The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister. Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are admissible when (...) the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. (shrink)

We examine the proof-theoretic verificationist justification procedure proposed by Dummett. After some scrutiny, two distinct interpretations with respect to bases are advanced: the independent and the dependent interpretation. We argue that both are unacceptable as a semantics for propositional intuitionistic logic.

Several proof-theoretic notions of validity have been proposed in the literature, for which completeness of intuitionistic logic has been conjectured. We define validity for intuitionistic propositional logic in a way which is common to many of these notions, emphasizing that an appropriate notion of validity must be closed under substitution. In this definition we consider atomic systems whose rules are not only production rules, but may include rules that allow one to discharge assumptions. Our central result shows that Harrop’s rule (...) is valid under substitution, which refutes the completeness conjecture for intuitionistic logic. (shrink)

On analyse l’interprétation BHK de constantes logiques sur la base d’une prise en compte systématique de Prawitz, résultant en une reformulation de l’interprétation BHK dans laquelle l’assertabilité de propositions atomiques est déterminée par des systèmes de Post. On démontre que l’interprétation BHK reformulée rend davantage de propositions assertables que la logique propositionnelle intuitionniste rend prouvable. La loi de Mints est examinée en tant qu’exemple d’une telle proposition. La logique propositionnelle intuitionniste devrait par conséquent être considérée comme étant incomplète. Nous concluons (...) par une discussion sur l’adéquation de l’interprétation BHK de l’implication. (shrink)

On analyse l’interprétation BHK de constantes logiques sur la base d’une prise en compte systématique de Prawitz, résultant en une reformulation de l’interprétation BHK dans laquelle l’assertabilité de propositions atomiques est déterminée par des systèmes de Post. On démontre que l’interprétation BHK reformulée rend davantage de propositions assertables que la logique propositionnelle intuitionniste rend prouvable. La loi de Mints est examinée en tant qu’exemple d’une telle proposition. La logique propositionnelle intuitionniste devrait par conséquent être considérée comme étant incomplète. Nous concluons (...) par une discussion sur l’adéquation de l’interprétation BHK de l’implication. (shrink)

In this paper we are going to examine intuitionistic sequent calculus and its negation rules. We state new negation rules defining, in this way, a new sequent system. It will be used to clarify Gentzen's NJ and LJ systems isomorphism. These new negation rules are a direct reading of new natural deduction negation rules obtained by a slight modification of NJ rules. We also show that the new system is equivalent to LJ and that the Hauptsatz holds for it.

In the present paper we analyse how intuitionist negation relates to the concept of triviality. A proposition is trivial if it implies every other proposition. We claim that for natural deduction intuitionist logic such concept affords us a negation introduction rule schema that corresponds by the inversion principle to the usual negation elimination shcema, ex contradictionerm quodlibet.1.

The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister . Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are admissible (...) when the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus. (shrink)

JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: [email protected] Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: sanz@fchf.ufg.br -/- Consider two doxastic states belief and disbelief. Belief is taking a proposition to be true and disbelief taking it to be false. Judging also dichotomizes: accepting a proposition results in belief and rejecting in disbelief. Stating follows suit: asserting a proposition conveys belief and denying conveys (...) disbelief. Traditional logic implicitly focused on logical relations and processes needed in expanding and organizing systems of beliefs. Deducing a conclusion from beliefs results in belief of the conclusion. Deduction presupposes consequence: one proposition is a consequence of a set of a propositions if the latter logically implies the former. The role of consequence depends on its being truth-preserving: every consequence of a set of truths is true. This paper, which builds on previous work by the second author, explores roles of logic in expanding and organizing systems of disbeliefs. Aducing a conclusion from disbeliefs results in disbelief of the conclusion. Aduction presupposes contrequence: one proposition is a contrequence of a set of propositions if the set of negations or contradictory opposites of the latter logically implies that of the former. The role of contrequence depends on its being falsity-preserving: every contrequence of a set of falsehoods is false. A system of aductions that includes, for every contrequence of a given set, an aduction of the contrequence from the set is said to be complete. Historical and philosophical discussion is illustrated and enriched by presenting complete systems of aductions constructed by the second author. One such, a natural aduction system for Aristotelian categorical propositions, is based on a natural deduction system attributed to Aristotle by the first author and others. ADDED NOTE: Wagner Sanz reconstructed Aristotle’s logic the way it would have been had Aristole focused on constructing “anti-sciences” instead of sciences: more generally, on systems of disbeliefs. (shrink)

Após uma breve análise do problema da relação de relevancia entre o antecedente e o consequente de um condicional, fazemos uma análise de qual deve ser a estrutura de um critério de adequação para uma definição de relevancia em uma demonstração.

The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...) Seldin's normalization strategy to Peirce's rule by showing that every derivation Π in the implicational fragment can be transformed into a derivation Π' such that no application of Peirce's rule in Π' occurs above applications of →-introduction and →-elimination. As a corollary of Seldin's normalization strategy we obtain a form of Glivenko's theorem for the classical {→}-fragment. (shrink)

We present PhrasIS, a benchmark dataset composed of natural occurring Phrase pairs with Inference and Similarity annotations for the evaluation of semantic representations. The described dataset fills the gap between word and sentence-level datasets, allowing to evaluate compositional models at a finer granularity than sentences. Contrary to other datasets, the phrase pairs are extracted from naturally occurring text in image captions and news headlines. All the text fragments have been annotated by experts following a rigorous process also described in the (...) manuscript achieving high inter annotator agreement. In this work we analyse the dataset, showing the relation between inference labels and similarity scores. With 10K phrase pairs split in development and test, the dataset is an excellent benchmark for testing meaning representation systems. (shrink)

Why do humans menstruate while most mammals do not? Here, we present our answer to this long‐debated question, arguing that (i) menstruation occurs as a mechanistic consequence of hormone‐induced differentiation of the endometrium (referred to as spontaneous decidualization, or SD); (ii) SD evolved because of maternal–fetal conflict; and (iii) SD evolved by genetic assimilation of the decidualization reaction, which is induced by the fetus in non‐menstruating species. The idea that menstruation occurs as a consequence of SD has been proposed in (...) the past, but here we present a novel hypothesis on how SD evolved. We argue that decidualization became genetically stabilized in menstruating lineages, allowing females to prepare for pregnancy without any signal from the fetus. We present three models for the evolution of SD by genetic assimilation, based on recent advances in our understanding of the mechanisms of endometrial differentiation and implantation. Testing these models will ultimately shed light on the evolutionary significance of menstruation, as well as on the etiology of human reproductive disorders like endometriosis and recurrent pregnancy loss. (shrink)

I begin with a discussion of the value of privacy and what we lose without it. I then turn to the difficulties of preserving privacy for genetic information and other medical records in the face of advanced information technology. I suggest three alternative public policy approaches to the problem of protecting individual privacy and also preserving databases for genetic research:(1) governmental guidelines and centralized databases, (2) corporate self-regulation, and (3) my hybrid approach. None of these are unproblematic; I discuss strengths (...) and drawbacks of each, emphasizing the importance of protecting the privacy of sensitive medical and genetic information as well as letting information technology flourish to aid patient care, public health and scientific research. (shrink)

The article focuses on the study on moral conflicts and ethical relativism. There are few theories in the history ethics that stated that a moral dilemma can not be adhered by to moral requirements. According to philosophy professor David Wong, occurrence of irresolvable moral disagreement is one of the normative problems. On the other hand, the author asserted that single-agent moral conflicts do not necessarily fall under the relativism theory.

This paper begins with a discussion of the value of privacy,especially for medical records in an age of advancing technology.I then examine three alternative approaches to protection ofmedical records: reliance on governmental guidelines, the useof corporate self-regulation, and my own third hybrid view onhow to maintain a presumption in favor of privacy with respectto medical information, safeguarding privacy as vigorously andcomprehensively as possible, without sacrificing the benefitsof new information technology in medicine. None of the threemodels I examine are unproblematic, yet (...) it is crucial to weighthe strengths and weaknesses of these alternative approaches. (shrink)

Individuals care about and guard their privacy intensely in many areas. With respect to patient medical records, people are exceedingly concerned about privacy protection, because they recognize that health care generates the most sensitive sorts of personal information. In an age of advancing technology, with the switch from paper medical files to massive computer databases, privacy protection for medical information poses a dramatic challenge. Given high-speed computers and Internet capabilities, as well as other advanced communications technologies, the potential for abuse (...) is much greater than ever before. At every stage in the process of collection and storage, dangers can arise, including entry errors, improper access, exploitation, and unauthorized disclosure. Secondary use and aggregation of data are all far easier, faster, and less expensive, and thus pose additional threats to an individual's control over the disposition of medical information. (shrink)

O positivismo jurídico é predominantemente ensinado e aplicado há décadas por profissionais da área jurídica brasileira, geralmente com referência à construção teórica de Hans Kelsen (1881-1973), deixando à margem muitos outros estudos que oferecem importantes formulações e conceitos para a compreensão do Direito contemporâneo. Este artigo se junta a algumas poucas pesquisas sobre outros referenciais teóricos acerca do positivismo jurídico, analisando a regra de reconhecimento no pensamento teórico de Herbert Hart (1907-1992), apresentando-a como incremento e superação da teoria imperativista de (...) John Austin (1790-1859). A partir de pesquisa bibliográfica, mostramos que, em Hart, a regra de reconhecimento (modalidade de regra secundária) apresenta-se indispensável para a certeza necessária ao Direito, bem como para aferir a validade do sistema jurídico. (shrink)

A wide-ranging, comprehensive overview of pressing issues in bioethics today, this handbook takes into account current affairs and historical precedents. Interdisciplinary authorship and global examples make the handbook applicable to a variety of scholar, student, and practitioner types.

Although testing for substance abuse can be intrusive, inaccurate, and ineffective at ferreting out those who are a threat to others, it can be morally justified in certain carefully circumscribed cases.

Free speech has historically been viewed as a special and preferred democratic value in the United States, by the public as well as by the legislatures and courts. In 1937, Justice Benjamin Cardozo wrote in Palko v. Connecticut that protection of speech is a “fundamental” liberty due to America's history, political and legal, and he recognized its importance, saying, “[F]reedom of thought and speech” is “the matrix, the indispensable condition, of nearly every other form of freedom.” It is likely notable (...) that in the Bill of Rights free speech is protected in the First Amendment rather than later. (shrink)

Most of us have certain intuitions about moral rights, at least partially captured by the ideas that: (A) rights carry special weight in moral argument; (B) persons retain their rights even when they are legitimately infringed; although (C) rights undoubtedly do conflict with one another, and are sometimes overridden as well by nonrights considerations. I show that Dworkin's remarks about rights allow us to affirm (A), (B), and (C), yet those remarks are extremely vague. I then argue that Feinberg's more (...) comprehensive and precise theory, designed to do justice to all three theses, cannot assure us of (A), that rights are not merely one consideration to be weighed in the balance with heterogeneous others. I show how Feinberg accepts (C) despite being drawn toward an alternative absolutist theory of rights and commits himself to (B) through his rejection of prima facie rights. But his promising distinction between recognition and enforcement of a right, which helps give some sense to (B) despite its tension with (C), undermines the force of rights in moral argument apparently intended by (A). We thus learn that Feinberg's and Dworkin's accounts of rights are incompatible, though each is correct in important ways. Contrasting their views allows us to clarify the implications and consistency of alternative theses about rights, one step toward meeting the challenge of developing a theory which shows more adequately how respect for rights is to be combined with other intuitions about rights and their relation to other values. (shrink)

I first discuss reasons for feminists to attend to the role of women in the military, despite past emphasis on antimilitarism. I then focus on the exclusion of women from combat duty, reviewing its sanction by the U.S. Supreme Court and the history of its adoption. I present arguments favoring the exclusion, defending strong replies to each, and demonstrate that reasoning from related cases and feminist analyses of equality explain why exclusion remains entrenched.

Unionization in the Academy presents an authoritative, balanced, and comprehensive treatment of academic unions—their history, purpose, and the conflicts they cause.