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

2019 ◽  
Vol 19 (5-6) ◽  
pp. 671-687 ◽  
Author(s):  
JORGE FANDINNO

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.

2000 ◽  
Vol 65 (2) ◽  
pp. 923-945 ◽  
Author(s):  
Ágnes Kurucz

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.


Author(s):  
Pedro Cabalar ◽  
Jorge Fandinno ◽  
Luis Fariñas del Cerro

Epistemic logic programs constitute an extension of the stable model semantics to deal with new constructs called "subjective literals." Informally speaking, a subjective literal allows checking whether some objective literal is true in all or some stable models. However, its associated semantics has proved to be non-trivial, since the truth of subjective literals may interfere with the set of stable models it is supposed to query. As a consequence, no clear agreement has been reached and different semantic proposals have been made in the literature. In this paper, we review an extension of the well-known splitting property for logic programs to the epistemic case. This "epistemic splitting property" is defined as a general condition that can be checked on any arbitrary epistemic semantics. Its satisfaction has desirable consequences both in the representation of conformant planning problems and in the encoding of the so-called subjective constraints.


Author(s):  
PEDRO CABALAR ◽  
JORGE FANDINNO ◽  
LUIS FARIÑAS DEL CERRO

Abstract Epistemic logic programs constitute an extension of the stable model semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some objective literal is true in all or some stable models. As it can be imagined, the associated semantics has proved to be non-trivial, since the truth of subjective literals may interfere with the set of stable models it is supposed to query. As a consequence, no clear agreement has been reached and different semantic proposals have been made in the literature. Unfortunately, comparison among these proposals has been limited to a study of their effect on individual examples, rather than identifying general properties to be checked. In this paper, we propose an extension of the well-known splitting property for logic programs to the epistemic case. We formally define when an arbitrary semantics satisfies the epistemic splitting property and examine some of the consequences that can be derived from that, including its relation to conformant planning and to epistemic constraints. Interestingly, we prove (through counterexamples) that most of the existing approaches fail to fulfill the epistemic splitting property, except the original semantics proposed by Gelfond 1991 and a recent proposal by the authors, called Founded Autoepistemic Equilibrium Logic.


2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen

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.


1992 ◽  
Vol 16 (3-4) ◽  
pp. 231-262
Author(s):  
Philippe Balbiani

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.


2008 ◽  
Vol 29 (2) ◽  
pp. 507-525
Author(s):  
J H Van Wyk

“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.


2021 ◽  
Author(s):  
◽  
Samuele Tonello

<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>


2021 ◽  
Author(s):  
◽  
Samuele Tonello

<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>


2011 ◽  
Vol 37 (9) ◽  
pp. 999-1010 ◽  
Author(s):  
Ignaas Devisch

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.


1969 ◽  
Vol 62 (1) ◽  
pp. 99-107 ◽  
Author(s):  
Ralph Walter Klein

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.


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