We introduce the horizontal and vertical topologies on the product of topological spaces, and study their relationship with the standard product topology. We show that the modal logic of products of topological spaces with horizontal and vertical topologies is the fusion S4 ⊕ S4. We axiomatize the modal logic of products of spaces with horizontal, vertical, and standard product topologies.We prove that both of these logics are complete for the product of rational numbers ℚ × ℚ with the appropriate topologies.

For a Euclidean space , let L n denote the modal logic of chequered subsets of . For every n 1, we characterize L n using the more familiar Kripke semantics, thus implying that each L n is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics L n form a decreasing chain converging to the logic L of chequered subsets of . As a result, we obtain that L is also a logic (...) over Grz, and that L has the finite model property. We conclude the paper by extending our results to the modal language enriched with the universal modality. (shrink)

For a Euclidean space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^n $$ \end{document}, let Ln denote the modal logic of chequered subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^n $$ \end{document}. For every n ≥ 1, we characterize Ln using the more familiar Kripke semantics, thus implying that each Ln is a tabular logic over the well-known modal system Grz of Grzegorczyk. We show that the logics Ln form a decreasing chain (...) converging to the logic L∞ of chequered subsets of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}^\infty $$ \end{document}. As a result, we obtain that L∞ is also a logic over Grz, and that L∞ has the finite model property. We conclude the paper by extending our results to the modal language enriched with the universal modality. (shrink)

We develop the theory of Krull dimension forS4-algebras and Heyting algebras. This leads to the concept of modal Krull dimension for topological spaces. We compare modal Krull dimension to other well-known dimension functions, and show that it can detect differences between topological spaces that Krull dimension is unable to detect. We prove that for aT1-space to have a finite modal Krull dimension can be described by an appropriate generalization of the well-known concept of a nodec space. This, in turn, can (...) be described by modal formulaszemnwhich generalize the well-known Zeman formulazem. We show that the modal logicS4.Zn:=S4+ zemnis the basic modal logic ofT1-spaces of modal Krull dimension ≤n, and we construct a countable dense-in-itselfω-resolvable Tychonoff spaceZnof modal Krull dimensionnsuch thatS4.Znis complete with respect toZn. This yields a version of the McKinsey-Tarski theorem forS4.Zn. We also show that no logic in the interval [S4n+1S4.Zn) is complete with respect to any class ofT1-spaces. (shrink)

We prove that the existence of a measurable cardinal is equivalent to the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the powerset of a two element set.

We prove that the modal logic of a crowded locally compact generalized ordered space is $\textsf {S4}$. This provides a version of the McKinsey–Tarski theorem for generalized ordered spaces. We then utilize this theorem to axiomatize the modal logic of an arbitrary locally compact generalized ordered space.

In this article, we develop a bimodal perspective on possibility semantics, a framework allowing partiality of states that provides an alternative modelling for classical propositional and modal logics. In particular, we define a full and faithful translation of the basic modal logic K over possibility models into a bimodal logic of partial functions over partial orders, and we show how to modulate this analysis by varying across logics and model classes that have independent topological motivations. This relates the two realms (...) under comparison both semantically and syntactically at the level of derivations. Moreover, our analysis clarifies the interplay between the complexity of translations and axiomatizations of the corresponding logics: adding axioms to the target bimodal logic simplifies translations, or vice versa, complex translations can simplify frame conditions. We also investigate a transfer of first-order correspondence theory between possibility semantics and its bimodal counterpart. Finally, we discuss the conceptual trade-off between giving translations and giving new semantics for logical systems, and we identify a number of further research directions to which our analysis gives rise. (shrink)

This paper explores a new language of neighbourhood structures where existential information can be given about what kind of worlds occur in a neighbourhood of a current world. The resulting system of ‘instantial neighbourhood logic’ INL has a nontrivial mix of features from relational semantics and from neighbourhood semantics. We explore some basic model-theoretic behavior, including a matching notion of bisimulation, and give a complete axiom system for which we prove completeness by a new normal form technique. In addition, we (...) relate INL to other modal logics by means of translations, and determine its precise SAT complexity. Finally, we discuss proof-theoretic fine-structure of INL in terms of semantic tableaux and some expressive fine-structure in terms of fragments, while discussing concrete illustrations of the instantial neighborhood language in topological spaces, in games with powers for players construed in a new way, as well as in dynamic logics of acquiring or deleting evidence. We conclude with some coalgebraic perspectives on what is achieved in this paper. Many of these final themes suggest follow-up work of independent interest. (shrink)

We propose a new perspective on logics of computation by combining instantial neighborhood logic \ with bisimulation safe operations adapted from \. \ is a recent modal logic, based on an extended neighborhood semantics which permits quantification over individual neighborhoods plus their contents. This system has a natural interpretation as a logic of computation in open systems. Motivated by this interpretation, we show that a number of familiar program constructors can be adapted to instantial neighborhood semantics to preserve invariance for (...) instantial neighborhood bisimulations, the appropriate bisimulation concept for \. We also prove that our extended logic \ is a conservative extension of dual-free game logic, and its semantics generalizes the monotone neighborhood semantics of game logic. Finally, we provide a sound and complete system of axioms for \, and establish its finite model property and decidability. (shrink)

We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.

We define analogues of modal Sahlqvist formulas for the modal mu-calculus, and prove a correspondence theorem for them.

The filtration method for proving decidability in a focused minimal manner is a highlight of modal logic, widely used, but also posing a bit of a challenge as to its scope and what makes it tick. In this paper, we bring together a number of modern perspectives on filtration, including model-theoretic and proof-theoretic ones. We also include a few more unusual recent connections with dynamic logics of model change and logics of questions and issues. Finally, we analyze where the filtration (...) method fails in full first-order logic, and what it still has to say there. (shrink)

The variety of Heyting algebras has two well-behaved locally finite reducts, the variety of bounded distributive lattices and the variety of implicative semilattices. The variety of bounded distributive lattices is generated by the →-free reducts of Heyting algebras, while the variety of implicative semilattices is generated by the ∨-free reducts. Each of these reducts gives rise to canonical formulas that generalize Jankov formulas and provide an axiomatization of all superintuitionistic logics. The ∨-free reducts of Heyting algebras give rise to the (...) -canonical formulas that we studied in an earlier work. Here we introduce the -canonical formulas, which are obtained from the study of the →-free reducts of Heyting algebras. We prove that every si-logic is axiomatizable by -canonical formulas. We also discuss the similarities and differences between these two kinds of canonical formulas. One of the main ingredients of these formulas is a designated subset D of pairs of elements of a finite subdirectly irreducible Heyting algebra A. When D=A2, we show that the -canonical formula of A is equivalent to the Jankov formula of A. On the other hand, when D=∅, the -canonical formulas produce a new class of si-logics we term stable si-logics. We prove that there are continuum many stable si-logics and that all stable si-logics have the finite model property. We also compare stable si-logics to splitting and subframe si-logics. (shrink)

We introduce relativized modal algebra homomorphisms and show that the category of modal algebras and relativized modal algebra homomorphisms is dually equivalent to the category of modal spaces and partial continuous p-morphisms, thus extending the standard duality between the category of modal algebras and modal algebra homomorphisms and the category of modal spaces and continuous p-morphisms. In the transitive case, this yields an algebraic characterization of Zakharyaschev’s subreductions, cofinal subreductions, dense subreductions, and the closed domain condition. As a consequence, we (...) give an algebraic description of canonical, subframe, and cofinal subframe formulas, and provide a new algebraic proof of Zakharyaschev’s theorem that each logic over K4 is axiomatizable by canonical formulas. (shrink)

We generalize the \}\)-canonical formulas to \}\)-canonical rules, and prove that each intuitionistic multi-conclusion consequence relation is axiomatizable by \}\)-canonical rules. This yields a convenient characterization of stable superintuitionistic logics. The \}\)-canonical formulas are analogues of the \}\)-canonical formulas, which are the algebraic counterpart of Zakharyaschev’s canonical formulas for superintuitionistic logics. Consequently, stable si-logics are analogues of subframe si-logics. We introduce cofinal stable intuitionistic multi-conclusion consequence relations and cofinal stable si-logics, thus answering the question of what the analogues of cofinal (...) subframe logics should be. This is done by utilizing the \}\)-reduct of Heyting algebras. We prove that every cofinal stable si-logic has the finite model property, and that there are continuum many cofinal stable si-logics that are not stable. We conclude with several examples showing the similarities and differences between the classes of stable, cofinal stable, subframe, and cofinal subframe si-logics. (shrink)

We generalize the theory of canonical formulas for K4, the logic of transitive frames, to wK4, the logic of weakly transitive frames. Our main result establishes that each logic over wK4 is axiomatizable by canonical formulas, thus generalizing Zakharyaschev’s theorem for logics over K4. The key new ingredients include the concepts of transitive and strongly cofinal subframes of weakly transitive spaces. This yields, along with the standard notions of subframe and cofinal subframe logics, the new notions of transitive subframe and (...) strongly cofinal subframe logics over wK4. We obtain axiomatizations of all four kinds of subframe logics over wK4. We conclude by giving a number of examples of different kinds of subframe logics over wK4. (shrink)

We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on [9]. (...) Furthermore, for each function f: omega -> omega, we construct an extension Lf of KG such that Lf has the fmp, but does not have the f-size model property. We also give a new simple proof of another result of Gerčiu [9] characterizing the only extension of KG that bounds the fmp for extensions of KG. We conclude the paper by proving that RN.KC = RN + (¬p vee ¬¬p) is the only pre-locally tabular extension of KG, introduce the internal depth of an extension L of RN, and show that L is locally tabular if and only if the internal depth of L is finite. (shrink)

This paper analyses the use of strategies and instruments for organising ethics by small and large business in the Netherlands. We find that large firms mostly prefer an integrity strategy to foster ethical behaviour in the organisation, whereas small enterprises prefer a dialogue strategy. Both large and small firms make least use of a compliance strategy that focuses on controlling and sanctioning the ethical behaviour of workers. The size of the business is found to have a positive impact on the (...) use of several instruments, like code of conduct, ISO certification, social reporting, social handbook and confidential person. Also being a subsidiary of a larger firm has a significant positive influence on the use of instruments. The most popular instrument used by small firms is to let one member of the board be answerable for ethical questions, which fits the informal culture of most small firms. With respect to sectorial differences, we find that firms in the metal manufacturing and construction sectors are more actively using formal instruments than firms in the financial service sector and retail sector. The distinction between family and non-family firms hardly affects the use of instruments. (shrink)

Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [8]), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam [22]), STIT (Belnap et al. [5]), Process Algebra and Game Semantics (Abramsky [1]). This variety is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two systems (...) that both address the dynamics of knowledge and information flow in multi-agent systems. One is IS/ETL (IS and ETL are, from a technical point of view, the same up to model transformations, cf. [20]), which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. These models provide a Grand Stage where histories of some process unfold constrained by a protocol, and a matching epistemic-temporal language describes what happens. The other framework is Dynamic Epistemic Logic (DEL, [10, 4, 34]) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. Temporal evolution is then computed from some initial epistemic model through a process of successive ‘product updates’. It has long been unclear how to best compare IS/ETL and DEL. Various aspects have been investigated in [10, 30, 32], but in this paper, we study the interface in a more systematic way. Often, DEL and ETL are presented as alternative ways of adding dynamics to multi-agent epistemic models. In this paper, we rather focus on how merging the two different modeling choices leads to interesting new questions. Our leading interest here will be a view of informational processes as evolving over time. To see what we mean, consider the simplest version of DEL, viz. the logic of public announcements PAL ([23]) which adds a very specific type of communicative 1 action to epistemic models: a public announcement.. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Microscope of Experience: Christian Garve’s Translation of Cicero’s De Officiis (1783)Johan van der ZandeDuring the negotiations leading to the Treaty of Teschen of 1779, ending the phony War of Bavarian Succession, Frederick II and his court stayed in Breslau, the capital of Silesia. There, in conversation with Christian Garve, the city’s most famous son, the king strongly recommended a new German translation of Cicero’s On Moral Duties (...) (De Officiis), one of the classical texts of humanist philosophy and his favorite book. Frederick’s faithful subject dutifully obliged his sovereign. Four years later, in the subservient language of a dedication to a royal patron, Garve offered in due obedience to Frederick a result that, “perhaps flawed,” was “vindicated by the efforts directed toward the execution of the command.” 1Yet Garve’s interest in Cicero differed markedly from that of Frederick. After all, as Garve wrote in the preface to the philosophical commentary on his translation, Cicero’s book was written for “persons of the higher classes who participated in the affairs of state” and for whom “moral prescription often transformed into political instruction.” Clearly that was not the world in which Garve lived. The son of an artisan, Garve, after a brief stint as a professor of philosophy in Leipzig in the early 1770s, was forced by his illness to spend the rest of his life as a reclusive private scholar in his hometown. He admitted that Cicero sometimes “condescended to deal with those classes who occupy themselves as educators and scholars.” The producing classes, however, “this vast, indispensable, and valuable part of humankind,” could only find prescriptions [End Page 75] for the virtuous life in Cicero’s work insofar as they were human beings, not in relation to their station in life. In general terms Garve thought that Cicero had neglected to deal sufficiently with domestic duties, a reproach which he also leveled against another intellectual pedigree, Adam Ferguson. This did not mean, however, that Garve reduced the citizen’s actions to the private sphere, where they could be productive economically and concerned only with their own Bildung. On the contrary, for Garve useful citizens were those who committed themselves to sociability and to political engagement. Moral actions were not only to be judged according to their motivation (as Kant asserted) but also on their effects on society at large.This different emphasis, I suggest, was typical of the German popular philosophers, who in the time span between Christian Wolff and Immanuel Kant formulated a philosophy of life and among whom Garve emerged as the foremost representative. As a group they constituted a philosophical movement in their own right and were not merely, as they are usually described, the popularizers of Wolff’s philosophy. Rather, popular philosophy was a characteristic compound of Wolffian rationalism and British empiricism. Some popular philosophers, mostly the older generation, were more inclined to the rationalist and others, among them Garve, to the empirical end of this spectrum. Little concerned with epistemological problems or with the irrational cult of life as were the life philosophies of the nineteenth century, the popular philosophers were primarily interested in the virtuous life, in a philosophical theory of moral and aesthetic action. Theirs was a “science of man,” that is, a combination of practical philosophy and literary skills with the goal of morally educating a literate but non-specialized public to be useful citizens of the absolute state. They wanted to speak with propriety on all themes of human existence rather than pursue those philosophical questions not directly related to human life. 2 I entirely agree with a recent commentator who describes Garve’s concerns as non-bourgeois, or better, pre-bourgeois and deeply rooted in humanist values. 3This approach shows in Garve’s Cicero translation and commentary. In Leipzig he had attended the lectures of the classical philologist Friedrich Wilhelm Reiz, who trained his students in precise, critical scholarship. When Garve became a professor himself, he and Reiz anonymously published a Latin edition of Aristotle’s Rhetoric. Later, Garve wrote that his own philosophy was indebted to Reiz who had pointed out to him the close relationship between linguistic and... (shrink)

It is morally impossible, Locke argued, for individuals to consensually establish absolute rule over themselves. That would be to transfer to rulers a power that is not ours, but God’s alone: owner...

This paper presents a new modal logic for ceteris paribus preferences understood in the sense of "all other things being equal". This reading goes back to the seminal work of Von Wright in the early 1960's and has returned in computer science in the 1990' s and in more abstract "dependency logics" today. We show how it differs from ceteris paribus as "all other things being normal", which is used in contexts with preference defeaters. We provide a semantic analysis and (...) several completeness theorems. We show how our system links up with Von Wright's work, and how it applies to game-theoretic solution concepts, to agenda setting in investigation, and to preference change. We finally consider its relation with infinitary modal logics. (shrink)

In this huge study the author presents a systematic and thematic overview of all concepts and ideas, that are basic and gave shape to Western thinking about history: Jewish and Christian concepts of redemptive history, particularism vs. universal concepts, ethnocentric concepts, typology, eschatology and the apocalyptic. He considers concepts of history in the Classical Age, the Middle Ages, Reformation, the Age of Enlightenment, the Romantic Age, Humanism, Positivism, the impact of the Holocaust and Postmodernism. He offers a critical treatment of (...) themes as the periodizing of history, continuity and discontinuity, optimistic and pessimistic theories, repetitive and non-repetitive theories. (shrink)

Taking Löb's Axiom in modal provability logic as a running thread, we discuss some general methods for extending modal frame correspondences, mainly by adding fixed-point operators to modal languages as well as their correspondence languages. Our suggestions are backed up by some new results – while we also refer to relevant work by earlier authors. But our main aim is advertizing the perspective, showing how modal languages with fixed-point operators are a natural medium to work with.

Minimal predicates P satisfying a given first-order description ϕ(P) occur widely in mathematical logic and computer science. We give an explicit first-order syntax for special first-order 'PIA conditions' ϕ(P) which quarantees unique existence of such minimal predicates. Our main technical result is a preservation theorem showing PIA-conditions to be expressively complete for all those first-order formulas that are preserved under a natural model-theoretic operation of 'predicate intersection'. Next, we show how iterated predicate minimization on PIA-conditions yields a language MIN(FO) equal (...) in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. (shrink)

Epistemic agents may have different powers of observation and reasoning, and we show how this diversity fits into dynamic update logics.RésuméLes agents épistémiques peuvent avoir différents pouvoirs d’observation et de raisonnement, et nous montrons comment cette diversité prend place en logique dynamique de mise à jour.

Les agents épistémiques peuvent avoir différents pouvoirs d’observation et de raisonnement, et nous montrons comment cette diversité prend place en logique dynamique de mise à jour.

It is morally impossible, Locke argued, for individuals to consensually establish absolute rule over themselves. That would be to transfer to rulers a power that is not ours, but God’s alone: ownership of our lives. This article analyses the conceptual presuppositions of Locke’s argument for the moral impossibility of self-enslavement through a comparison with other classical social contract theorists, including Grotius, Hobbes and Pufendorf. Despite notoriously defending the permissibility of voluntary enslavement of individuals and even entire peoples, Grotius similarly endorsed (...) divine ownership of human life. He could do so coherently, we show, because he denied that despotic power gives rulers rights in the lives of their subjects. Masters do not own slaves in the way we own material things. Reworking received Roman law categories, Grotius maintained that ‘perfect slavery’ consists in masters having a personal right to the slave’s perpetual service; a condition equivalent to what Locke called ‘drudgery’ and deemed permissible. Our analysis of this unpalatable set of ideas reveals that Locke’s argument is premised upon idiosyncratic conceptions of slavery and absolutism, disavowed by prominent defenders of absolutism in the classical social contract tradition. It is hence less powerful than commonly believed. (shrink)

This article offers a rejoinder to Felix Waldmann. In a critical note published in Locke Studies, Waldmann challenges our recent reconstruction of Locke’s thesis, developed across the Second Treatise of Government, that humans cannot possibly agree to subject themselves to absolute rule. Call this thesis No Contractual Absolutism. Our reconstruction, Waldmann objects, “neglects a basic datum of scholarship”: i.e., that Locke’s Second Treatise intended to counter Filmer’s political theory. Our reply is two-pronged. First, we argue that No Contractual Absolutism cannot (...) plausibly be construed as an attack on Filmer, since it challenges a thesis that he did not hold. Indeed, as for him no form of government can be contractual in origin, Filmer would have agreed with Locke that absolute rule cannot be instituted by agreement. As our initial article suggested, the standard view about whom the polemical target is of the Second Treatise requires qualification with respect to No Contractual Absolutism. Second, we contend that Waldmann’s concerns rest on discipline-specific methodological assumptions, which are unhelpful for the kind of analytical reconstruction we advanced. We conclude with a plea for methodological pluralism in the study of Locke’s thought. (shrink)

Transparency is a crucial condition to implement a CSR policy based on the reputation mechanism. The central question of this contribution is how a transparency policy ought to be organised in order to enhance the CSR behaviour of companies. Governments endorsing CSR as a new means of governance have different strategies to foster CSR transparency. In this paper we discuss the advantages and disadvantages of two conventional policy strategies: the facilitation policy and the command and control strategy. Using three criteria (...) (efficiency, freedom and virtue) we conclude that both strategies are defective. Most attention is paid to the facilitation strategy since governments nowadays mainly use this. In evaluating this strategy we analyse the Dutch case. As an alternative we introduce a third government policy: the development of a self-regulating sub-system. By construing an analogy with the historical development of corporate financial disclosure, we point out that the vital step in the creation of a self-regulating subsystem is the creation of strong informational intermediate organisations. (shrink)

Parameters of a Bertalanffy type of temperature dependent growth model are fitted using data from a population of stone loach ( Barbatula barbatula ). Over two periods respectively in 1990 and 2010 length data of this population has been collected at a lowland stream in the central part of the Netherlands. The estimation of the maximum length of a fully grown individual is given special attention because it is in fact found as the result of an extrapolation over a large (...) interval of the entire lifetime. It is concluded that this parameter should not at forehand be set at one fixed value for the population at that location due to varying conditions over the years. (shrink)

ABSTRACT George Gargov was an active pioneer in the ‘Sofia School’ of modal logicians. Starting in the 1970s, he and his colleagues expanded the scope of the subject by introducing new modal expressive power, of various innovative kinds. The aim of this paper is to show some general patterns behind such extensions, and review some very general results that we know by now, 20 years later. We concentrate on simulation invariance, decidability, and correspondence. What seems clear is that ‘modal logic’ (...) as a genre of logical systems has a much wider scope than originally conceived, and that we have not reached its limits yet. (shrink)

We make a proposal for formalizing simultaneous games at the abstraction level of player's powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of 'concurrent game logic' CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.

BackgroundTo prevent sexual boundary violations (SBV) in mental health care institutions overall governments require these institutions to report SBV incidents to a central registry and to develop institutional guidelines how to react. In Europe SBV policies are only recently developed or implemented, as is also the case in Flanders (Belgium). The implementation of a new institutional policy is always a challenge and can encounter resistance, especially when it concerns SBV, because they remain delicate and complex.MethodThis study evaluated the extent to (...) which mandatory policies on SBV have been implemented in mental health care institutions in Flanders, and possible factors for (non-)implementation of these policies. An online survey was sent to the executives of all mental health care institutions in Flanders (N = 162).ResultsIn total 56 executives of mental health care institutions filled out the survey (response rate 35%). Results showed that the implementation of an SBV policy in mental health care institutions is unfortunately inadequate and not all SBV incidents were reported to the central registry. Type of institution and opinions on the SBV policy were related to the (non-)implementation of the requirements.ConclusionsIt is recommended that governments regularly communicate with mental health care institutions to better understand the concerns and difficulties concerning implementation of the required SBV policy and to support/stimulate an organisational culture of more openness and safety on this topic. (shrink)

Preservation and interpolation results are obtained for L ∞ω and sublogics $\mathscr{L} \subseteq L_{\infty\omega}$ such that equivalence in L can be characterized by suitable back-and-forth conditions on sets of partial isomorphisms.

We propose strategic games wherein the strategies consist of players asking each other questions and answering those questions. We study simplifications of such games wherein two players simultaneously ask each other a question that the opponent is then obliged to answer. The motivation for our research is to model conversation including the dynamics of questions and answers, to provide new links between game theory and dynamic logics of information, and to exploit the dynamic/strategic structure that, we think, lies implicitly inside (...) epistemic models for epistemic languages, and to make that structure an explicit subject of logical study. Our main contributions are: the notion of a two-person question-answer game with information goals, the existence and computation of equilibria for these games, the correspondence with Bayesian games and their equilibria, and a connection between logic and game theory namely the existence of equilibria for positive goal formulae. (shrink)