge for a more detailed analysis of definite descriptions in Tichý’s Transparent Intensional Logic.

Soames and others have proposed that propositions are types of acts of predication. Soames has extended the act-type theory by proposing a distinction between direct and mediate predication. He does this in order to distinguish between the propositions expressed by sentences containing complex singular terms and those expressed by sentences containing proper names which denote the objects that those complex singular terms denote. In particular, he uses his extension to account for the cognitive distinctness of such propositions. I argue that Soames’ extension of the act-type theory is not the best way to do so. I propose an alternative version of the act-type theory, which makes the distinctions that Soames wants to make without Soames’ extension.

In this paper I propose a way of saving the traditional view of contents and attitudes from the threat posed by famous scenarios such as Perry’s messy shopper. I argue that, with the solution I suggest, traditionally construed beliefs and contents can play all the roles we traditionally want them to play, including the notoriously problematic explanation of action. I dub the view laid out here the Double Belief Theory because it analyzes de se attitudes as, in fact, two conjoined beliefs, one of which is a second-order belief about the other.

It is no surprise to anyone familiar with Fregean and Millian Theories that they struggle to explain the intuitive truth-value of sentences with proper names in modal and cognitive (such as belief) contexts, respectively. In this paper, I suggest that we can avoid the problems these theories face while at the same time preserving important intuitions by drawing a sharp distinction between semantic content (truth-conditions) and cognitive content (the content of cognitive attitudes), and by fixing the scope of Fregean and Millian theories to cognitive and semantic content, respectively. An immediate worry for this type of hybrid account is to explain the contribution of cognitive contents to the truth-conditions of attitude ascriptions. If they are different contents and the cognitive content is not part of the semantics, how can the truth-value of belief ascriptions be sensitive to cognitive content? If the semantic content follows Millianism, how can belief ascriptions that are otherwise identical but have different co-referring names have different truth-values? To answer these questions, I use Predelli’s (2005) semantic framework and argue that the truth-value of belief ascriptions is relativized not only to a world but also to a point of evaluation used to interpret the world. It is the point of evaluation that brings the cognitive content back to semantics and explains away the contradiction.

In Context and Coherence (2021), Una Stojnić defends two theses about demonstrative reference: that the deictic gestures accompanying uses of demonstratives are syntactically encoded in multi-modal syntactic constructions, and that deictic gestures so encoded are syntactically individuated by objects and individuals. Critical scrutiny of both theses reveals surprising lessons about the relationship between demonstratives and logic, but such scrutiny also reveals weaknesses in Stojnić’s arguments for the theses.

We investigate a number of semantically defined fragments of Tarski's algebra of binary relations, including the function-preserving fragment. We address the question whether they are generated by a finite set of operations. We obtain several positive and negative results along these lines. Specifically, the homomorphism-safe fragment is finitely generated (both over finite and over arbitrary structures). The function-preserving fragment is not finitely generated (and, in fact, not expressible by any finite set of guarded second-order definable function-preserving operations). Similarly, the total-function-preserving fragment is not finitely generated (and, in fact, not expressible by any finite set of guarded second-order definable total-function-preserving operations). In contrast, the forward-looking function-preserving fragment is finitely generated by composition, intersection, antidomain, and preferential union. Similarly, the forward-and-backward-looking injective-function-preserving fragment is finitely generated by composition, intersection, antidomain, inverse, and an `injective union' operation.

Sequential model synchronisation is the task of propagating changes from one model to another correlated one to restore consistency. It is challenging to perform this propagation in a least-changing way that avoids unnecessary deletions (which might cause information loss). From a theoretical point of view, so-called short-cut (SC) rules have been developed that enable provably correct propagation of changes while avoiding information loss. However, to be able to react to every possible change, an infinite set of such rules might be necessary. Practically, only small sets of pre-computed basic SC rules have been used, severely restricting the kind of changes that can be propagated without loss of information. In this work, we close that gap by developing an approach to compute more complex required SC rules on-the-fly during synchronisation. These higher-order SC rules allow us to cope with more complex scenarios when multiple changes must be handled in one step. We implemented our approach in the model transformation tool eMoflon. An evaluation shows that the overhead of computing higher-order SC rules on-the-fly is tolerable and at times even improves the overall performance. Above that, completely new scenarios can be dealt with without the loss of information.

As the development of formal proofs is a time-consuming task, it is important to devise ways of sharing the already written proofs to prevent wasting time redoing them. One of the challenges in this domain is to translate proofs written in proof assistants based on impredicative logics to proof assistants based on predicative logics, whenever impredicativity is not used in an essential way. In this paper we present a transformation for sharing proofs with a core predicative system supporting prenex universe polymorphism. It consists in trying to elaborate each term into a predicative universe-polymorphic term as general as possible. The use of universe polymorphism is justified by the fact that mapping each universe to a fixed one in the target theory is not sufficient in most cases. During the elaboration, we need to solve unification problems in the equational theory of universe levels. In order to do this, we give a complete characterization of when a single equation admits a most general unifier. This characterization is then employed in a partial algorithm which uses a constraint-postponement strategy for trying to solve unification problems. The proposed translation is of course partial, but in practice allows one to translate many proofs that do not use impredicativity in an essential way. Indeed, it was implemented in the tool Predicativize and then used to translate semi-automatically many non-trivial developments from Matita's library to Agda, including proofs of Bertrand's Postulate and Fermat's Little Theorem, which (as far as we know) were not available in Agda yet.

Game semantics is a denotational semantics presenting compositionally the computational behaviour of various kinds of effectful programs. One of its celebrated achievement is to have obtained full abstraction results for programming languages with a variety of computational effects, in a single framework. This is known as the semantic cube or Abramsky's cube, which for sequential deterministic programs establishes a correspondence between certain conditions on strategies (''innocence'', ''well-bracketing'', ''visibility'') and the absence of matching computational effects. Outside of the sequential deterministic realm, there are still a wealth of game semantics-based full abstraction results; but they no longer fit in a unified canvas. In particular, Ghica and Murawski's fully abstract model for shared state concurrency (IA) does not have a matching notion of pure parallel program-we say that parallelism and interference (i.e. state plus semaphores) are entangled. In this paper we construct a causal version of Ghica and Murawski's model, also fully abstract for IA. We provide compositional conditions parallel innocence and sequentiality, respectively banning interference and parallelism, and leading to four full abstraction results. To our knowledge, this is the first extension of Abramsky's semantic cube programme beyond the sequential deterministic world.

We consider the following decision problem: given two simply typed $\lambda$-terms, are they $\beta$-convertible? Equivalently, do they have the same normal form? It is famously non-elementary, but the precise complexity - namely TOWER-complete - is lesser known. One goal of this short paper is to popularize this fact. Our original contribution is to show that the problem stays TOWER-complete when the two input terms belong to Blum and Ong's safe $\lambda$-calculus, a fragment of the simply typed $\lambda$-calculus arising from the study of higher-order recursion schemes. Previously, the best known lower bound for this safe $\beta$-convertibility problem was PSPACE-hardness. Our proof proceeds by reduction from the star-free expression equivalence problem, taking inspiration from the author's work with Pradic on "implicit automata in typed $\lambda$-calculi". These results also hold for $\beta\eta$-convertibility.

We explore asynchronous programming with algebraic effects. We complement their conventional synchronous treatment by showing how to naturally also accommodate asynchrony within them, namely, by decoupling the execution of operation calls into signalling that an operation's implementation needs to be executed, and interrupting a running computation with the operation's result, to which the computation can react by installing interrupt handlers. We formalise these ideas in a small core calculus and demonstrate its flexibility using examples ranging from a multi-party web application, to pre-emptive multi-threading, to (cancellable) remote function calls, to a parallel variant of runners of algebraic effects. In addition, the paper is accompanied by a formalisation of the calculus's type safety proofs in Agda, and a prototype implementation in OCaml.

The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in long-distance Q-Resolution proof system (LD-Q-Res), where the syntactic side-conditions, while prohibiting all unsound resolutions, also end up prohibiting some sound resolutions. However, while the advantage of M-Res over many other resolution-based QBF proof systems was already demonstrated, a comparison with LD-Q-Res itself had remained open. In this paper, we settle this question. We show that M-Res has an exponential advantage over not only LD-Q-Res, but even over LQU$^+$-Res and IRM, the most powerful among currently known resolution-based QBF proof systems. Combining this with results from Beyersdorff et al. 2020, we conclude that M-Res is incomparable with LQU-Res and LQU$^+$-Res. Our proof method reveals two additional and curious features about M-Res: (i) M-Res is not closed under restrictions, and is hence not a natural proof system, and (ii) weakening axiom clauses with existential variables provably yields an exponential advantage over M-Res without weakening. We further show that in the context of regular derivations, weakening axiom clauses with universal variables provably yields an exponential advantage over M-Res without weakening. These results suggest that M-Res is better used with weakening, though whether M-Res with weakening is closed under restrictions remains open. We note that even with weakening, M-Res continues to be simulated by eFrege $+$ $\forall$red (the simulation of ordinary M-Res was shown recently by Chew and Slivovsky).

We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of Kleene algebra, this is no longer the case when we consider an additional constant ``top'' for the full element. Indeed, the full relation satisfies more laws than the full language, and we show that those additional laws can all be derived from a single additional axiom. We recover that the two equational theories coincide if we slightly generalise the notion of relational model, allowing sub-algebras of relations where top is a greatest element but not necessarily the full relation. We use models of closed languages and reductions in order to prove our completeness results, which are relative to any axiomatisation of the algebra of regular events. For one of our constructions, we extend the concept of finite monoid recognisability to guarded-string languages; this device makes it possible to obtain a PSpace algorithm for the equational theory of binary relations.

There is a common understanding among logicians today that nonmonotonic types of reasoning, such as defeasible or presumptive, can clearly warrant a rational acceptance of its conclusion. Recognition of the significance and legitimacy of these forms of arguments, which were considered for long as fallacious, is believed to be very recent and many logicians tended to reject any discussions around it within the tradition of logic after Aristotle. In contrast, Islamic jurisprudence (fiqh), since medieval age, has recognised the validity and importance of non-deductive forms of reasoning, analysed the structures of such arguments and demonstrated how the conventionally understood fallacies are not essentially fallacies. Qiyās – generally represents analogical reasoning – is taken here as a case of defeasible reasoning in Islamic argumentation. This paper will show through works of two emblematic medieval Muslim jurist-logicians, al-Juwainī and al-Ghazzālī, that understanding the legitimacy and the structure of non-deductive forms of arguments is at the core of Islamic legal theories (usūl al-fiqh), and that they recognised its legitimacy and proposed a dialectical method (jadal) of approaching it. Les logiciens comprennent généralement que les types de raisonnement non monotones peuvent justifier l’acceptation rationnelle des conclusions. L’importance et la légitimité de ces formes d’arguments, qui ont longtemps été considérées comme fallacieuses, ont été controversées parmi les logiciens de la tradition logique aristotélicienne. En revanche, la jurisprudence islamique (fiqh) a depuis longtemps reconnu l’importance des formes de raisonnement non déductives et a démontré que les sophismes conventionnellement compris ne sont pas essentiellement des sophismes. Le qiyās – qui représente généralement le raisonnement analogique – est un exemple de raisonnement réfutable dans l’argumentation islamique. Je montre à travers les travaux de deux juristes-logiciens musulmans médiévaux emblématiques, al-Juwainī et al-Ghazzālī, que la compréhension de la légitimité des formes d’arguments non déductives est au cœur des théories juridiques islamiques (usūl al-fiqh), qui ont proposé une méthode d’approche dialectique (jadal).

Argumentation theorists know that their work has real-life application, and similarly, they draw inspiration for that work from real-life experiences. Sometimes, it comes from some public medium – the newspaper, a blog, a debate stage. But we also draw from more private reason-exchanges – a conversation with a neighbor, small-talk with a colleague, or a lovers’ spat. A few worries about publicly theorizing about those more private cases arise. We may be making public something that was unguarded, and so betray a trust. Our theoretical reflections may themselves warp the relationship we’d originally savored, particularly when our partners know about the possibility of them being publicly scrutinized. Novelists and poets regularly struggle with this challenge with their work, and we argumentation theorists should, too. Les théoriciens de l’argumentation savent que leur travail a des applications concrètes et, de la même manière, ils s’inspirent d’expériences réelles. Parfois, ces idées proviennent d’un média public – un journal, un blog, une tribune de débat. Mais nous nous inspirons aussi d’échanges de raisonnement plus privés – une conversation avec un voisin, une petite conversation avec un collègue ou une dispute amoureuse. Nous craignons de théoriser publiquement sur ces cas plus privés. Nous pouvons rendre public des commentaires irréfléchis et ainsi trahir une confiance. Nos réflexions théoriques peuvent déformer la relation que nous avions initialement très appréciée, en particulier lorsque nos partenaires savent qu’ils peuvent être scrutés publiquement. Les romanciers et les poètes sont régulièrement confrontés à ce défi dans leur travail, et nous, les théoriciens de l’argumentation, devrions également le faire.

At the time of writing, in the summer of 2024, we are confronted with a ‘polycrisis’ (e.g., Tooze 2022). This term is used to describe a situation in which multiple crises do not simply add up to a somewhat bigger crisis, but rather create a significantly different, amplified crisis in which the sub-crises influence each other in interdependent ways. As numerous studies have demonstrated (e.g., Heitmeyer 2024; Roberts 2022; Nowotny 2016), crises engender feelings of uncertainty, insecurity, and subsequently fear (Bauman 2006). The aim of this paper is to pose the overarching question: How do governments and citizens cope with such uncertainties? Les crises provoquent la peur, la panique, l’incertitude et l’impuissance. L’incertitude et l’insécurité mettent à l’épreuve tous les acteurs concernés ; chacun attend des instructions, une planification, des explications et la sécurité. Cependant, nous affrontons des alarmismes, des simplifications, une série de stratégies de légitimation et d’erreurs. Plus précisément, les erreurs sont souvent placées avant les intérêts communautaires, nationaux ou même locaux. Ces évolutions sont illustrées par une analyse qualitative et quantitative détaillée du discours des débats en Autriche, à l’été 2023. Je soutiens que les appels fallacieux au bon sens et à la normalité dépendent de leur contexte, avec des contenus, des fonctions et des effets différents observables. De tels appels instrumentalisent une « politique des émotions » de différentes manières. Ainsi, une nouvelle logique politique est normalisée, remplaçant le discours rationnel, la délibération et la formulation de politiques dirigées par des experts.

Our intuition is straightforward: yes, argumentation changes minds. It can’t be otherwise! But many cognitive and discursive habits seem to suggest otherwise. As the literature in the psychology of reasoning incessantly emphasizes, we hardly change our minds (and the minds of others) because a predisposed robust confirmation bias (or myside bias) is at work every time we argue, among other persistent cognitive illusions (Pohl, 2012), heuristics and biases (Santibáñez, 2023). To adequately answer the questions of why and how argumentation changes minds, if at all, this paper frames the problem in an evolutionary perspective. My main thesis is that argumentative competence changes minds because its ultimate goal (Laland et al., 2011; Scott-Phillips, Dickins & West, 2011) is to construct the future to predict more accurately (Suddendorf, Redshaw & Bulley, 2022). This idea converges with some evolutionary analysis of other cognitive skills and cultural inventions. To explain my perspective, I use the distinction between ultimate and proximal goals of a trait, and the cultural background of argumentative competence plays a fundamental role within this distinction. Notre intuition est simple: oui, l’argumentation change les men-talités. Mais de nombreuses habitudes cognitives et discursives suggèrent le contraire. Comme le soulignent sans cesse les écrits sur la psychologie du raisonnement, nous ne changeons guère d’avis parce qu’un biais de con-firmation robuste (ou biais de-mon-côté) prédisposé est à l’oeuvre lorsque nous argumentons. Pour répondre adéquatement aux questions de pour-quoi, comment et si l’argumentation change les mentalités, je pose le prob-lème dans une perspective évolution-niste. Je soutiens que la compétence ar-gumentative change les mentalités parce que son but ultime est de con-struire l’avenir, de prédire avec plus de précision. Cela converge avec les anal-yses évolutionnistes d’autres compé-tences cognitives et inventions cul-turelles. Pour expliquer ma perspec-tive, j’utilise la distinction entre les buts ultimes et proximaux d’un trait.

The aim of this paper is to develop the notions of particularism and generalism in argumentation theory. Generalism is the claim that to argue we need general rules that specify which data support which conclusions, while particularism denies it. The problem is that it is not always clear what these rules consist of, and in what sense argumentation depend on them. To clarify this, I will first introduce the discussion in moral philosophy and show how it has been adapted to argumentation theory. Then I will distinguish some ways of understanding rules and contend that their alleged necessity might be supported in at least three ways. This will allow me to identify some variants of generalism and, on this basis, to outline what I consider to be the most promising reading of particularism. L’objectif de cet article est de développer les notions de particularisme et de généralisme en théorie de l’argu-mentation. Le généralisme est l’affirma-tion selon laquelle pour argumenter, nous avons besoin de règles générales qui pré-cisent quelles données soutiennent que-lles conclusions, alors que le particula-risme le nie. Le problème est qu’il n’est pas toujours clair en quoi consistent ces règles et dans quel sens l’argumentation en dépend. Pour clarifier cela, je com-mencerai par introduire la discussion en philosophie morale et montrerai com-ment elle a été adaptée à la théorie de l’argumentation. Ensuite, je distinguerai quelques façons de comprendre les règles et soutiendrai que leur prétendue nécessité pourrait être soutenue d’au moins trois façons. Cela me permettra d’identifier certaines variantes du géné-ralisme et, sur cette base, d’esquisser ce que je considère comme la lecture la plus prometteuse du particularisme.

Abstract Process metaphysics is both internally coherent and coherent with what we know about the basic ‘what there is’ of the world, whereas a particle-as-particular metaphysics is neither. One consequence of a process metaphysics is that metaphysical emergence becomes explicable, and, in turn, normative emergence. This point is developed with models of the emergence of normative function and of representation. These are steps toward an integrated naturalistic understanding of the world.

We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of free algebras into directly indecomposable factors.

In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin’s Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.

We study natural deduction systems for a fragment of intuitionistic logic with propositional identity from the point of view of proof-theoretic semantics. We argue that the identity connective is a natural operator to be treated under the elimination rules as basic approach.

This paper considers a specification rewriting meachanism for a specific fragment of Linear Temporal Logic for Finite traces, DECLAREd, working through an equational logic and rewriting mechanism under customary practitioner assumptions from the Business Process Management literature. By rewriting the specification into an equivalent formula which might be easier to compute, we aim to streamline current state-of-the-art temporal artificial intelligence algorithms working on temporal logic. As this specification rewriting mechanism is ultimately also able to determine with the provided specification is a tautology (always true formula) or a formula containing a temporal contradiction, by detecting the necessity of a specific activity label to be both present and absent within a log, this implies that the proved mechanism is ultimately a SAT-solver for DECLAREd. We prove for the first time, to the best of our knowledge, that this fragment is a polytime fragment of LTLf, while all the previously-investigated fragments or extensions of such a language were in polyspace. We test these considerations over formal synthesis (Lydia), SAT-Solvers (AALTAF) and formal verification (KnoBAB) algorithms, where formal verification can be also run on top of a relational database and can be therefore expressed in terms of relational query answering. We show that all these benefit from the aforementioned assumptions, as running their tasks over a rewritten equivalent specification will improve their running times, thus motivating the pressing need of this approach for practical temporal artificial intelligence scenarios. We validate such claims by testing such algorithms over a Cybersecurity dataset.

The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered.

In this paper, we defined the concept \(\mathcal{SUP}\)-hesitant fuzzy interior ideals in \(\Gamma\)-semigroups, which is generalized of hesitant fuzzy interior ideals in \(\Gamma\)-semigroups. Additionally, we study fundamental properties of \(\mathcal{SUP}\)-hesitant fuzzy interior ideals in \(\Gamma\)-semigroups. Finally, we investigate characterized properties of those.

Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free component of the larger framework. Modifying MALL, researchers have explored weaker logics such as Noncommutative MALL (Bilinear Logic, BL) and Cyclic MALL (CyMALL) to investigate variations in commutativity. In this paper, we focus on Cyclic Nonassociative Bilinear Logic (CyNBL), a variant that combines noncommutativity and nonassociativity. We introduce a sequent system for CyNBL, which includes an auxiliary system for incorporating nonlogical axioms. Notably, we establish the cut elimination property for CyNBL. Moreover, we establish the strong conservativeness of CyNBL over Full Nonassociative Lambek Calculus (FNL) without additive constants. The paper highlights that all proofs are constructed using syntactic methods, ensuring their constructive nature. We provide insights into constructing cut-free proofs and establishing a logical relationship between CyNBL and FNL.

A many-valued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic \(\rm \mathbf{LK(A)}\) is axiomatized by extending \(\rm \mathbf{K(A)}\) with the modal axiom schemas \(\Box(\varphi\vee\psi)\rightarrow(\Box\varphi\vee\Box\psi)\) and \((\Box\varphi\wedge\Box\psi)\rightarrow\Box(\varphi\wedge\psi)\). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated.

Regions-based theories of space aim—among others—to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed, one should show that they are points of a geometrical or a topological space constructed in a specific way. This paper intends to show how the development of mathematical tools allows showing that Whitehead’s method of extensive abstraction provides a construction of objects that are fundamental building blocks of specific topological spaces.

In this paper, considering L-algebras, which include a significant number of other algebraic structures, we present a definition of modules on L-algebras (L-modules). Then we provide some examples and obtain some results on L-modules. Also, we present definitions of prime ideals of L-algebras and L-submodules (prime L-submodules) of L-modules, and investigate the relationship between them. Finally, by proving a number of theorems, we provide some conditions for having prime L-submodules.

The main goal of this paper is to introduce the notion of stabilizers in \(L\)-algebras and develop stabilizer theory in \(L\)-algebras. In this paper, we introduced the notions of left and right stabilizers and investigated some related properties of them. Then, we discussed the relations among stabilizers, ideal and co-annihilators. Also, we obtained that the set of all ideals of a \(CKL\)-algebra forms a relative pseudo-complemented lattice. In addition, we proved that right stabilizers in \(CKL\)-algebra are ideals. Then by using the right stabilizers we produced a basis for a topology on \(L\)-algebra. We showed that the generated topology by this basis is Baire, connected, locally connected and separable and we investigated the other properties of this topology.

Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games.

In two-player games on graphs, the simplest possible strategies are those that can be implemented without any memory. These are called positional strategies. In this paper, we characterize objectives recognizable by deterministic B\"uchi automata (a subclass of omega-regular objectives) that are half-positional, that is, for which the protagonist can always play optimally using positional strategies (both over finite and infinite graphs). Our characterization consists of three natural conditions linked to the language-theoretic notion of right congruence. Furthermore, this characterization yields a polynomial-time algorithm to decide half-positionality of an objective recognized by a given deterministic B\"uchi automaton.

Session types are formal specifications of communication protocols, allowing protocol implementations to be verified by typechecking. Up to now, session type disciplines have assumed that the communication medium is reliable, with no loss of messages. However, unreliable broadcast communication is common in a wide class of distributed systems such as ad-hoc and wireless sensor networks. Often such systems have structured communication patterns that should be amenable to analysis by means of session types, but the necessary theory has not previously been developed. We introduce the Unreliable Broadcast Session Calculus, a process calculus with unreliable broadcast communication, and equip it with a session type system that we show is sound. We capture two common operations, broadcast and gather, inhabiting dual session types. Message loss may lead to non-synchronised session endpoints. To further account for unreliability we provide with an autonomous recovery mechanism that does not require acknowledgements from session participants. Our type system ensures soundness, safety, and progress between the synchronised endpoints within a session. We demonstrate the expressiveness of our framework by implementing Paxos, the textbook protocol for reaching consensus in an unreliable, asynchronous network.

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph-based algorithm.

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics via translations to and from the $\mu$-calculus and modal logic, which allow us to transfer known upper and lower bounds. We also use these translations to introduce terminating and non-terminating tableau systems for the logics we study, based on Kozen's tableau for the $\mu$-calculus and the one of Fitting and Massacci for modal logic. Finally, we describe these tableaux with $\mu$-calculus formulas, thus reducing the satisfiability of each of these logics to the satisfiability of the $\mu$-calculus, resulting in a general 2EXP upper bound for satisfiability testing.

We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order expansions of Presburger arithmetic by a single Sturmian word are uniformly $\omega$-automatic, and then deduce the decidability of the theory of the class of such structures. Using an implementation of this decision algorithm called Pecan, we automatically reprove classical theorems about Sturmian words in seconds, and are able to obtain new results about antisquares and antipalindromes in characteristic Sturmian words.

In this paper, we give a deterministic pushdown transducer and a normal sequence of digits compressed by it. This solves positively a question left open in a previous paper by V. Becher, P. A. Heiber and the first author.