It is shown that both classical and intuitionistic propositional logics of an associative binary modality are undecidable. The proof is based on the deduction theorem for these logics.

It is shown that the expressive power of second-order propositional modal logic whose modalities are S4.2 or weaker is the same as that of second-order predicate logic.

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...) prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper. (shrink)

Entscheidungen verweisen in einem begrifflichen Sinne auf Gründe. Entscheidungssysteme bieten eine probabilistische Verlässlichkeit als Rechtfertigung von Empfehlungen an. Doch nicht für alle Situationen mögen Verlässlichkeitsgründe auch angemessene Gründe sein. Damit eröffnet sich die Idee, die Güte von Gründen von ihrer Angemessenheit zu unterscheiden. Der Aufsatz betrachtet an einem Beispiel, einem KI-Lügendetektor, die Frage, ob eine (zumindest aktuell nicht gegebene) hohe Verlässlichkeit den Einsatz rechtfertigen kann. Gleicht er nicht einem Richter, der anhand einer Statistik Urteile fällen würde?

This book presents the proceedings of the 2nd Karl Schwarzschild Meeting on Gravitational Physics, focused on the general theme of black holes, gravity and information. Specialists in the field of black hole physics and rising young researchers present the latest findings on the broad topic of black holes, gravity, and information, highlighting its applications to astrophysics, cosmology, particle physics, and strongly correlated systems.

Persons infected with the Human Immunodeficiency Virus often experience intermittent life-threatening infections, a progressive decrease in cognitive abilities, and a loss of capacity to communicate their wishes to their family and medical care providers. Accordingly, AIDS patients are among those most likely to benefit from the increased availability of legally recognized forms of advance care planning. Although the three countries examined in this article differ greatly in the prevalence of HIV infection, the legal status of advance directives, and in the (...) attitudes toward their use, a collection of case studies is used to demonstrate that an ability to address the specific needs, values and goals of individual patients is promoted by the availability of a variety of options for implementing advance directives or health care proxies. The conclusion of the analysis is that the best option in a specific context will depend upon differences in individual values and medical objectives of the sort discussed in the case studies. Das mit der HIV-Infektion verbundene Krankheitsbild ist durch wechselnde lebensbedrohliche Infektionen und den fortschreitenden Verfall kognitiver Fähigkeiten gekennzeichnet. Es führt zudem häufig zum Verlust der Möglichkeit, Behandlungswünsche gegenüber Ärzten und Angehörigen zu äußern. Deshalb gehören besonders AIDS-Patienten zu denjenigen, die von rechtlich anerkannten vorsorglichen Patientenverfügungen profitieren werden.In diesem Artikel werden drei Länder betrachtet, die sich hinsichtlich der Häufigkeit des Auftretens der HIV-Infektion sowie des rechtlichen Status von und der Einstellung zu Patientenverfügungen erheblich unterscheiden. Fallstudien belegen allerdings, daß nicht allein die kulturellen und sozialen Bedingungen für die jeweils beste Form der Patientenverfügung ausschlaggebend sind. Voraussetzung für die Möglichkeit, den Bedingungen, Wert- und Zielvorstellungen des individuellen Patienten zu entsprechen, ist auf jeden Fall die Verfügbarkeit unterschiedlicher Formen von Patienten- und Betreuungsverfügungen. Auch innerhalb eines Kulturkreises müssen daher verschiedene Formen vorsorglicher Willensäußerungen des Patienten rechtlich anerkannt werden. Welche Art von Verfügung jeweils die beste Option darstellt, ist dabei abhängig von medizinischen Bedingungen und persönlichen Wertvorstellungen, wie sie in den Fallstudien diskutiert werden. (shrink)

Infants can see someone pointing to one of two buckets and infer that the toy they are seeking is hidden inside. Great apes do not succeed in this task, but, surprisingly, domestic dogs do. However, whether children and dogs understand these communicative acts in the same way is not yet known. To test this possibility, an experimenter did not point, look, or extend any part of her body towards either bucket, but instead lifted and shook one via a centrally pulled (...) rope. She did this either intentionally or accidentally, and did or did not address her act to the subject using ostensive cues. Young 2-year-old children but not dogs understood the experimenter’s act in intentional conditions. While ostensive pulling of the rope made no difference to children’s success, it actually hindered dogs’ performance. We conclude that while human children may be capable of inferring communicative intent from a wide variety actions, so long as these actions are performed intentionally, dogs are likely to be less flexible in this respect. Their understanding of communicative intention may be more dependent upon bodily markers of communicative intent, including gaze, orientation, extended limbs, and vocalisations. This may be because humans have come under selective pressure to develop skills for communicating with absent interlocutors – where bodily co-presence is not possible. (shrink)

Religious beliefs, it has been noted, are often hard to disprove. While this would be a shortcoming for beliefs whose utility was connected to their accuracy, it is actually necessary in the case of beliefs whose function bears no connection to how accurate they are. In the case of religions and other ideologies that serve to promote prosocial behaviour this leads to the need to protect belief systems against potentially disruptive counterevidence while maintaining their relevance. Religions turn out to be (...) particularly adept at this because of the use they make of existing cognitive by-products to make them plausible without exposingthem overly to investigation. (shrink)

Scientificity is essentially methodology. The use of information technology as methodological instruments in science has been increasing for decades, this raises the question: Does this transform science? This question is the subject of the Special Issue in Minds and Machines “The epistemological significance of methods in computer simulation and machine learning”. We show that there is a technological change in this area that has three methodological and epistemic consequences: methodological opacity, reproducibility issues, and altered forms of justification.

"Konrad Talmont-Kaminski offers a very thoughtful and thought-provoking critique of the field and an alternative approach to magic, religion, and science that should spark some debate and further research Talmont-Kaminski has thrown down a challenge to the mainstream of anthropological thought about religion, and it is a challenge that we necessarily and gladly pick up." -- Anthropology Review Database "A philosophical naturalist's delight, this book - crisply written and carefully argued - weaves together insights about evolution, mind, and (...) society to explain how religions work and how secularisation threatens them." - Robert N. McCauley, Emory University Is religious belief a product of the mind? This book brings to light the multifaceted relationship between reason and religion. Religion as Magical Ideology examines the relationship between rationality and supernatural beliefs arguing that such beliefs are products of evolution, cognition and culture. The book does not offer a false rapprochement between reason and religion; instead, it explores their interrelationship as a series of complex adaptations between cognitive and cultural processes. Exploring the nature of the tension between religious traditions and reason, Religion as Magical Ideology develops a dual inheritance theory of religion - which combines the cognitive byproduct and prosocial adaptation accounts - and analyses the connection between the function of a belief and the degree of protection it gets from potential counter-evidence. With discussion ranging from individual cognitive mechanisms, general functional considerations, to the limits of evolutionary and cognitive processes, the book offers readers a systematic account of how cognition shapes religious beliefs and practices. (shrink)

Both science and religion are human endeavours that recruit and modify pre-existing human capacity to engage in epistemic vigilance. However, while science relies upon a focus on content vigilance, religion focusses on source vigilance. This difference is due, in turn, to the function of religious claims not being connected to their accuracy – unlike the function of scientific claims. Understanding this difference helps to understand many aspects of scientific and religious institutions.

The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars.