We establish a completeness theorem for first-order basic predicate logic BQC, a proper subsystem of intuitionistic predicate logic IQC, using Kripke models with transitive underlying frames. We develop the notion of functional well-formed theory as the right notion of theory over BQC for which strong completeness theorems are possible. We also derive the undecidability of basic arithmetic, the basic logic equivalent of intuitionistic Heyting Arithmetic and classical Peano Arithmetic.

We characterize the first-order formulas with one free variable that are preserved under bisimulation and persistence or strong persistence over the class of Kripke models with transitive frames and unary persistent predicates.

In classical propositional calculus for each proposition A(p) the following holds: $\vdash A(p) \leftrightarrow A^3(p)$ . In this paper we consider what remains of this in the intuitionistic case. It turns out that for each proposition A(p) the following holds: there is an n ∈ N such that $\vdash A^n(p) \leftrightarrow A^{n + 2}(p)$ . As a byproduct of the proof we give some theorems which may be useful elsewhere in propositional calculus.

We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being E1, a theory axiomatized by T → ⊥. The intersection CPC ∩ E1 is axiomatizable by the Principle of the Excluded Middle A V ∨ ⌝A. If B is a formula (...) such that → B is not derivable, then the lattice of formulas built from one propositional variable p using only the binary connectives, is isomorphically preserved if B is substituted for p. A formula → B is derivable exactly when B is provably equivalent to a formula of the form → A) →. (shrink)

We generalize the double negation construction of Boolean algebras in Heyting algebras to a double negation construction of the same in Visser algebras. This result allows us to generalize Glivenko’s theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras.

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, (...) in every sense of relative ubiquity considered here, the set of dense linear orderings on ω is ubiquitous in the set of linear orderings on ω. (shrink)

A latarre is a lattice with an arrow. Its axiomatization looks natural. Latarres have a nontrivial theory which permits many constructions of latarres. Latarres appear as an end result of a series of generalizations of better known structures. These include Boolean algebras and Heyting algebras. Latarres need not have a distributive lattice.

Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C 1, C 2 be formulas over ?, such that A∧C 1⊢C (...) 2. Then there exists a formula B over ℳ such that A⊢B and B∧C 1⊢C 2. (shrink)

Kolmogorov established the principle of the double negation translation by which to embed Classical Predicate Logic |${\operatorname {CQC}}$| into Intuitionistic Predicate Logic |${\operatorname {IQC}}$|⁠. We show that the obvious generalizations to the Basic Predicate Logic of [3] and to |${\operatorname {BQC}}$| of [12], a proper subsystem of |${\operatorname {IQC}}$|⁠, go through as well. The obvious generalizations of Kuroda’s embedding are shown to be equivalent to the Kolmogorov variant. In our proofs novel nontrivial techniques are needed to overcome the absence of (...) full modus ponens in Basic Predicate Logic. In [3] we argued that |${\operatorname {IQC}}$| is not the logic of constructive mathematics. Our doubts were far from new. New was that we put forward an alternative, |${\operatorname {BQC}}$|⁠. One concern is that |${\operatorname {BQC}}$| is too weak for serious mathematics, or even trivial. This paper is one step to alleviate such concerns. (shrink)

We present axiom systems, and provide soundness and strong completeness theorems, for classes of Kripke models with restricted extension rules among the node structures of the model. As examples we present an axiom system for the class of cofinal extension Kripke models, and an axiom system for the class of end-extension Kripke models. We also show that Heyting arithmetic is strongly complete for its class of end-extension models. Cofinal extension models of HA are models of Peano arithmetic.

We define two notions for intuitionistic predicate logic: that of a submodel of a Kripke model, and that of a universal sentence. We then prove a corresponding preservation theorem. If a Kripke model is viewed as a functor from a small category to the category of all classical models with morphisms between them, then we define a submodel of a Kripke model to be a restriction of the original Kripke model to a subcategory of its domain, where every node in (...) the subcategory is mapped to a classical submodel of the corresponding classical model in the range of the original Kripke model. We call a sentence universal if it is built inductively from atoms using ∧, ∨, ∀, and →, with the restriction that antecedents of → must be atomic. We prove that an intuitionistic theory is axiomatized by universal sentences if and only if it is preserved under Kripke submodels. We also prove the following analogue of a classical model-consistency theorem: The universal fragment of a theory Γ is contained in the universal fragment of a theory Δ if and only if every rooted Kripke model of Δ is strongly equivalent to a submodel of a rooted Kripke model of Γ. Our notions of Kripke submodel and universal sentence are natural in the sense that in the presence of the rule of excluded middle, they collapse to the classical notions of submodel and universal sentence. (shrink)

From classical, Fraïissé-homogeneous, ($\leq \omega$)-categorical theories over finite relational languages, we construct intuitionistic theories that are complete, prove negations of classical tautologies, and admit quantifier elimination. We also determine the intuitionistic universal fragments of these theories.

This article deals with the question of how self-organization in living organisms is realized. Self-organization may be observed in open systems that are out of equilibrium. Many disequilibria-conversion phenomena exist where free energy conversion occurs by spontaneously formed engines. However, how is self-organization realized in living entities? Living cells turn out to be self-organizing disequilibria-converting systems of a special kind. Disequilibrium conversion is realized in a typical way, through employing information specifying protein complexes acting as nano engines. The genetic code (...) enables processing of information—derived from coding DNA—to produce these molecular machines. Hence, information is at the core of living systems. Two promising approaches to explaining living cells containing sequences carrying information are mentioned. Also discussed is the question of whether a second concept of self-organization—namely, the Kantian concept—applies. (shrink)

An arms race for an artificial general intelligence would be detrimental for and even pose an existential threat to humanity if it results in an unfriendly AGI. In this paper, an all-pay contest model is developed to derive implications for public policy to avoid such an outcome. It is established that, in a winner-takes-all race, where players must invest in R&D, only the most competitive teams will participate. Thus, given the difficulty of AGI, the number of competing teams is unlikely (...) ever to be very large. It is also established that the intention of teams competing in an AGI race, as well as the possibility of an intermediate outcome, is important. The possibility of an intermediate prize will raise the probability of finding the dominant AGI application and, hence, will make public control more urgent. It is recommended that the danger of an unfriendly AGI can be reduced by taxing AI and using public procurement. This would reduce the pay-off of contestants, raise the amount of R&D needed to compete, and coordinate and incentivize co-operation. This will help to alleviate the control and political problems in AI. Future research is needed to elaborate the design of systems of public procurement of AI innovation and for appropriately adjusting the legal frameworks underpinning high-tech innovation, in particular dealing with patenting by AI. (shrink)

Budgetary austerity has been implemented by all levels of government in Belgium since 1982. The public attention has focussed on the achievements of the centra[ level. However, also at the local level a remarkable budgetary retrenchment has been realised. This study investigates the various aspects of decremental budgeting of the Belgian municipolities, both at the expenditures and the revenues side.

BackgroundResearch misconduct and questionable research practices have been the subject of increasing attention in the past few years. But despite the rich body of research available, few empirical works also include the perspectives of non-researcher stakeholders.MethodsWe conducted semi-structured interviews and focus groups with policy makers, funders, institution leaders, editors or publishers, research integrity office members, research integrity community members, laboratory technicians, researchers, research students, and former-researchers who changed career to inquire on the topics of success, integrity, and responsibilities in science. (...) We used the Flemish biomedical landscape as a baseline to be able to grasp the views of interacting and complementary actors in a system setting.ResultsGiven the breadth of our results, we divided our findings in a two-paper series with the current paper focusing on the problems that affect the integrity and research culture. We first found that different actors have different perspectives on the problems that affect the integrity and culture of research. Problems were either linked to personalities and attitudes, or to the climates in which researchers operate. Elements that were described as essential for success were often thought to accentuate the problems of research climates by disrupting research culture and research integrity. Even though all participants agreed that current research climates need to be addressed, participants generally did not feel responsible nor capable of initiating change. Instead, respondents revealed a circle of blame and mistrust between actor groups.ConclusionsOur findings resonate with recent debates, and extrapolate a few action points which might help advance the discussion. First, the research integrity debate must revisit and tackle the way in which researchers are assessed. Second, approaches to promote better science need to address the impact that research climates have on research integrity and research culture rather than to capitalize on individual researchers’ compliance. Finally, inter-actor dialogues and shared decision making must be given priority to ensure that the perspectives of the full research system are captured. Understanding the relations and interdependency between these perspectives is key to be able to address the problems of science.Study registrationhttps://osf.io/33v3m. (shrink)

This paper provides an early evaluation of Artificial Intelligence against COVID-19. The main areas where AI can contribute to the fight against COVID-19 are discussed. It is concluded that AI has not yet been impactful against COVID-19. Its use is hampered by a lack of data, and by too much data. Overcoming these constraints will require a careful balance between data privacy and public health, and rigorous human-AI interaction. It is unlikely that these will be addressed in time to be (...) of much help during the present pandemic. In the meantime, extensive gathering of diagnostic data on who is infectious will be essential to save lives, train AI, and limit economic damages. (shrink)

What impact has Christianity had on law and policies in the Lowlands from the eleventh century through the end of the twentieth century? Taking the gradual 'secularization' of European legal culture as a framework, this volume explores the lives and times of twenty legal scholars and professionals to study the historical impact of the Christian faith on legal and political life in the Low Countries. The process whereby Christian belief systems gradually lost their impact on the regulation of secular affairs (...) passed through several stages, not in the least the Protestant Reformation, which led to the separation of the Low Countries in a Protestant North and a Catholic South in the first place. The contributions take up general issues such as the relationship between justice and mercy, Christianity and politics as well as more technical topics of state-church law, criminal law and social policy. (shrink)

In his encyclical 'Aeterni Patris' (1879), Pope Leo XIII expressed the conviction that the renewed study of the philosophical legacy of Saint Thomas Aquinas would help Catholics to engage in a dialogue with secular modernity while maintaining respect for Church doctrine and tradition. As a result, the neo-scholastic framework dominated Catholic intellectual production for nearly a century thereafter. This volume assesses the societal impact of the Thomist revival movement, with particular attention to the juridical dimension of this epistemic community. Contributions (...) from different disciplinary backgrounds offer a multifaceted and in-depth analysis of many different networks and protagonists of the neo-scholastic movement, its institutions and periodicals, and its conceptual frameworks. Although special attention is paid to the Leuven Institute of Philosophy and Faculty of Law, the volume also discloses the neo-Thomist revival in other national and transnational contexts. By highlighting diverse aspects of its societal and legal impact, 'Neo-Thomism in Action' argues that neo-scholasticism was neither a sterile intellectual exercise nor a monolithic movement. The book expands our understanding of how Catholic intellectual discourse communities were constructed and how they pervaded law and society during the late 19th century and the first half of the 20th century. (shrink)

Studies of early modern scholasticism are experiencing a boom today. Legal scholars, philosopher, theologians, and economists are approaching the texts of the “Spanish late scholastics” and “Catholic natural law theorists” from their own perspectives. Both beginners and experts will find the tools in this volume for conducting independent research on the sources and cross-disciplinary insight regarding the state of research.

In this article two questions are discussed with regard to semiosis in protein biosynthesis for nano engines. (1) What kind of semiosis is involved in the construction of these proteins? and (2) How can we explain the semiotic process observed? With regard to the first issue we draw attention to comparisons between semiosis in protein biosynthesis and human natural language. The notion of normativity appears to be of great importance for both. A comparison also demonstrates differences. Nevertheless, because of the (...) normative symbolic information processing in it, we suggest to employ the term symbolic reference (employed in linguistics as a distinguishing feature of human language) to indicate the semiotic processes in protein biosynthesis. With regard to explaining semiosis in protein synthesis we compare different approaches. We conclude that a Kantian approach should be preferred. In such an approach strengths of the mechanistic and organicist approaches can be combined, and the observed symbolic information processing acknowledged. (shrink)

This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even (...) economies. (shrink)

This article describes and analyses the development of modern irrigation in Java within the context of the establishment and transformation of the colonial state in the Dutch East Indies / Indonesia. In order to make this relationship comprehensible the concept “large technical system” has been adopted. The colonial socio-technical irrigation system was built between 1830 and 1942. Engineers, civil servants and agricultural experts were the main system builders and they formed specific coalitions practising specific irrigation approaches. After Indonesia gained its (...) independence, the colonial irrigation system remained in existence and, consequently, irrigation engineering remained top-down, large-scale and focused on agricultural-technical management. (shrink)

Creatively operationalizing Claude Lévi-Strauss’ predicament that food is good to think with, I initiate a methodological conceptualization of food by exploring the ways in which it is apt to study Sri Lankan domestic and collective village life. Food is approached as an assemblage that is an emergent resultant of heterogeneous aspects with which it is deeply entangled and by way of which it turns into a potent agent shaping life. More specifically, I explore the vibrancy of these different components that (...) co-create the overall soundscape of food that as such becomes the conductor of Sri Lankan life. Food shapes domestic life by way of its preparation and consumption, and through its cultivation also conducts the collective rhythms at the village level. The conceptualization of food as an assemblage seeks to develop it as a methodology that opens up for a holistic integration and interdisciplinary collaboration. (shrink)

Coping with stress has been primarily investigated as an individual-level phenomenon. In work settings, however, an individual’s exposure to demands is often shared with co-workers, and the process of dealing with these demands takes place in the interaction with them. Coping, therefore, may be conceptualized as a multilevel construct. This paper introduces the team coping concept and shows that including coping as a higher-level team property may help explain individual-level outcomes. Specifically, we investigated the effects of exposure to danger during (...) deployment on burnout symptoms in military service members and examined to what extent this relationship was moderated by individual-level and team-level functional coping. We hypothesized that the relationship between individuals’ exposure to danger and burnout is contingent on both. In line with our predictions, we found that service members who were highly exposed to danger, and did not engage in much functional coping, suffered most from burnout symptoms, but only when their teammates did not engage in much functional coping either. When their teammates did engage in much functional coping, the effect of exposure to danger on burnout was buffered. Hence, team members’ coping efforts functioned as a resilience resource for these service members. (shrink)

Six of today's greatest thinkers take on a plethora of issues and unanswered questions of late twentieth-century science, such as the boundaries of scientific inquiry, the possibility of conducting studies of creativity, and other topics.

In this article thinking on corporate social responsibility is compared with the dominant political theory of the market: theneoclassical theory. The comparison shows that thinking on CSR fundamentally collides with that theory. For example, their respectivenormative views on man are incompatible, as are their respective views on the modus operandi of the market. Given that CSR is desirable it follows that a new political theory of the market is needed. This article suggests some initial steps toward developing that new political (...) theory of the market. For example, it defends the proposition that the neoclassical idea of the market as a harmonic sphere must be replaced by the idea of the market as a fragile system. (shrink)

Influential work on reasoning and decision-making has popularised the idea that sound reasoning requires correction of fast, intuitive thought processes by slower and more demanding deliberation. We present seven studies that question this corrective view of human thinking. We focused on the very problem that has been widely featured as the paradigmatic illustration of the corrective view, the well-known bat-and-ball problem. A two-response paradigm in which people were required to give an initial response under time pressure and cognitive load allowed (...) us to identify the presumed intuitive response that preceded the final response given after deliberation. Across our studies, we observe that correct final responses are often non-corrective in nature. Many reasoners who manage to answer the bat-and-ball problem correctly after deliberation already solved it correctly when they reasoned under conditions that minimised deliberation in the initial response phase. This suggests that sound bat-and-ball reasoners do not necessarily need to deliberate to correct their intuitions; their intuitions are often already correct. Pace the corrective view, findings suggest that in these cases, they deliberate to verify correct intuitive insights. (shrink)

Liberalist thinking argues that moral agents have a right to pursue an ordinary life. It also insists that moral agent can be bystanders. A bystander is involved with morally bad states of affairs in the sense that they are bound by moral duty, but for a non-blameworthy reason. A common view on the morality of commercial life argues that commercial agents cannot and ought not to assume the status of bystander, when confronted with child labor, pollution, or other overwhelmingly big (...) morally bad states of affairs. According to the common view, the agent will get overdemanded. In this paper, the overdemandingness charge is interpreted as a criticism of the liberalist position. According to this charge, bystander status must be given up in the market because otherwise the right to pursue a personal life is crushed. In this paper, we demonstrate that the overdemandingness charge fails. It does not make sense if bystander status is grounded in the duty of beneficence. It would make sense if the status were grounded in the duty of rescue but that duty does not apply in relation to oMBS. The condition of ‘subjective urgency’ is not fulfilled. Hence, liberalist thinking can withstand the charge of overdemandingness and commercial agents cannot assume a right never to acknowledge bystander status. (shrink)

Legal information retrieval is in need of the provision of legal knowledge for the improvement of search strategies. For this purpose, the LOIS project is concerned with the construction of a multilingual WordNet for cross-lingual information retrieval in the legal domain. In this article, we set out how a hybrid approach, featuring lexically and legally grounded conceptual representations, can fit the cross-lingual information retrieval needs of both legal professionals and laymen.