On axiomatising products of Kripke frames

2000 ◽  
Vol 65 (2) ◽  
pp. 923-945 ◽  
Author(s):  
Ágnes Kurucz
Keyword(s):  
Modal Logic ◽  
The Other ◽  
Modal Language ◽  
First Order ◽  
Kripke Frames ◽  
Other Hand ◽  
The Many ◽  
By Products

AbstractIt is shown that the many-dimensional modal logic Kn, determined by products of n-many Kripke frames, is not finitely axiomatisable in the n-modal language, for any n > 2. On the other hand, Kn is determined by a class of frames satisfying a single first-order sentence.

scholarly journals Recursive enumerability and elementary frame definability in predicate modal logic

2019 ◽  
Vol 30 (2) ◽  
pp. 549-560 ◽  
Author(s):  
Mikhail Rybakov ◽  
Dmitry Shkatov
Keyword(s):  
Modal Logic ◽  
Modal Logics ◽  
The Other ◽  
Kripke Semantics ◽  
First Order ◽  
Elementary Class ◽  
Recursive Enumerability ◽  
Kripke Frames ◽  
Recursively Enumerable ◽  
The Relationship

Abstract We investigate the relationship between recursive enumerability and elementary frame definability in first-order predicate modal logic. On one hand, it is well known that every first-order predicate modal logic complete with respect to an elementary class of Kripke frames, i.e. a class of frames definable by a classical first-order formula, is recursively enumerable. On the other, numerous examples are known of predicate modal logics, based on ‘natural’ propositional modal logics with essentially second-order Kripke semantics, that are either not recursively enumerable or Kripke incomplete. This raises the question of whether every Kripke complete, recursively enumerable predicate modal logic can be characterized by an elementary class of Kripke frames. We answer this question in the negative, by constructing a normal predicate modal logic which is Kripke complete, recursively enumerable, but not complete with respect to an elementary class of frames. We also present an example of a normal predicate modal logic that is recursively enumerable, Kripke complete, and not complete with respect to an elementary class of rooted frames, but is complete with respect to an elementary class of frames that are not rooted.

scholarly journals Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

2019 ◽  
Vol 19 (5-6) ◽  
pp. 671-687 ◽  
Author(s):  
JORGE FANDINNO
Keyword(s):  
Modal Logic ◽  
Logic Programming ◽  
Epistemic Logic ◽  
The Other ◽  
Stable Model ◽  
Logic Programs ◽  
Splitting Property ◽  
Other Hand ◽  
The Many ◽  
Programming Semantics

AbstractIn a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond’s original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

scholarly journals “Is Christus verdeeld?” Nadenke oor die teologiese regverdiging van kerkverdeeldheid en kerkskeuring

2008 ◽  
Vol 29 (2) ◽  
pp. 507-525
Author(s):  
J H Van Wyk
Keyword(s):  
The Other ◽  
Other Hand ◽  
Church Unity ◽  
Reformation Theology ◽  
Church Schism ◽  
The Many ◽  
The One

“Is Christ divided?” Reflections on the theological justification of church disunity and church schismIn this article the author investigates the question whether a church schism could ever be justified. He considers on the one hand the Biblical message on church unity and on the other hand the many justifications of church disunity (schism). He concludes that most of these justifications are unacceptable rasionalisations and that Post-Reformation theology distanced itself far away from Biblical ecclesiology in this regard.

scholarly journals Resolving The Democratic Dilemma: Contestation, Anti-Power and Democracy

2021 ◽  
Author(s):  
◽  
Samuele Tonello
Keyword(s):  
Thought Experiment ◽  
The Other ◽  
Main Question ◽  
Political Systems ◽  
Social Differences ◽  
Other Hand ◽  
The Social ◽  
Democratic Dilemma ◽  
The Many ◽  
The One

<p>This thesis in divided in two main parts. First, I develop the claim that current democracies are unable to properly defend what I deem the pivotal feature to evaluate the quality of a political system - namely the people’s liberty - due to what I call a twofold democratic dilemma. On the one hand, common citizens are affected by biases that compromise their ability to successfully maintain forms of self-government. On the other hand, even representative forms of democracy that limit to a certain degree the people’s power are threatened by an oligarchic power. That is, oligarchs are using their wealth power to sway governments towards pursuing oligarchic interests rather than common ones, thus hindering the people’s liberty. For this reason, I argue that we ought to rely on Pettit’s view of liberty as non-domination to resolve the democratic dilemma. The thesis conceives these two threats as two forms of domination that must be avoided and focuses on adding a supplementary editorial and contestatory dimension of democracy to the classical participatory one. Republicanism could offer a solution to both sides of the dilemma. On the one hand, citizens’ political task would be more compatible with the people’s biases, since citizens would limit their participation to control that government’s policies do not entail oligarchic domination. On the other hand, framing liberty as a battle between dominating masters and dominated slaves, republicanism could offer the many the institutional means to counteract elites’ political domination. In this way, I conclude the first part of the thesis, but this opens the gates to the main question of the thesis, namely to how we should structure this contestatory democracy. The problem is that whereas republican scholars agree on the importance of setting freedom as non-domination at the basis of our political systems, there is no such agreement on the best way to institutionally enhance the republican ideal. I analyse this debate, maintaining that while Pettitt’s ideal is the view to pursue, we should reject his editorial solution because small committees of experts are likely to increase oligarchic domination rather than to protect the people’s liberty. Rejecting Pettit’s model does not yet imply refusing any editorial model, since I argue that critical scholars mistakenly identify the editorial component of democracy with Pettit’s answer only. In this way, they neglect alternative solutions to Pettit’s, such as Bellamy’s and McCormick’s. Having explained that Bellamy’s solution does not resolve the democratic dilemma, since this scholar rejects editorial bodies, I argue that McCormick’s “Machiavellian Democracy” framed on a divided conception of the populace offers instead the solution I am looking for. Institutionally recognizing the social differences among the populace, we could create modern bodies similar to the Roman “Tribune of the Plebs” to offer the weaker part of the population a class-specific institution to use as defence from oligarchic domination. The problem is how to implement a modern “Tribune of the plebs” making sure that these bodies are effective but popular in character at the same time. I thus explain how modern editorial tribunates could work in practice, drawing from McCormick’s “thought experiment”. I agree with most of McCormick’s ideas – lottery selection, wealth threshold exclusion, large size tribunates, etc. - but I suggest that we must review some of his suggestions with features more concerned with improving the people’s knowledge – specialization, education selection, etc. Hence, I conclude the thesis describing my thought experiment of a system of Specialized Ministerial Tribunates. In this way, I argue that we could better resolve the democratic dilemma. On the one hand, tribunates’ editorship would be more specific and would not require members of the tribunate to analyse the operation of governments on a too broad spectrum, thus reducing the problems of the people’s biases. On the other hand, tribunates’ operation could be primarily connected to detecting oligarchic features in the policies enacted by single ministries, thus challenging more precisely any oligarchic influence over governments. In sum, I argue that an editorial dimension could produce significant improvements to the people’s liberty. Thanks to a modern “Tribune of the plebs”, citizens could participate more meaningfully in politics, while taming more efficiently the influence oligarchs have on how modern societies are politically directed.</p>

scholarly journals Resolving The Democratic Dilemma: Contestation, Anti-Power and Democracy

2021 ◽  
Author(s):  
◽  
Samuele Tonello
Keyword(s):  
Thought Experiment ◽  
The Other ◽  
Main Question ◽  
Political Systems ◽  
Social Differences ◽  
Other Hand ◽  
The Social ◽  
Democratic Dilemma ◽  
The Many ◽  
The One

<p>This thesis in divided in two main parts. First, I develop the claim that current democracies are unable to properly defend what I deem the pivotal feature to evaluate the quality of a political system - namely the people’s liberty - due to what I call a twofold democratic dilemma. On the one hand, common citizens are affected by biases that compromise their ability to successfully maintain forms of self-government. On the other hand, even representative forms of democracy that limit to a certain degree the people’s power are threatened by an oligarchic power. That is, oligarchs are using their wealth power to sway governments towards pursuing oligarchic interests rather than common ones, thus hindering the people’s liberty. For this reason, I argue that we ought to rely on Pettit’s view of liberty as non-domination to resolve the democratic dilemma. The thesis conceives these two threats as two forms of domination that must be avoided and focuses on adding a supplementary editorial and contestatory dimension of democracy to the classical participatory one. Republicanism could offer a solution to both sides of the dilemma. On the one hand, citizens’ political task would be more compatible with the people’s biases, since citizens would limit their participation to control that government’s policies do not entail oligarchic domination. On the other hand, framing liberty as a battle between dominating masters and dominated slaves, republicanism could offer the many the institutional means to counteract elites’ political domination. In this way, I conclude the first part of the thesis, but this opens the gates to the main question of the thesis, namely to how we should structure this contestatory democracy. The problem is that whereas republican scholars agree on the importance of setting freedom as non-domination at the basis of our political systems, there is no such agreement on the best way to institutionally enhance the republican ideal. I analyse this debate, maintaining that while Pettitt’s ideal is the view to pursue, we should reject his editorial solution because small committees of experts are likely to increase oligarchic domination rather than to protect the people’s liberty. Rejecting Pettit’s model does not yet imply refusing any editorial model, since I argue that critical scholars mistakenly identify the editorial component of democracy with Pettit’s answer only. In this way, they neglect alternative solutions to Pettit’s, such as Bellamy’s and McCormick’s. Having explained that Bellamy’s solution does not resolve the democratic dilemma, since this scholar rejects editorial bodies, I argue that McCormick’s “Machiavellian Democracy” framed on a divided conception of the populace offers instead the solution I am looking for. Institutionally recognizing the social differences among the populace, we could create modern bodies similar to the Roman “Tribune of the Plebs” to offer the weaker part of the population a class-specific institution to use as defence from oligarchic domination. The problem is how to implement a modern “Tribune of the plebs” making sure that these bodies are effective but popular in character at the same time. I thus explain how modern editorial tribunates could work in practice, drawing from McCormick’s “thought experiment”. I agree with most of McCormick’s ideas – lottery selection, wealth threshold exclusion, large size tribunates, etc. - but I suggest that we must review some of his suggestions with features more concerned with improving the people’s knowledge – specialization, education selection, etc. Hence, I conclude the thesis describing my thought experiment of a system of Specialized Ministerial Tribunates. In this way, I argue that we could better resolve the democratic dilemma. On the one hand, tribunates’ editorship would be more specific and would not require members of the tribunate to analyse the operation of governments on a too broad spectrum, thus reducing the problems of the people’s biases. On the other hand, tribunates’ operation could be primarily connected to detecting oligarchic features in the policies enacted by single ministries, thus challenging more precisely any oligarchic influence over governments. In sum, I argue that an editorial dimension could produce significant improvements to the people’s liberty. Thanks to a modern “Tribune of the plebs”, citizens could participate more meaningfully in politics, while taming more efficiently the influence oligarchs have on how modern societies are politically directed.</p>

Nancian virtual doubts about ‘Leformal’ democracy

2011 ◽  
Vol 37 (9) ◽  
pp. 999-1010 ◽  
Author(s):  
Ignaas Devisch
Keyword(s):  
Specific Form ◽  
The Other ◽  
Political Regime ◽  
Berlin Wall ◽  
Global Democracy ◽  
Claude Lefort ◽  
Other Hand ◽  
Contemporary Politics ◽  
To Come ◽  
The Many

French philosopher Jean-Luc Nancy is acting uneasily when it comes to contemporary politics. There is a sort of agitation in his work in relation to this question. At several places we read an appeal to deal thoroughly with this question and ‘ qu’il y a un travail à faire’, that there is still work to do. From the beginning of the 1980s with the ‘Centre de Recherches Philosophiques sur le Politique’ and the two books resulting out of that, until the many, rather short texts he published on this topic during the last years of the century, the question of politics crosses very clearly Nancy’s work. He not only fulminates against the contemporary philosophical ‘content’ with democracy. Instead of defending a political regime, he wants to think the form of politics in the most critical and sceptical way. To Nancy, the worst thing we can do in thinking contemporary politics, is taking it for granted that we know what politics is about today, given the evidence of the global democracy. So to him, we almost have to be at unease when it comes to politics. On the other hand, in thinking contemporary democracy, the work of Claude Lefort is undeniably the main reference. Long before the collapse of the Berlin Wall and the upsurge of an all-too-easy anti-Marxism, Lefort articulated in a nuanced way the formal differences between totalitarianism and democracy. According to Lefort, the specific ‘form’ of democracy is that it never becomes an accomplished and fulfilled form as such. In a certain sense, the only ‘form’ of democracy is formlessness, a form without form. In a democracy, the place of power becomes literally ‘ infigurable’ as Lefort says. Democracy stands for formlessness or the relation to a void. Nancy objects so to say against a ‘Leformal’ conception of democracy – the empty place, the formless, the ‘ infigurable’ or ‘ sans figure’, the ever yet to come. … This conception of democracy would still be caught in the infinite metaphysical, dialectical horizon of immanentism, while it pretends to have already left that horizon behind it, presenting itself as the finite alternative to the infinite totalitarian politics. Democracy as formlessness is indeed no longer based on a metaphysical Idea, Figure, or Truth. We want to clear up the philosophical sky of Nancy’s remarks by confronting them with some thoughts of Lefort.

Old Readings in 1 Esdras: The List of Returnees From Babylon (Ezra 2 // Nehemiah 7)

1969 ◽  
Vol 62 (1) ◽  
pp. 99-107 ◽  
Author(s):  
Ralph Walter Klein
Keyword(s):  
Hebrew Text ◽  
The Other ◽  
Greek Text ◽  
Text Type ◽  
Other Hand ◽  
The Many

In a recent study of the Greek text of 1 Esdras we argued that it frequently reflected an old, often nonexpanded Semitic Vorlage despite the many corruptions and secondary expansions peculiar to the “apocryphal” text. Esdras B [hereafter: G], on the other hand, was also found to differ from the received Hebrew text, but its variants were small enough that its underlying text-type could be called Proto-Massoretic. This analysis conflicts with that of Bernhard Walde, Wilhelm Rudolph, and others, who would assign the same geographical and chronological horizons and nearly identical Vorlagen to 1 Esdras and G. We shall test our interpretation, therefore, by studying the differences in the Hebrew texts of Ezra 2 and Nehemiah 7 on the basis of the translation of Ezra 2 in 1 Esdras 5. Although the latter has many omissions and doublets —in fact, it is in relatively poor shape —not enough attention has been paid to its alternation between Ezra-type and Nehemiah-type texts.

Remarks on Receiving the C. Anderson Aldrich Award

PEDIATRICS ◽  
1975 ◽  
Vol 56 (2) ◽  
pp. 332-334
Author(s):  
Anna Freud
Keyword(s):  
Child Care ◽  
Child Psychology ◽  
Body Part ◽  
The Other ◽  
Hospitalized Children ◽  
Child Guidance ◽  
Other Hand ◽  
The Many ◽  
Medical Specialities ◽  
Child Psychiatrists

I take the honour which is being bestowed on me today as another welcome sign that the estrangement between pediatrics and child psychology is nearing its end and the partners on either side are contemplating a serious engagement, if not the propect of future marriage with each other. There are many other indications which point in the same direction. I only need to mention the fact that there are now places of learning where the head of the department combines in his own person training and functions in physical as well as mental child care; or that pediatricians are considered essential consultants in child guidance clinics, or that some pediatricians participate in the discussions of interdisciplinary hospital groups, or that, occasionally, child psychiatrists and even child analysts are called to the bedside of hospitalized children for consultation. There is no reason, on the other hand, to feel entirely optimistic and to relax efforts towards further re-alignment. Cooperative attitudes between the two disciplines can also be regarded still as few and far between and, above all, confined to selected medical specialities and a small number of selected, furthest advanced, and enlightened centers. There exist still many children's wards where bodily care is so paramount that any thought about the child's mental concerns is excluded as intrusive and disruptive. There are, above all, the many surgeons who, rightly or wrongly, feel that their difficult task cannot be accomplished except by determined and exclusive concentration on the defective body part which needs repair.

One-Handed Musicians—More Than a Gimmick

2012 ◽  
Vol 27 (4) ◽  
pp. 231-237 ◽  
Author(s):  
KH Woldendorp ◽  
W van Gils
Keyword(s):  
Healthcare Professional ◽  
Muscle Strength ◽  
Upper Extremity ◽  
Physical Condition ◽  
Interdisciplinary Approach ◽  
The Other ◽  
Other Hand ◽  
The Many

There are many musicians with acquired limitations in making music, and there are many people with a disability who would like to play a music instrument in a modified way. There is discouragingly little information about this topic in literature. This article gives an overview of “making music in a modified way.” It focuses on the possibilities for musicians with one-handed functionality to overcome problems with regards to their physical condition, insufficient muscle strength, or missing parts of the upper extremity. Five categories of possibilities for the functional one-handed musicians are described: 1) one-hand reconstructed instruments, 2) one-hand compositions, 3) adaptations of the instrument for the other hand, 4) prostheses to make it possible to play with both hands/arms, and 5) other techniques which enable the use of the leg(s). The solutions described make clear that playing music in an adaptive way requires an interdisciplinary approach. The purpose of this article is to inform, and to inspire, the healthcare professional about the many possibilities for functional one-handed musicians.

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