We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

Recent work has shown that the input-output behavior of some common machine learning classifiers can be captured in symbolic form, allowing one to reason about the behavior of these classifiers using symbolic techniques. This includes explaining decisions, measuring robustness, and proving formal properties of machine learning classifiers by reasoning about the corresponding symbolic classifiers. In this work, we present a theory for unveiling the _reasons_ behind the decisions made by Boolean classifiers and study some of its theoretical and practical implications. (...) At the core of our theory is the notion of a _complete reason,_ which can be viewed as a necessary and sufficient condition for why a decision was made. We show how the complete reason can be used for computing notions such as sufficient reasons (also known as PI-explanations and abductive explanations), how it can be used for determining decision and classifier bias and how it can be used for evaluating counterfactual statements such as “a decision will stick even if...because....” We present a linear-time algorithm for computing the complete reasoning behind a decision, assuming the classifier is represented by a Boolean circuit of appropriate form. We then show how the computed complete reason can be used to answer many queries about a decision in linear or polynomial time. We finally conclude with a case study that illustrates the various notions and techniques we introduced. (shrink)

We address in this paper the problem of counting the models of a propositional theory under incremental changes to its literals. Specifcally, we show that if a propositional theory Δ is in a special form that we call smooth, deterministic, decomposable negation normal form, then for any consistent set of literals S, we can simultaneously count the models of Δ ∪ S and the models of every theory Δ ∪ T where T results from adding, removing or flipping a literal (...) in S. We present two results relating to the time and space complexity of compiling propositional theories into sd-DNNF. First, we show that if a conjunctive normal form has a bounded treewidth, then it can be compiled into an sd-DNNF in time and space which are linear in its size. Second, we show that sd-DNNF is a strictly more space efficient representation than Free Binary Decision Diagrams. Finally, we discuss some applications of the counting results to truth maintenance systems, belief revision, and model-based diagnosis. (shrink)

We address in this paper the problem of counting the models of a propositional theory under incremental changes to its literals. Specifcally, we show that if a propositional theory Δ is in a special form that we call smooth, deterministic, decomposable negation normal form (sd-DNNF), then for any consistent set of literals S, we can simultaneously count (in time linear in the size of Δ) the models of Δ ∪ S and the models of every theory Δ ∪ T where (...) T results from adding, removing or flipping a literal in S. We present two results relating to the time and space complexity of compiling propositional theories into sd-DNNF. First, we show that if a conjunctive normal form (CNF) has a bounded treewidth, then it can be compiled into an sd-DNNF in time and space which are linear in its size. Second, we show that sd-DNNF is a strictly more space efficient representation than Free Binary Decision Diagrams (FBDDs). Finally, we discuss some applications of the counting results to truth maintenance systems, belief revision, and model-based diagnosis. (shrink)

Being in a romantic relationship is characterized by a high degree of intimacy and affective involvement. Affective behavior indicates the emotional content in couple interactions and therefore promotes an understanding of the evolution of romantic relationships. When couples are also parents, their affective behavior reflects their romantic and coparental bonds. In this paper, we present an observation of parent couples’ affective behavior during a coparenting conflict discussion task to document whether and how much it improved during couple therapy. Two contrasting (...) cases of affective behavior change are included. Observational coding of affective behavior within pre- and post-intervention coparenting conflict discussion tasks was carried out to compute means and CIs for each partner in both cases. In addition, the partners’ coparental and romantic satisfaction were evaluated through validated self-report questionnaires in pre- and post-intervention assessments; this helped document whether the partners’ coparental and romantic satisfaction were dissimilar between the two cases. Finally, a clinical analysis of both cases was realized with the contribution of the therapists to investigate possible differences within therapy sessions. Statistical analyses revealed negative means of affective behavior for couple A in the pre-intervention assessment and positive means in the post-intervention assessment. Partners from couple B had negative means of affective behavior in the pre- and post-intervention assessments. Results concerning coparental and romantic satisfaction differed: Couple A’s coparental satisfaction slightly increased and the romantic satisfaction somewhat decreased, whereas couple B’s coparental satisfaction remained stable and the romantic satisfaction slightly increased between the pre- and post-intervention assessments. The clinical analysis revealed that the interactional quality of couple A slightly improved within therapy sessions and that both partners succeeded in working together as coparents, notwithstanding their romantic distress. Couple B conveyed coparental distress and exhibited poor interactional quality throughout therapy sessions (e.g., repeated criticism and contempt). This study contributes to enriching the more traditional empirical research methods in the field of couple psychotherapy, as it takes into account microlevel affective changes within parent couples’ interactions in addition to self-reported data. Furthermore, the analysis of therapy sessions supports the importance of working with affective behavior in couple therapy. (shrink)

La pensée de Heidegger sur le dieu cherche à trouver, retrouver ou découvrir pour celui-ci et dans son histoire une dimension originaire et inaugurale et en même temps non-métaphysique, une voix qui parle dans un autre langage à venir et qui soit celle du monde et des mortels. Cette considération du dieu se rencontre aussi dans les tentaives mystiques d'Orient, en particulier dans le soufisme de la voie (tarika, طريقة) d'Ibn 'Arabi, qui retrouve son dieu autrement que dans sa dimension (...) de créateur. Ce dieu se révèle comme intrinsèque au monde - il n'est jamais sans monde, et surtout il s'avère avoir l'homme pour gardien, pour berger de sa parole et de ce même monde. Le points de convergence des deux pensées sont multiples. Nous offrons ici l'ébauche d'un dialogue qui s'avérera certainement très fructueux pour la pensée du dieu, surtout compte tenu des recherches actuelles concernant le sens du spirituel et du religieux. Le recueillement, l'intériorité qui dépasse la volonté et le défi qu'ils posent à la subjectivité sont au cœur des articlations que nous établissons das ce texte. (shrink)

The purpose of this article is twofold. It first seeks to prove that the notion of facticity in Heidegger’s work saw a major change after Being and Time. While several studies did deal with facticity as it appeared before the magnus opus and show the influence it had on the latter’s development, hardly any have dealt with what happens to facticity after Sein und Zeit. This is mostly because facticity, as it imploded, took on different names which fall under the (...) heading of ground-attunements. Secondly, I will show the ambivalent character of this new facticity, where many essential notions, such as thrownness, truth, attunement and guilt, shifted meanings, sometimes almost imperceptibly or surreptitiously. I will show that this ambivalence comes from the fact that the shift in question allowed for an opening of facticity while at the same time bringing in restrictive limits, and thus a closing-off of certain essential issues. This has left several adumbrated questions, such as responsibility, in abeyance. (shrink)

Ce livre propose d'aller au plus intime de la pensée heideggerienne dans sa maturité, qui récapitule ses moments clefs au sein de la constellation des quatre : les dieux, les mortels, la terre et le ciel ; pour découvrir, comme vérité de la relation entre eux, la dimension divine, disposée, dispensée, plurivoque et déterminante dans l'avènement à partir de l'événement appropriant, l'Ereignis. Arriver à cet envoi destinal du divin comme essentiel à la pensée de Heidegger, n'a pu se faire, qu'en (...) prenant d'abord le chemin du dieu heideggerien, pour en dégager le sens et le dépasser vers son fondement puis ce qui a rendu ce dernier possible : ce sur quoi il repose, même dans un oubli, dont les textes ne donnent le sens que sous des moments précis, aboutissant, dans leur être-ensemble et les-uns-pour-les-autres, à l'installation d'un monde par l'Ereignis sous le signe du divin. Il a fallu donc dégager ce qu'est le dieu de ses sens accumulés - en passant par le Dieu créateur, au dieu qui sauvegarde puis au dieu Inconnu - pour retrouver ce qui le donne comme tel, et ensuite chercher la trace de ce don. Ce travail nous a permis de déceler, au fur des textes - non sans surprise et même quelque joie - les traces et les opérations du divin auprès de chacun des éléments de ce qui est devenu le Quadriparti. Une fois ce dégagement effectué avec le plus de précision possible, nous avons pu en identifier les modalités au sein du Geviert, sa manière de " s'installer ", toujours différente, et ses conséquences sur le monde et le destinal. Cela nous a permis enfin d'entreprendre un changement éclairant dans le sens de plusieurs topoi heideggeriens, à savoir l'histoire, l'art, la parole et le poème - éclairage qui donne à chacun son sens fondamental depuis l'expression divine. Ce travail se veut aussi, dans ses dernières pages, un questionnement renouvelé sur les problèmes fondamentaux du divin chez Heidegger, et demande donc de reprendre les textes dans une la perspective qu'il ouverte pour en développer toute la portée. (shrink)

On se propose de penser enfin et de retrouver le sens du Göttliche heideggerien en tant que tel, nettement distingué du seul Dieu et du Sacré, dans la constellation des quatre du Geviert. Nous considérons alors le divin dans les premiers travaux sur Hölderlin, où Heidegger reconnaît déjà sa présence dans la pensée sur les mortels, la terre, le ciel et le monde, et dans leurs relations respectives qui restaient encore à élucider. Par la suite, le travail sur le rassemblement (...) qui caractérise la Kehre permettra à Heidegger de déterminer le divin comme don au sein du Sacré. A partir de là, nous assistons à un développement pluriel du sens du divin selon sa position en vis-à-vis et auprès de chacun des quatre, puis dans l’histoire destinale et au sein de la différence et du cercle rassemblant : la quadrature du cercle en tant qu’énigme-mystère s’avère alors comme lieu de rencontre du divin en tant que l’Inconnu.This paper aims at finally ponder about and find some meaning in the Heidegerrian Göttliche as such, clearly distinguished from the mere God or the Holy, in the constellation of the Geviert’s four elements. We consider the divine in the first work done on Hölderlin where Heidegger detects its presence in the thought dealing with mortals, earth, heaven and the world, and in their several respective relationships he was further to elucidate. Later, the work done on the gathering which marks the Kehre enables Heidegger to determine the divine as a gift from within the Holy. We then find a multiple development of the divine’s meaning through its position over-against and along each one of the four, then in destinal history and within the difference and the gathering circle : the four sidedness of the circle as a riddle turns out to be the meeting place for the divine as the unknown. (shrink)

On se propose de penser enfin et de retrouver le sens du Göttliche heideggerien en tant que tel, nettement distingué du seul Dieu et du Sacré, dans la constellation des quatre du Geviert. Nous considérons alors le divin dans les premiers travaux sur Hölderlin, où Heidegger reconnaît déjà sa présence dans la pensée sur les mortels, la terre, le ciel et le monde, et dans leurs relations respectives qui restaient encore à élucider. Par la suite, le travail sur le rassemblement (...) qui caractérise la Kehre permettra à Heidegger de déterminer le divin comme don au sein du Sacré. À partir de là, nous assistons à un développement pluriel du sens du divin selon sa position en vis-à-vis et auprès de chacun des quatre, puis dans l'histoire destinale et au sein de la différence et du cercle rassemblant : la quadrature du cercle en tant qu'énigme-mystère s'avère alors comme lieu de rencontre du divin en tant que l'Inconnu. This paper aims at finally ponder about and find some meaning in the Heidegerrian Göttliche as such, clearly distinguished from the mere God or the Holy, in the constellation of the Geviert's four elements. We consider the divine in the first work done on Hölderlin where Heidegger detects its presence in the thought dealing with mortals, earth, heaven and the world, and in their several respective relationships he was further to elucidate. Later, the work done on the gathering which marks the Kehre enables Heidegger to determine the divine as a gift from within the Holy. We then find a multiple development of the divine's meaning through its position over-against and along each one of the four, then in destinai history and within the difference and the gathering circle : the four sidedness of the circle as a riddle turns out to be the meeting place for the divine as the unknown. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp hypotheses were (...) defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...) that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)

This paper presents the model of ‘bounded revision’ that is based on two-dimensional revision functions taking as arguments pairs consisting of an input sentence and a reference sentence. The key idea is that the input sentence is accepted as far as (and just a little further than) the reference sentence is ‘cotenable’ with it. Bounded revision satisfies the AGM axioms as well as the Same Beliefs Condition (SBC) saying that the set of beliefs accepted after the revision does not depend (...) on the reference sentence (although the posterior belief state does depend on it). Bounded revision satisfies the Darwiche–Pearl (DP) axioms for iterated belief change. If the reference sentence is fixed to be a tautology or a contradiction, two well-known one-dimensional revision operations result. Bounded revision thus naturally fills the space between conservative revision (also known as natural revision) and moderate revision (also known as lexicographic revision). I compare this approach to the two-dimensional model of ‘revision by comparison’ investigated by Fermé and Rott (Artif Intell 157:5–47, 2004 ) that satisfies neither the SBC nor the DP axioms. I conclude that two-dimensional revision operations add substantially to the expressive power of qualitative approaches that do not make use of numbers as measures of degrees of belief. (shrink)

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in (...) the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann. (shrink)

Belief revision theory aims to describe how one should change one’s beliefs when they are contradicted by newly input information. The guiding principle of belief revision theory is to change one’s prior beliefs as little as possible in order to maintain consistency with the new information. Learning theory focuses, instead, on learning power: the ability to arrive at true beliefs in a wide range of possible environments. The goal of this paper is to bridge the two approaches by providing a (...) learning theoretic analysis of the learning power of belief revision methods proposed by Spohn, Boutilier, Darwiche and Pearl, and others. The results indicate that learning power depends sharply on details of the methods. Hence, learning power can provide a well-motivated constraint on the design and implementation of concrete belief revision methods. (shrink)

Close connections between probability theory and the theory of belief change emerge if the codomain of probability functions is extended from the real-valued interval [0, 1] to a hyperreal interval with the same limits. Full beliefs are identified as propositions with a probability at most infinitesimally smaller than 1. Full beliefs can then be given up, and changes in the set of full beliefs follow a pattern very close to that of AGM revision. In this contribution, iterated revision is investigated. (...) The iterated changes in the set of full beliefs generated by repeated revisions of a hyperreal probability function can, semantically, be modelled with the same basic structure as the sphere models of belief change theory. The changes on the set of full beliefs induced by probability revision satisfy the Darwiche–Pearl postulates for iterated belief change. (shrink)

In this paper we study changes of beliefs in a ranking-theoretic setting using non-extremal implausibility thresholds for belief. We represent implausibilities as ranks and introduce natural rank changes subject to a minimal change criterion. We show that many of the traditional AGM postulates for revision and contraction are preserved, except for the postulate of Preservation which is invalid. The diagnosis for belief contraction is similar, but not exactly the same. We demonstrate that the one-shot versions of both revision and contraction (...) can be represented as revisions based on semiorders, but in two subtly different ways. We provide sets of postulates that are sound and complete in the sense that they allow us to prove representation theorems. We show that, and explain why, the classical duality between revision and contraction, as exhibited by the Levi and Harper identities, is partly broken by threshold-based belief changes. We also study the logic of iterated threshold-based revision and contraction. The traditional Darwiche-Pearl postulates for iterated revision continue to hold, as well as two additional postulates that characterize ranking-based revision as a restricted `improvement' operator. We investigate the dual notion of iterated threshold-based belief contraction and provide a new set of postulates for it, characterizing contraction as a restricted 'degrading' operator. (shrink)

In this paper, I outline and defend an alternative to Hartian legal theory that accepts the Hartian theory of a legal system yet rejects the Hartian theory of legal content in favor of a non-positivist alternative. I call this the- ory the justificatory view. A key argument advanced here in support of the justificatory view relies on the problem of theoretical disagreement that Ronald Dworkin poses for Hartian positivism. Moreover, I argue that a vir- tue of the justificatory view is (...) that its hybrid nature shields it from the forceful criticism that Brian Leiter marshals against Dworkin’s legal theory. As Leiter observes, though Dworkin’s legal theory may do better than posi- tivism with respect to explaining the marginal phenomenon of theoretical disagreement among legal officials, Dworkinian legal theory suffers the much greater failing of being unable to explain the background of massive decisional agreement characteristic of legal systems. I argue that because the justificatory view accepts and rests upon the Hartian theory of a legal system, it is no less able than Hartian legal theory to explain this back- ground of massive decisional agreement.Resumen:En este artículo esbozo y defiendo una alternativa a la teoría jurídica hartiana, que si bien acepta la teoría hartiana del sistema jurídico, re- chaza sin embargo la teoría hartiana del contenido jurídico y aboga por una alternativa no-positivista. Llamo a esta teoría la postura de justificación. Un argumento clave para defender la postura de justificación se erige sobre el problema del desacuerdo teórico que Ronald Dworkin formuló al positivismo hartiano. Además, sostengo que una de las virtudes de esta postura de justificación es que su naturaleza híbrida la protege de las enérgicas críticas que plantea Brian Leiter contra la teoría jurídica de Dworkin. Como observa Leiter, aunque la teoría jurídica de Dworkin sea más consistente que la teoría positivista para explicar el fenómeno marginal de los desacuerdos teóricos entre los oficiales del derecho, la teoría dworkiniana padece mucho más el problema de no poder explicar el contexto de acuerdos masivos en las decisiones que caracterizan a un sistema jurídico. Y esto lo sostengo porque la postura de justificación acepta y se basa en la teoría hartiana del sistema jurídico; por ello es igual de capaz que la teoría jurídica de Hart de explicar este contexto de decisiones que gozan de un acuerdo masivo. (shrink)

This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be suffcient to (...) establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

In this paper we propose a conditional logic called IBC to represent iterated belief revision systems. We propose a set of postulates for iterated revision which are a small variant of Darwiche and Pearl''s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. We establish a correspondence between iterated belief revision systems and IBC-models. Our representation theorem does not entail Gärdenfors'' Triviality Result.

In this paper we (Laura Giordano, Nicola Olivetti and myself) propose a conditional logic to represent iterated belief revision systems. We propose a set of postulates for belief revision which are a small variant of Darwiche and Pearl's ones.The resulting conditional logic has a standard semantics in terms of selection function models, and provides a natural representation of epistemic states. A Representation Theorem establishes a correspondence between iterated belief revision systems and conditional models. Our Representation Theorem does not entail Gärdenfors' (...) Triviality Result. (shrink)

Two of the major problems in AGM-style belief revision, namely the difficulties in accounting for iterated change and for Ramsey test conditionals, have satisfactory solutions in descriptor revision. In descriptor revision, the input is a metalinguistic sentence specifying the success condition of the operation. The choice mechanism selects one of the potential outcomes in which the success condition is satisfied. Iteration of this operation is unproblematic. Ramsey test conditionals can be introduced without giving rise to the paradoxical results that they (...) generate in other systems. In addition to standard Ramsey test conditionals, a more general variant of epistemic conditionals is defined, representing statements of the form ”if the belief state is changed to satisfy condition A then it will satisfy condition B”. An axiomatic characterization of such descriptor conditionals is presented. It is related in intricate ways to the KLM postulates for cumulative reasoning. (shrink)

Discussions of the issue of iterated belief revision are commonly accompanied by the presentation of three “concrete” operators: natural, restrained and lexicographic. This raises a natural question: What is so distinctive about these three particular methods? Indeed, the common axiomatic ground for work on iterated revision, the AGM and Darwiche-Pearl postulates, leaves open a whole range of alternative proposals. In this paper, we show that it is satisfaction of an additional principle of “Independence of Irrelevant Alternatives”, inspired by the literature (...) on Social Choice, that unites and sets apart our three “elementary” revision operators. A parallel treatment of iterated belief contraction is also given, yielding a family of elementary contraction operators that includes, besides the well-known “conservative” and “moderate” operators, a new contraction operator that is related to restrained revision. (shrink)