We present new probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment, called Zλ- and lexλ-entailment, which are parameterized through a value λ ∈ [0,1] that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of λ = 0 and λ = 1, the notions of Zλ- and lexλ-entailment coincide with probabilistic generalizations of Pearl’s entailment in System Z and Lehmann’s lexicographic entailment that have been recently introduced by the author. We show (...) that the notions of Zλ- and lexλ-entailment have similar properties as their classical counterparts. In particular, they both satisfy the rationality postulates of System P and the property of Rational Monotonicity. Moreover, Zλ-entailment is weaker than lexλ-entailment, and both Zλ- and lexλ-entailment are proper generalizations of their classical counterparts. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default reasoning in System (...) . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations of (...) both their classical counterparts and the classical notion of logical entailment for conditional constraints. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

The ability to conduct logical reasoning is a fundamental aspect of intelligent behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, symbolic methods from the field of knowledge representation and reasoning have been used to equip agents with capabilities that resemble human reasoning qualities. More recently, however, there has been an increasing interest in applying alternative approaches based on machine learning rather than logic-based formalisms to tackle this kind of tasks. Here, we make use of (...) state-of-the-art methods for training deep neural networks to devise a novel model that is closely coupled to symbolic reasoning methods, and thus able to learn how to effectively perform basic ontology reasoning. This term describes an important and at the same time very natural kind of problem settings where the rules for conducting reasoning are specified alongside with the actual information. Many problems in practice may be viewed as such reasoning tasks, which is why the presented approach is applicable to a plethora of important real-world problems. To demonstrate the effectiveness of the suggested method, we present the outcomes of several experiments that have been conducted on both toy datasets as well as real-world data, which show that our model learned to perform precise reasoning on a number of diverse inference tasks that require comprehensive deductive proficiencies. Furthermore, it turned out that the suggested model suffers much less from different obstacles that prohibit symbolic reasoning. (shrink)

ABSTRACT Reiter's default logic is one of the most prominent and well-studied approaches to nonmonotonic reasoning. Its evolution has resulted in diverse variants enjoying many interesting properties. This process however seems to be diverging because it has led to default logics that are difficult to compare due to different formal characterizations—sometimes even dealing with different objects of discourse. This problem is addressed in this paper in two ways. One the one hand, we elaborate on the relationships between different types of (...) default logics and discuss their differences wrt some basic properties. In particular, we show how two recently proposed variants, namely rational and CA-default logic, are related to each other and existing default logics. As an interesting byproduct, we obtain a cumulative counterpart to Lukasiewicz' variant of default logic. The resulting system is insofar surprising since it necessitates to refine the canonical way of assuring cumulativity in default logics. On the other hand, we pursue an integrating approach. We give a translation embedding rational and CA-default logic into a recently developed framework for default logics. This allows us not only to classify these variants, but it moreover provides us with semantical underpinnings that have been lacking so far. (shrink)

This paper examines the relationships between the many-valued logics G~ and Gn~ of Esteva, Godo, Hajek, and Navara, i.e., Godel logic G enriched with Łukasiewicz negation, and neighbors of intuitionistic logic. The popular fragments of Rauszer's Heyting-Brouwer logic HB admit many-valued extensions similar to G which may likewise be enriched with Łukasiewicz negation; the fuzzy extensions of these logics, including HB, are equivalent to G ~, as are their n-valued extensions equivalent to Gn~ for any n ≥ 2. These enriched (...) systems extend Wansing's logic I4C4, showing that Łukasiewicz negation is a species of Nelson's negation of constructible falsity and yielding a Kripke-style semantics for G~ and Gn~ to complement the many-valued semantics. (shrink)

Issues of reliability are claiming center-stage in the epistemology of machine learning. This paper unifies different branches in the literature and points to promising research directions, whilst also providing an accessible introduction to key concepts in statistics and machine learning – as far as they are concerned with reliability.

Big Ideas for Little Kids includes everything a teacher, a parent, or a college student needs to teach philosophy to elementary school children from picture books. Written in a clear and accessible style, the book explains why it is important to allow young children access to philosophy during primary-school education. Wartenberg also gives advice on how to construct a "learner-centered" classroom, in which children discuss philosophical issues with one another as they respond to open-ended questions by saying whether they agree (...) or disagree with what others have said. (shrink)

Cette étude essaye d’établir qu’il y a deux notions très différentes de « fondation » à l’œuvre dans les Recherches logiques de Husserl. Dans la IIIème Recherche, où le terme est formellement introduit, lorsqu’il se demande quels sont les contenus qui peuvent exister d’une manière autonome (indépendants) et lesquels peuvent exister uniquement en tant que moments d’autre chose (dépendants), Husserl suit ce que j’appelle un « modèle ontologique ». Selon ce modèle, le concret possède une priorité sur à l’abstrait qui (...) est fondé en lui. Dans la VIème Recherche, en revanche, Husserl s’oriente principalement sur un « modèle gnoséologique » qui voit le complexe comme fondé sur ce qui est relativement simple, étant donné que les expériences d’ordre supérieur (telles les perceptions de types d’objets plus complexes) sont « fondées sur » des expériences plus simples, bien qu’elles ne puissent pas y être réduites. L’exemple principal ici est celui des intuitions catégoriales : fondées sur les intuitions sensibles, elles n’y sont pas réductibles. Mais cette distinction entre deux sens différents du terme de « fondation » peut également nous aider à mieux comprendre de nombreuses thèses husserliennes plutôt controversées. Par exemple, elle peut nous permettre de mieux comprendre dans quelle mesure faire l’expérience d’un être humain comme un tout se fonde sur l’expérience d’un corps physique, et cela même si l’étant que nous rencontrons inclut à la fois des aspects corporels et des aspects spirituels – les deux étant vus, d’une manière essentielle, comme des moments de cette unique personne qui fait l’objet de notre expérience. (shrink)

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

In this book, T. M. Scanlon offers new answers to these questions, as they apply to the central part of morality that concerns what we owe to each other.

This paper is an exposition and evaluation of the Agustín Rayo's views about the epistemology and metaphysics of mathematics, as they are presented in his book The Construction of Logical Space.

In recent years an increasing number of psychologists have begun to explore the prevalence, causes and effects of ordinary people’s intuitions about moral realism. Many of these studies have lacked in construct validity, i.e., they have failed to measure moral realism. My aim in this paper accordingly is to motivate and guide methodological improvements. In analysis of prominent existing measures, I develop general recommendations for overcoming ten prima facie serious worries about research on folk moral realism. G1 and G2 require (...) studies’ answer choices to be as metaethically comprehensive as methodologically feasible. G3 and G4 prevent fallacious inferences from intuitions about related debates. G5 and G6 limit first-order moral and epistemic influences. G7 address studies’ instructions. And G8 and G9 suggest tests of important psychological presuppositions. (shrink)

This volume is a study of the influence of Timaeus on the development of Western cosmology in three axial periods of European culture: Late Antiquity, Middle Ages and Renaissance.

Thomas Reid is now recognized as one of the towering figures of the Enlightenment. Best known for his published writings on epistemology and moral theory, he was also an accomplished mathematician and natural philosopher, as an earlier volume of his manuscripts edited by Paul Wood for the Edinburgh Reid Edition, Thomas Reid on the Animate Creation, has shown. The Correspondence of Thomas Reid collects all of the known letters to and from Reid in a fully annotated form. (...) Letters already published by Sir William Hamilton and others have been reedited, and roughly half of the letters included appear in print for the first time. Writing in 1802, Reid's disciple and biographer Dugald Stewart doubted that Reid's correspondence &"would be generally interesting.&" This collection proves otherwise, for the letters illuminate virtually every aspect of Reid's life and career and, in some instances, provide us with invaluable evidence about activities otherwise undocumented in his manuscripts or published works. Through his correspondence we can trace Reid's relations with contemporaries such as David Hume and his colleagues at both King's College, Aberdeen, and the University of Glasgow, as well as his engagement with the most controversial philosophical, scientific, and political issues of his day. If anything, the letters assembled here serve as the starting point for understanding Reid and his place in the Enlightenment. (shrink)

O logice Stoików pisali Prantl, Zeller, Brochard. Żaden z nich nie zrozumiał tej logiki, bo żaden z nich nie miał dostatecznego wykształcenia logicznego. Co prawda, nie można im nawet robić z tego zarzutu, bo skądże się mieli logiki nauczyć? Sądy ich o logice stoickiej nie mają żadnej wartości. Dopiero dziś wiemy, dzięki logice matematycznej, że logika Stoików jest systemem całkowicie różnym od syllogistyki Arystotelesa. Logika stoicka bowiem jest odpowiednikiem dzisiejszej "teorji dedu...

Feeling good: four ways -- Finding that feeling -- The place of pleasure -- Knowing what's what -- Making things happen -- Being good -- Love and friendship -- Putting it together.

Conciliatory theories of disagreement require that one lower one’s confidence in a belief in the face of disagreement from an epistemic peer. One question about which people might disagree is who should qualify as an epistemic peer and who should not. But when putative epistemic peers disagree about epistemic peerhood itself, then Conciliationism makes contradictory demands and paradoxes arise.