We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

Solovay's 1976 completeness result for modal provability logic employs the recursion theorem in its proof. It is shown that the uses of the recursion theorem can in this proof replaced by the diagonalization lemma for arithmetic and that, in effect, the proof neatly fits the framework of another, enriched, system of modal logic so that any arithmetical system for which this logic is sound is strong enough to carry out the proof, in particular $\text{I}\Delta _{0}+\text{EXP}$ . The method is adapted (...) to obtain a similar completeness result for the Rosser logic. (shrink)

The problem of Uniqueness and Explicit Definability of Fixed Points for Interpretability Logic is considered. It turns out that Uniqueness is an immediate corollary of a theorem of Smoryński.

A definition is given for formulae $A_1,\ldots,A_n$ in some theory $T$ which is formalized in a propositional calculus $S$ to be (in)dependent with respect to $S$. It is shown that, for intuitionistic propositional logic $\mathbf{IPC}$, dependency (with respect to $\mathbf{IPC}$ itself) is decidable. This is an almost immediate consequence of Pitts' uniform interpolation theorem for $\mathbf{IPC}$. A reasonably simple infinite sequence of $\mathbf{IPC}$-formulae $F_n(p, q)$ is given such that $\mathbf{IPC}$-formulae $A$ and $B$ are dependent if and only if at least (...) on the $F_n(A, B)$ is provable. (shrink)

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.

This paper contains a completeness proof for the system ILW, a rather bewildering axiom system belonging to the family of interpretability logics. We have treasured this little proof for a considerable time, keeping it just for ourselves. Johan’s ftieth birthday appears to be the right occasion to get it out of our wine cellar.

In this paper the system IL for relative interpretability is studied.

Standard unary modal logic and binary modal logic, i.e. modal logic with one binary operator, are shown to be definitional extensions of one another when an additional axiom |$U$| is added to the basic axiomatization of the binary side. This is a strengthening of our previous results. It follows that all unary modal logics extending Classical Modal Logic, in other words all unary modal logics with a neighborhood semantics, can equivalently be seen as binary modal logics. This in particular applies (...) to standard modal logics, which can be given simple natural axiomatizations in binary form. We illustrate this in the logic K. We call such logics binary expansions of the unary modal logics. There are many more such binary expansions than the ones given by the axiom |$U$|⁠. We initiate an investigation of the properties of these expansions and in particular of the maximal binary expansions of a logic. Our results directly imply that all sub- and superintuitionistic logics with a standard modal companion also have binary modal companions. The latter also applies to the weak subintuitionistic logic WF of our previous papers. This logic doesn’t seem to have a unary modal companion. (shrink)

It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R⁻. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts onself to "usual" proof predicates.

This first chapter contains an introduction to modal logic. In section 1.1 the syntactic side of the matter is discussed, and in section 1.2 the subject is approached from a semantic point of view.

Semantic Automata Johan van Ben them. INTRODUCTION An attractive, but never very central idea in modern semantics has been to regard linguistic expressions ...

In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic (...) images of frames and that ONNILLI-formulas are stable formulas as introduced by Bezhanishvili and Bezhanishvili in 2013. Thus, ONNILLI is a syntactically defined set of formulas axiomatizing all stable logics. This resolves a problem left open in 2013. (shrink)

We study the modal properties of intuitionistic modal logics that belong to the provability logic or the preservativity logic of Heyting Arithmetic. We describe the □-fragment of some preservativity logics and we present fixed point theorems for the logics iL and iPL, and show that they imply the Beth property. These results imply that the fixed point theorem and the Beth property hold for both the provability and preservativity logic of Heyting Arithmetic. We present a frame correspondence result for the (...) preservativity principle Wp that is related to an extension of Löb's principle. (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)

We give alternative characterizations of exact, extendible and projective formulas in intuitionistic propositional calculus IPC in terms of n-universal models. From these characterizations we derive a new syntactic description of all extendible formulas of IPC in two variables. For the formulas in two variables we also give an alternative proof of Ghilardi’s theorem that every extendible formula is projective.

In this paper, we study IL(), the interpretability logic of . As is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to : IL() is not or . IL() does, of course, contain all the principles known to be part of IL, the interpretability logic of the principles common to all reasonable arithmetical theories. In this paper, we take two arithmetical properties of and see what their consequences in the modal logic (...) IL() are. These properties are reflected in the so-called Beklemishev Principle , and Zambella’s Principle , neither of which is a part of IL. Both principles and their interrelation are submitted to a modal study. In particular, we prove a frame condition for . Moreover, we prove that follows from a restricted form of . Finally, we give an overview of the known relationships of IL() to important other interpretability principles. (shrink)

We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.

Following A.N. Whitehead’s rhythm of education, the author provides a guide for parents and educators on raising children to thrive in times of tempestuous change. Each chapter presents exemplary educational events rich in context, and then draws on seminal research to ground her recommendations in a robust theoretical foundation.

The commons have emerged as a key notion and underlying experience of many efforts around the world to promote justice and democracy. A central question for political theories of the commons is whether the visions of social order and regimes of political economy they propose are complementary or opposed to public goods that are backed up by governmental coordination and compulsion. This essay argues that the post-Marxist view, which posits an inherent opposition between the commons as a sphere of inappropriable (...) usage and statist public infrastructure, is mistaken, because justice and democracy are not necessarily furthered by the institution of inappropriability. I articulate an alternative pluralist view based on James Tully’s work, which discloses the dynamic interplay between public and common modes of provision and enjoyment, and their civil and civic orientations respectively. Finally, the essay points to the Janus-faced character of the commons and stresses the co-constitutive role of public goods and social services for just and orderly social life while remaining attentive to the dialectic of empowerment and tutelage that marks provision by government. (shrink)

Michael Oakeshott’s account of political economy is claimed to have found its ‘apotheosis under Thatcherism’. Against critics who align him with a preference for small government, this article points to Oakeshott’s stress on the indispensability of an infrastructure of government-provided public goods, in which individual agency and associative freedom can flourish. I argue that Oakeshott’s account of political economy invites a contestatory politics over three types of public goods, which epitomize the unresolvable tension he diagnosed between nomocratic and teleocratic conceptions (...) of the modern state. These three types are the system of civil law, the by-products of the operation of civil law and public goods which result from policies. The article concludes that Oakeshott offers an important corrective to political theories which favour either market mediation or radical democratic governance of the commons as self-sustaining modes of providing and enjoying goods. (shrink)

The hopes and fears expressed in the debate on human enhancement are not always based on a realistic assessment of the expected possibilities. Discussions about extreme scenarios may at times obscure the ethical and policy issues that are relevant today. This paper aims to contribute to an adequate and ethically sound societal response to actual current developments. After a brief outline of the ethical debate concerning neuro-enhancement, it describes the current state of the art in psychopharmacological science and current uses (...) of psychopharmacological enhancement, as well as the prospects for the near future. It then identifies ethical issues regarding psychopharmacological enhancements that require attention from policymakers, both on the professional and on the governmental level. These concern enhancement research, the gradual expansion of medical categories, off-label prescription and responsibility of doctors, and accessibility of enhancers on the Internet. It is concluded that further discussion on the advantages and drawbacks of enhancers on a collective social level is still needed. (shrink)

Michael Oakeshott’s account of political economy is claimed to have found its ‘apotheosis under Thatcherism’. Against critics who align him with a preference for small government, this article poin...

The leopoldistic version of the events before Berchtesgaden - politically the most important period in the Question Royale during the occupation - is from the start till the end historically not grounded. The known facts prove that the King was absolutely not passive in political matters. He doesn't reject the proposal for a meeting with Hitler. Already on May 31 he declares to agree in principle to meet the Führer. On June 26 he again expresses this willingness. In October he (...) sends his sister Marie-José, crownprincess of Italy, to Hitler, collecting the requested invitation for a meeting. The meeting Hitler-Leopold III at Berchtesgaden reveals not only a humanitarian, but also an indeniable political character.There is too great a difference between the leopoldistic version and the facts - as far as known at this moment and from limited sources. One is inclined to ask oneself if the editors of the Whitebook and of the report of the Servais-commission, had knowledge of all the facts, which normally should have been at their disposal. If the answer is no, than one has to assume «a secret of the King». (shrink)

THE PURPOSE OF THE PRESENT EXPOSITION is to put forward an interpretation of Locke's and Hooker's conception of the finding of the law. The topics which will be examined are the knowledge and content of the different types of law and, above all, the standard of the good law. That Locke and Hooker used the same language, to a large extent, in treating the concept of law can be seen immediately in a comparison of Locke's Essays on the Law of (...) Nature, Two Treatises on Government, and Essay on Human Understanding with the first book of Hooker's Laws of Ecclesiastical Polity. This similarity facilitated Locke's recourse to Hooker's texts when he wanted to strengthen some of the arguments of the Second Treatise. But is the use of similar language not deceptive in the present case? Do terms used in 1690 intend the same meaning as they did when used in 1660? After nearly four decades of conflicting interpretations of Locke's political and philosophical texts, one can hardly expect to offer a new answer. This analysis will explore the similarity within the framework of a traditional, natural law interpretation of Locke. We shall find that, in Hooker's Laws and Locke's Two Treatises, we are faced with the same pattern of exposition concerning natural law and its source. Following this path of inquiry represents a decision to put aside, for the time being, the influential but highly problematic suggestion that Locke wished to deceive his readers in the exposition of some of the most central parts of his political theory. (shrink)

This article presents hospitality as a pivotal value in the context of increasing diversity that characterises the complex relations in which leadership emerges. After reviewing the concept of Otherness in philosophy, the notion of hospitality as developed by Richard Kearney in relation to his philosophy of religion is introduced. The case of Nobel Peace Prize Laureate Chief Albert Luthuli is then presented as a biographical leadership study from the African context to illustrate how hospitality as open response to radical Otherness (...) may inspire collaboration and foster positive change. The article then addresses ways in which the notions of hospitality and Otherness present new opportunities to leadership studies for responding to the relational challenges of the globalised world. Amidst an increased scholarly focus on relationality and the need for relational intelligence, globalisation routinely confronts leaders and their followers with radical Otherness. Through dialogue between theology, philosophy of religion and leadership studies and by presenting a case from the African context, the article offers in print what is called for in the global context, namely an open response to the alterity of the Other that enables collaboration amidst increasing diversity. CONTRIBUTION: Proceeding from a transdisciplinary engagement, the article illustrates that leadership studies stood to benefit from dialogue with theology and philosophy of religion, which offers ways of addressing the Otherness that characterise the globalised context of leadership. (shrink)

When is state coercion for the provision of public goods justified? And how should the social surplus of public goods be distributed? Philosophers approach these questions by distinguishing between essential and discretionary public goods. This article explains the intractability of this distinction, and presents two upshots. First, if governments provide configurations of public goods that simultaneously serve essential and discretionary purposes, the scope for justifiable complaints by honest holdouts is narrower than commonly assumed. Second, however, claims to distributive fairness in (...) the provision of public goods also turn out to be more complex to assess. (shrink)

BackgroundAcrophobia is a specific phobia characterized by a severe fear of heights. The purpose of the present study was to investigate the efficacy of two therapies that may ameliorate symptoms of acrophobia and anxiety sensitivity, i.e., virtual reality exposure therapy (VRET) and eye movement desensitization and reprocessing (EMDR) therapy with a Waiting List Control Condition (WLCC).MethodsWe applied a three-armed randomized controlled pre-post-test design with 45 female adolescent students. Students who met DSM-5 criteria for acrophobia were randomly assigned to either VRET (...) (N = 15;Mage = 17.26; SD = 1.32), EMDR (N = 15;Mage = 17.15; SD = 1.57), or a WLCC (N = 15;Mage = 17.50; SD = 1.26). The study groups were evaluated one week before the intervention and one week after the last intervention session regarding symptoms of acrophobia (Severity Measure for Acrophobia) and anxiety sensitivity (Anxiety Sensitivity Index).ResultsThe data showed that both the application of VRET and EMDR therapy were associated with significantly reduced symptoms of acrophobia (d = 1.03 for VRET and d = 1.08 for EMDR) and anxiety sensitivity (d = 1.15 for VRET and d = 1.13 for EMDR) in comparison to the Waiting List.LimitationsThe sample consisted only of adolescent women. Due to the recognizable differences between the two interventions, the therapists and the participants were not blind to the conditions.ConclusionThe results suggest that both VRET and EMDR are interventions that can significantly improve symptoms of acrophobia and anxiety sensitivity in female adolescents.Clinical Trial Registrationhttps://www.irct.ir/trial/57391, identifier: IRCT20210213050343N1. (shrink)

BackgroundA patient who fulfils the due diligence requirements for euthanasia, and is medically suitable, is able to donate his organs after euthanasia in Belgium, the Netherlands and Canada. Since 2012, more than 70 patients have undergone this combined procedure in the Netherlands. Even though all patients who undergo euthanasia are suffering hopelessly and unbearably, some of these patients are nevertheless willing to help others in need of an organ. Organ donation after euthanasia is a so-called donation after circulatory death (DCD), (...) Maastricht category III procedure, which takes place following cardiac arrest, comparable to donation after withdrawal of life sustaining therapy in critically ill patients. To minimize the period of organ ischemia, the patient is transported to the operating room immediately after the legally mandated no-touch period of 5 min following circulatory arrest. This means that the organ donation procedure following euthanasia must take place in the hospital, which appears to be insurmountable to many patients who are willing to donate, since they already spent a lot of time in the hospital. Case presentationThis article describes the procedure of organ donation after euthanasia starting at home (ODAEH) following anesthesia in a former health care professional suffering from multiple system atrophy. This case is unique for at least two reasons. He spent his last conscious hours surrounded by his family at home, after which he underwent general anaesthesia and was intubated, before being transported to the hospital for euthanasia and organ donation. In addition, the patient explicitly requested the euthanasia to be performed in the preparation room, next to the operating room, in order to limit the period of organ ischemia due to transport time from the intensive care unit to the operating room. The medical, legal and ethical considerations related to this illustrative case are subsequently discussed.ConclusionsOrgan donation after euthanasia is a pure act of altruism. This combined procedure can also be performed after the patient has been anesthetized at home and during transportation to the hospital. (shrink)