Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completness with respect to various models and we study the problem of realization.

In this paper we discuss extensions of Feferman's theory T 0 for explicit mathematics by the so-called limit and Mahlo axioms and present a novel approach to constructing natural recursion-theoretic models for systems of explicit mathematics which is based on nonmonotone inductive definitions.

Justification logics are modal logics that include justifications for the agent's knowledge. So far, there are no decidability results available for justification logics with negative introspection. In this paper, we develop a novel model construction for such logics and show that justification logics with negative introspection are decidable for finite constant specifications.

This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal (...) explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic. (shrink)

We first look at an existing infinitary sequent system for common knowledge for which there is no known syntactic cut-elimination procedure and also no known non-trivial bound on the proof-depth. We then present another infinitary sequent system based on nested sequents that are essentially trees and with inference rules that apply deeply inside these trees. Thus we call this system “deep” while we call the former system “shallow”. In contrast to the shallow system, the deep system allows one to give (...) a straightforward syntactic cut-elimination procedure. Since both systems can be embedded into each other, this also yields a syntactic cut-elimination procedure for the shallow system. For both systems we thus obtain an upper bound of φ20 on the depth of proofs, where φ is the Veblen function. (shrink)

Buchholz’s Ω μ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz (Iterated (...) inductive definitions and subsystems of analysis: recent proof theoretic studies. Lecture notes in mathematics, vol. 897, pp. 189–233, Springer, Berlin, 1981). (shrink)

Common knowledge of a proposition A can be characterized by the following infinitary conjunction: everybody knows A and everybody knows that everybody knows A and everybody knows that everybody knows that everybody knows A and so on. We present a survey of deductive systems for the logic of common knowledge. In particular, we present two different Hilbert-style axiomatizations and two infinitary cut-free sequent systems. Further we discuss the problem of syntactic cut-elimination for common knowledge. The paper concludes with a list (...) of open problems. (shrink)

Internalization is a key property of justification logics. It states that justification logics internalize their own notion of proof which is essential for the proof of the realization theorem. The aim of this note is to show how to make use of internalization to track where an agent’s knowledge comes from and how to apply this to the problem of data privacy.

The problem of data privacy is to verify that confidential information stored in an information system is not provided to unauthorized users and, therefore, personal and other sensitive data remain private. One way to guarantee this is to distort a knowledge base such that it does not reveal sensitive information. In the present paper we will give a universal definition of the problem of knowledge base distortion. It is universal in the sense that is independent of any particular knowledge representation (...) formalism. We will then present a basic and general algorithm for knowledge base distortion to guarantee data privacy. This algorithm provides us with upper bounds for the complexity of the distortion problem. Moreover, we examine heuristics to improve its average performance. (shrink)

Systems of explicit mathematics provide an axiomatic framework for representing programs and proving properties of them. We introduce such a system with a new form of power types using a monotone power type generator. These power types allow us to model impredicative overloading. This is a very general form of type dependent computation which occurs in the study of object-oriented programming languages. We also present a set-theoretic interpretation for monotone power types. Thus establishing the consistency our system of explicit mathematics.

We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along (...) every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as a corollary. (shrink)

For some modal fixed point logics, there are deductive systems that enjoy syntactic cut-elimination. An early example is the system in Pliuskevicius [15] for LTL. More recent examples are the systems by the authors of this paper for the logic of common knowledge [5] and by Hill and Poggiolesi for PDL[8], which are based on a form of deep inference. These logics can be seen as fragments of the modal mu-calculus. Here we are interested in how far this approach can (...) be pushed in general. To this end, we introduce a nested sequent system with syntactic cut-elimination which is incomplete for the modal mu-calculus, but complete with respect to a restricted language that allows only fixed points of a certain form. This restricted language includes the logic of common knowledge and PDL. There is also a traditional sequent system for the modal mu-calculus by Jäger et al. [9], without a syntactic cut-elimination procedure. We embed that system into ours and vice versa, thus establishing cut-elimination also for the shallow system, when only the restricted language is considered. (shrink)

We observe that removing contraction from a standard sequent calculus for first-order predicate logic preserves completeness for the modal fragment.

When we say “I know why he was late”, we know not only the fact that he was late, but also an explanation of this fact. We propose a logical framework of “knowing why” inspired by the existing formal studies on why-questions, scientific explanation, and justification logic. We introduce the Kyi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {K}}{}\textit{y}}_i$$\end{document} operator into the language of epistemic logic to express “agent i knows why φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}” and propose a Kripke-style semantics of such expressions in terms of knowing an explanation of φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}. We obtain two sound and complete axiomatizations w.r.t. two different model classes depending on different assumptions about introspection. Finally we connect our logic with justification logic technically by providing an alternative semantics and an in-depth comparison on various design choices. (shrink)

This paper presents a justification counterpart for dyadic deontic logic, which is often argued to be better than Standard Deontic Logic at representing conditional and contrary-to-duty obligations, such as those exemplified by the notorious Chisholm’s puzzle. We consider the alethic-deontic system (E) and present the explicit version of this system (JE) by replacing the alethic Box-modality with proof terms and the dyadic deontic Circ-modality with justification terms. The explicit representation of strong factual detachment (SFD) is given and finally soundness and (...) completeness of the system (JE) with respect to basic models and preference models is established. (shrink)

Eines der medizinischen Felder, in dem die ethische Diskussion um die „wunscherfüllende Medizin“ am intensivsten geführt wird, ist die Reproduktionsmedizin, die die Erfüllung des „Kinderwunsches“ verspricht. Strittig ist besonders, ob Sterilität als Krankheit definiert wird, die eine medizinische Intervention rechtfertigt, ob sich aus der Sterilität oder Infertilität lediglich ein Abwehr- oder auch ein positives Anspruchsrecht auf medizinische Ressourcen ergibt, ob legitime Fortpflanzungsmedizin Grenzen hat. Nach einer Übersicht über Eckpunkte der nationalen und internationalen Debatte beschreiben wir im zweiten Teil Ansichten zum (...) Status ungewollter Kinderlosigkeit, zum Recht auf Fortpflanzungsmedizin und zur möglichen Legitimität ihrer Begrenzung anhand der Ergebnisse unserer vom Bundesministerium für Bildung und Forschung (BMBF) geförderten Studien. Während der letzten fünf Jahre haben wir u. a. Paare mit und ohne Sterilitätsproblematik sowie verschiedene Expertengruppen qualitativ und standardisiert befragt. Die stark divergierenden Auffassungen konfrontieren wir im dritten Abschnitt mit internationalen Standards, zum anderen mit dem „Capability-Ansatz“ und dem freiheitsfunktionalen Liberalismus von Sen und Pauer-Studer. Dies ergibt, dass die Bereitstellung verschiedener Möglichkeiten der In-vitro-Fertilisations-(IVF-)Behandlung nicht lediglich einen Wunsch auf Elternschaft erfüllt sondern als die gesollte Erfüllung eines normativen Bedürfnissanspruchs begriffen werden muss. (shrink)

ZusammenfassungEines der medizinischen Felder, in dem die ethische Diskussion um die „wunscherfüllende Medizin“ am intensivsten geführt wird, ist die Reproduktionsmedizin, die die Erfüllung des „Kinderwunsches“ verspricht. Strittig ist besonders, ob Sterilität als Krankheit definiert wird, die eine medizinische Intervention rechtfertigt, ob sich aus der Sterilität oder Infertilität lediglich ein Abwehr- oder auch ein positives Anspruchsrecht auf medizinische Ressourcen ergibt, ob legitime Fortpflanzungsmedizin Grenzen hat. Nach einer Übersicht über Eckpunkte der nationalen und internationalen Debatte beschreiben wir im zweiten Teil Ansichten zum (...) Status ungewollter Kinderlosigkeit, zum Recht auf Fortpflanzungsmedizin und zur möglichen Legitimität ihrer Begrenzung anhand der Ergebnisse unserer vom Bundesministerium für Bildung und Forschung (BMBF) geförderten Studien. Während der letzten fünf Jahre haben wir u. a. Paare mit und ohne Sterilitätsproblematik sowie verschiedene Expertengruppen qualitativ und standardisiert befragt. Die stark divergierenden Auffassungen konfrontieren wir im dritten Abschnitt mit internationalen Standards, zum anderen mit dem „Capability-Ansatz“ und dem freiheitsfunktionalen Liberalismus von Sen und Pauer-Studer. Dies ergibt, dass die Bereitstellung verschiedener Möglichkeiten der In-vitro-Fertilisations-(IVF-)Behandlung nicht lediglich einen Wunsch auf Elternschaft erfüllt sondern als die gesollte Erfüllung eines normativen Bedürfnissanspruchs begriffen werden muss. (shrink)

ZusammenfassungEines der medizinischen Felder, in dem die ethische Diskussion um die „wunscherfüllende Medizin“ am intensivsten geführt wird, ist die Reproduktionsmedizin, die die Erfüllung des „Kinderwunsches“ verspricht. Strittig ist besonders, ob Sterilität als Krankheit definiert wird, die eine medizinische Intervention rechtfertigt, ob sich aus der Sterilität oder Infertilität lediglich ein Abwehr- oder auch ein positives Anspruchsrecht auf medizinische Ressourcen ergibt, ob legitime Fortpflanzungsmedizin Grenzen hat. Nach einer Übersicht über Eckpunkte der nationalen und internationalen Debatte beschreiben wir im zweiten Teil Ansichten zum (...) Status ungewollter Kinderlosigkeit, zum Recht auf Fortpflanzungsmedizin und zur möglichen Legitimität ihrer Begrenzung anhand der Ergebnisse unserer vom Bundesministerium für Bildung und Forschung (BMBF) geförderten Studien. Während der letzten fünf Jahre haben wir u. a. Paare mit und ohne Sterilitätsproblematik sowie verschiedene Expertengruppen qualitativ und standardisiert befragt. Die stark divergierenden Auffassungen konfrontieren wir im dritten Abschnitt mit internationalen Standards, zum anderen mit dem „Capability-Ansatz“ und dem freiheitsfunktionalen Liberalismus von Sen und Pauer-Studer. Dies ergibt, dass die Bereitstellung verschiedener Möglichkeiten der In-vitro-Fertilisations-(IVF-)Behandlung nicht lediglich einen Wunsch auf Elternschaft erfüllt sondern als die gesollte Erfüllung eines normativen Bedürfnissanspruchs begriffen werden muss. (shrink)

ZusammenfassungEines der medizinischen Felder, in dem die ethische Diskussion um die „wunscherfüllende Medizin“ am intensivsten geführt wird, ist die Reproduktionsmedizin, die die Erfüllung des „Kinderwunsches“ verspricht. Strittig ist besonders, ob Sterilität als Krankheit definiert wird, die eine medizinische Intervention rechtfertigt, ob sich aus der Sterilität oder Infertilität lediglich ein Abwehr- oder auch ein positives Anspruchsrecht auf medizinische Ressourcen ergibt, ob legitime Fortpflanzungsmedizin Grenzen hat. Nach einer Übersicht über Eckpunkte der nationalen und internationalen Debatte beschreiben wir im zweiten Teil Ansichten zum (...) Status ungewollter Kinderlosigkeit, zum Recht auf Fortpflanzungsmedizin und zur möglichen Legitimität ihrer Begrenzung anhand der Ergebnisse unserer vom Bundesministerium für Bildung und Forschung geförderten Studien. Während der letzten fünf Jahre haben wir u. a. Paare mit und ohne Sterilitätsproblematik sowie verschiedene Expertengruppen qualitativ und standardisiert befragt. Die stark divergierenden Auffassungen konfrontieren wir im dritten Abschnitt mit internationalen Standards, zum anderen mit dem „Capability-Ansatz“ und dem freiheitsfunktionalen Liberalismus von Sen und Pauer-Studer. Dies ergibt, dass die Bereitstellung verschiedener Möglichkeiten der In-vitro-Fertilisations-Behandlung nicht lediglich einen Wunsch auf Elternschaft erfüllt sondern als die gesollte Erfüllung eines normativen Bedürfnissanspruchs begriffen werden muss. (shrink)

Auf welchen normativen Grundlagen beruhte das NS-System? Mit welcher Rechtfertigung konnte der Führerwille dort zu einer Quelle des Rechts werden? Wie war es gemäß der NS-Strafgesetzgebung möglich, Handlungen zu bestrafen, die gegen kein geschriebenes Gesetz verstießen? Die in diesem Band versammelten und kommentierten Originaltexte geben Einblick in das Denken von Rechtstheoretikern, die mit dem Nationalsozialismus sympathisierten, und belegen deren Versuch, autoritäre und dem Rechtsstaat widersprechende Rechtsprinzipien zu legitimieren. Dabei zeigt sich ein überraschender und bis jetzt von der rechts- und moralphilosophischen (...) Forschung weitgehend unbeachteter Aspekt des NS-Unrechtssystems: der Versuch einer »Ethisierung« des Rechts und die damit verbundene Totalisierung des machtstaatlichen Einflusses. (shrink)

The newly updated Right and Wrong 2nd Edition is an accessible introduction to the major traditions in western philosophical ethics, written in a lively and engaging style. It is designed for entry-level ethics courses and includes real-life ethical scenarios chosen to appeal directly to students. Greatly expanded and improved, this successful text introduces students to the major ethical traditions, and provides a simple methodology for resolving ethical dilemmas Treats teleological and deontological approaches to ethics as the two most important traditions, (...) but now includes chapters on virtue ethics and the ethics of care The very accessible writing style speaks directly to students’ own experience Draws examples from three types of real-life ethical scenarios submitted by students: academic dishonesty, partying, and personal relationships Provides a concise treatment of this notoriously complex subject, perfect for entry-level ethics and applied ethics courses. (shrink)

When making decisions, humans can observe many kinds of information about others' activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others' solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers' solutions, popularity of solution elements among peers, similarity of peers' solutions to their own, and relative payoffs from (...) individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers' payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers' solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration. (shrink)

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)

Some theories of goodness are descriptively rich: they have much to say about what makes things good. Neo-Aristotelian accounts, for instance, detail the various features that make a human being, a dog, a bee good relative to facts about those forms of life. Famously, such theories of relative goodness tend to be comparatively poor: they have little or nothing to say about what makes one kind of being better than another kind. Other theories of goodness—those that take there to be (...) absolute goodness—are comparatively rich: they offer grounds for judging some types of things better than others because they have more absolute goodness. Moorean accounts, for example, can tell us that humans and human experiences are superior to bees and blades of grass. But such theories tend to be descriptively poor: they struggle to tell us in virtue of what this is so. In this essay we motivate and flesh out a view that splits the difference between accounts of goodness as relative and accounts of goodness as absolute. Such a view holds promise only if the mechanics of this kind of metaphysics of goodness can be worked out. Here we present a view on which the paradigm for absolute goodness is God and the paradigm for each kind of relative goodness is a divine idea. (shrink)

Proceedings of a conference held in Apr. 2008 in Washington, D.C.

Father Williams explains how the conscience is formed through our training and experiences and informed by the Holy Spirit, making it an essential tool for daily living. He uses familiar and surprising characters to illustrate the positive choices conscience can direct--and the disaster that results when a conscience is undeveloped or ignored. Questions he tackles include "Is it more important to be smart or good?""Is there a morally right thing to do in every situation?" and "Is the Christian moral life (...) an exciting adventure, or a necessary burden?" Rich, provocative, and practical for everyday decision making, KNOWING RIGHT FROM WRONG is a must-read for all who hunger for personal holiness. (shrink)

It is somewhat misleading to think of the Franciscans as forming a “school” in ethics, since there was a fair bit of diversity among Franciscans. Nonetheless, one can identify certain characteristic tendencies of Franciscan moral thought, and certain “celebrity” Franciscans whose views in ethics and moral psychology are particularly noteworthy. I shall first offer an overview of the general character of Franciscan moral thought in the late thirteenth and early fourteenth centuries and then turn to a more detailed examination of (...) the thought of John Duns Scotus (1265/66-1308) and William Ockham (c. 1288-1347) on three central matters of debate: the nature of the virtues, the relationship between intellect and will, and the relationship between moral requirements and the divine will. (shrink)