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 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)

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)

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)

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 volume brings together for the first time a significant number of Reid's manuscript papers on natural history, physiology and materialist metaphysics. An important contribution not only to Reid studies but also to our understanding of eighteenth-century science and its context.

Thomas Reid was a philosopher who founded the Scottish school of 'common sense'. Much of Reid's work is a critique of his contemporary, David Hume, whose empiricism he rejects. In this work, written after Reid's appointment to a professorship at the university of Glasgow, and published in 1785, he turns his attention to ideas about perception, memory, conception, abstraction, judgement, reasoning and taste. He examines the work of his predecessors and contemporaries, arguing that 'when we find philosophers maintaining that (...) there is no heat in the fire, nor colour in the rainbow … we may be apt to think the whole to be only a dream of fanciful men, who have entangled themselves in cobwebs spun out of their own brain'. Written by one of the Scottish Enlightenment's most important thinkers, this work brings to life the intellectual debates of the time. (shrink)

Thomas Aquinas produced a voluminous body of work on moral theory, and much of that work is on virtue, particularly the status and value of the virtues as principles of virtuous acts, and the way in which a moral life can be organized around them schematically. Thomas Osborne presents Aquinas's account of virtue in its historical, philosophical and theological contexts, to show the reader what Aquinas himself wished to teach about virtue. His discussion makes the complexities of Aquinas's (...) moral thought accessible to readers despite the differences between Thomas's texts themselves, and the distance between our background assumptions and his. The book will be valuable for scholars and students in ethics, medieval philosophy, and theology. (shrink)

There has been an explosion of interest in the metaphysics of fundamentality in recent decades. The consensus view, called metaphysical foundationalism, maintains that there is something absolutely fundamental in reality upon which everything else depends. However, a number of thinkers have chal- lenged the arguments in favor of foundationalism and have proposed competing non-foundationalist ontologies. This paper provides a systematic and critical introduction to metaphysical foundationalism in the current literature and argues that its relation to ontological dependence and substance should (...) be qualified in important ways. (shrink)

In a recent paper Weinberg (2007) claims that there is an essential mark of trustworthiness which typical sources of evidence as perception or memory have, but philosophical intuitions lack, namely that we are able to detect and correct errors produced by these “hopeful” sources. In my paper I will argue that being a hopeful source isn't necessary for providing us with evidence. I then will show that, given some plausible background assumptions, intuitions at least come close to being hopeful, if (...) they are reliable. If this is true, Weinberg's new challenge comes down to the claim that philosophical intuitions are not reliable since they are significantly unstable. In the second part of my paper I will argue that and why the experimentally established instability of folk intuitions about philosophical cases does not show that philosopher's expert intuitions about these cases are instable. (shrink)

I critically examine some deflationary theories of properties, according to which properties are ‘shadows of predicates’ and quantification over them serves a mere quasi-logical function. I start by considering Hofweber’s internalist theory, and pose a problem for his account of inexpressible properties. I then introduce a theory of properties that closely resembles Horwich’s minimalist theory of truth. This theory overcomes the problem of inexpressible properties, but its formulation presupposes the existence of various kinds of abstract objects. I discuss some ways (...) to reduce these existence assumptions, but ultimately suggest that deflationists can hardly avoid quantification over abstract objects of one sort or another. I conclude that property deflationism is perhaps not as deflationary as some philosophers want it to be, but that it’s still apt to call the position ‘deflationary’. (shrink)

Looking back on it, it seems almost incredible that so many equally educated, equally sincere compatriots and contemporaries, all drawing from the same limited stock of evidence, should have reached so many totally different conclusions---and always with complete certainty.

Issues concerning patients' rights are at the center of bioethics, but the political basis for these rights has rarely been examined. In Bioethics in a Liberal Society: The Political Framework of Bioethics Decision Making , Thomas May offers a compelling analysis of how the political context of liberal constitutional democracy shapes the rights and obligations of both patients and health care professionals. May focuses on how a key feature of liberal society -- namely, an individual's right to make independent (...) decisions -- has an impact on the most important relational facets of health care, such as patients' autonomy and professionals' rights of conscience. Although a liberal political framework protects individual judgments, May asserts that this right is based on the assumption of an individual's competency to make sound decisions. May uses case studies to examine society's approach to medical decision making when, for reasons ranging from age to severe mental disorder, a person lacks sufficient competency to make independent and fully informed choices. To protect the autonomy of these vulnerable patients, May emphasizes the need for health care ethics committees and ethics consultants to help guide the decision-making process in clinical settings. Bioethics in a Liberal Society is essential reading for all those interested in understanding how bioethics is practiced within our society. (shrink)

What are the truth conditions of want ascriptions? According to an influential approach, they are intimately connected to the agent’s beliefs: ⌜S wants p⌝ is true iff, within S’s belief set, S prefers the p worlds to the not-p worlds. This approach faces a well-known problem, however: it makes the wrong predictions for what we call (counter)factual want ascriptions, wherein the agent either believes p or believes not-p—for example, ‘I want it to rain tomorrow and that is exactly what is (...) going to happen’ or ‘I want this weekend to last forever, but of course it will end in a few hours’. We solve this problem. The truth conditions for want ascriptions are, we propose, connected to the agent’s conditional beliefs. We substantiate this connection by pursuing a striking parallel between (counter)factual and non-(counter)factual want ascriptions on the one hand and counterfactual and indicative conditionals on the other. (shrink)

T. H. Green's Prolegomena to Ethics is a classic of modern philosophy. It begins with Green's idealist attack on empiricist metaphysics and epistemology and develops a perfectionist ethical theory that aims to bring together the best elements in the ancient and modern traditions, and that provides the moral foundations for Green's own distinctive brand of liberalism. David Brink's new edition will restore this great work to prominence, after two decades in which it has been hard to obtain. The present edition (...) uses the text of the fifth edition, accompanied by a new introductory essay, bibliographical essay, and index. Translations are provided for Green's quotations from other languages. Of particular importance is the editor's extended introductory essay, which situates the Prolegomena in its intellectual context, sympathetically but critically engages its main themes, and explains Green's enduring significance for the history of philosophy and contemporary ethical theory. Students and scholars of the history of ethics, ethical theory, political philosophy, and nineteenth century philosophy will find this new edition an invaluable resource. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)