Looking at proof theory as an attempt to ‘code’ the general pattern of the logical steps of a mathematical proof, the question of what kind of rules can make the meaning of a logical connective completely explicit does not seem to have been answered satisfactorily. The lambda calculus seems to have been more coherent simply because the use of ‘λ’ together with its projection 'apply' is specified by what can be called a 'reduction' rule: β‐conversion. We attempt to analyse the (...) role of proof rules, making use of a set of formal rules designed to capture both the notions of proof theory and those of the lambda‐calculus: Martin‐Löf's Intuitionistic Type Theory. (shrink)

The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension (...) to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic. (shrink)

As a celebration of theTractatus100th anniversary it might be worth revisiting its relation to the later writings. From the former to the latter, David Pears recalls that “everyone is aware of the holistic character of Wittgenstein’s later philosophy, but it is not so well known that it was already beginning to establish itself in theTractatus” (The False Prison, 1987). From the latter to the former, Stephen Hilmy’s (The Later Wittgenstein, 1987) extensive study of theNachlasshas helped removing classical misconceptions such as (...) Hintikka’s claim that “Wittgenstein in thePhilosophical Investigationsalmost completely gave up the calculus analogy.” Hilmy points out that even in theInvestigationsone finds the use of the calculus/game paradigm to the understanding of language, such as “in operating with the word” (Part I, §559) and “it plays a different part in the calculus”. Hilmy also quotes from a late (1946) unpublished manuscript (MS 130) “this sentence has use in the calculus of language”, which seems to be compatible with “asking whether and how a proposition can be verified is only a particular way of asking ‘How do you mean?’” Central in this back and forth there is an aspect which seems to deserve attention in the discussion of a semantics for the language of mathematics which might be based on (normalisation of) proofs and/or Hintikka/Lorenzen game-dialogue: the explication of consequences. Such a discussion is substantially supported by the use of the open and searchableThe Wittgenstein Archives at the University of Bergen. These findings are framed within the discussion of the meaning of logical constants in the context of natural deduction style rules of inference. (shrink)

The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, (...) known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (shrink)

An appropriate framework is put forward for the construction of $$\lambda $$ -models with $$\infty $$ -groupoid structure, which we call homotopic $$\lambda $$ -models, through the use of an $$\infty $$ -category with cartesian closure and enough points. With this, we establish the start of a project of generalization of Domain Theory and $$\lambda $$ -calculus, in the sense that the concept of proof (path) of equality of $$\lambda $$ -terms is raised to higher proof (homotopy).

One takes advantage of some basic properties of every homotopic \(\lambda\)-model (e.g. extensional Kan complex) to explore the higher \(\beta\eta\)-conversions, which would correspond to proofs of equality between terms of a theory of equality of any extensional Kan complex. Besides, Identity types based on computational paths are adapted to a type-free theory with higher \(\lambda\)-terms, whose equality rules would be contained in the theory of any \(\lambda\)-homotopic model.

Dividing chains have been used as conditions to isolate adequate subclasses of simple theories. In the first part of this paper we present an introduction to the area. We give an overview on fundamental notions and present proofs of some of the basic and well-known facts related to dividing chains in simple theories. In the second part we discuss various characterizations of the subclass of low theories. Our main theorem generalizes and slightly extends a well-known fact about the connection between (...) dividing chains and Morley sequences (in our case: independent sequences). Moreover, we are able to give a proof that is shorter than the original one. This result motivates us to introduce a special property of formulas concerning independent dividing chains: For any dividing chain there exists an independent dividing chain of the same length. We study this property in the context of low, short and ω -categorical simple theories, outline some examples and define subclasses of low and short theories, which imply this property. The results give rise to further studies of the relationships between some subclasses of simple theories. (shrink)

Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the of the 29th International Workshop on Logic, Language, Information, and Computation, WoLLIC 2023, held in Halifax, NS, Canada, during July 11–14, 2023. The 24 full papers (21 contributed, 3 invited) included in this book were carefully reviewed and selected from 46 submissions. The book also contains the abstracts for the 7 invited talks and 4 tutorials presented at WoLLIC 2023. The (...) WoLLIC conference series aims at fostering interdisciplinary research in pure and applied logic. (shrink)

The question of finding a suitable formal account of meaning for the logical signs has troubled many philosophers and logicians since the early days of formal logic, whenever it is even recognised as a problem. Here I attempt to show how two operational approaches to the problem can still be shown to be ‘technically’ equivalent, despite having emerged from two different readings of a single philosophical account, and being essentially distinct with respect to the rôle of ‘will’ in the mathematical (...) activity: on the one hand, the ‘semantics of use’, my own reformulation of P. Martin‐Löf's Intuitionistic Type Theory canonical‐values based semantics by taking the normalisation rules as the key semantical device; and, on the other hand, J. Hintikka's Game‐Theoretical Semantics, where the meaning of logical signs is given via semantical games. The philosophical account from which both emerge is precisely Wittgenstein's later account of propositions, where the notion of ‘language‐games’ is introduced as a key semantical device. Observing that the normalisation rules seem to be able to formalise the explanation of the consequences one can draw from a proposition,3 thus showing the function/purpose/usefulness of its main connective in the calculus of language, it seems reasonable to advocate that such a meta‐mathematical device can be a semantically useful notion which would lead to a more reasonable account of the problem of formulating the meaning of logical constants. (shrink)

The geometric system of deduction called N-Graphs was introduced by de Oliveira in 2001. The proofs in this system are represented by means of digraphs and, while its derivations are mostly based on Gentzen's sequent calculus, the system gets its inspiration from geometrically based systems, such as the Kneales' tables of development, Statman's proofs-as-graphs, Buss' logical flow graphs, and Girard's proof-nets. Given that all these geometric systems appeal to the classical symmetry between premises and conclusions, providing an intuitionistic version of (...) any of these is an interesting exercise in extending the range of applicability of the geometric system in question. In this article we produce an intuitionistic version of N-Graphs, based on Maehara's LJ' system, as described by Takeuti. Recall that LJ' has multiple conclusions in all but the essential intuitionistic rules, e.g., implication right and negation right. We show soundness and completeness of our intuitionistic N-Graphs with respect to LJ'. We also discuss how we expect to extend this work to a version of N-Graphs corresponding to the intuitionistic logic system FIL (Full Intuitionistic Logic) of de Paiva and Pereira and sketch future developments. (shrink)

Although narcissists often emerge as leaders, the relationship between leader narcissism and follower performance is ambiguous and often even found to be negative. For women, narcissism seems especially likely to lead to negative evaluations. Since narcissists have the tendency to be impulsive and change their minds on a whim, they may come across as inconsistent. We propose “inconsistent leader behavior” as a new mechanism in the relationship between leader narcissism and follower performance and argue that leader gender plays an important (...) role in whether narcissistic leaders are perceived as inconsistent. Specifically, we expect leader narcissism to have a negative relationship with follower performance through perceived inconsistent leader behavior, especially for female leaders. Thus, we examine leader gender as a personal factor moderating the relationship between narcissism and perceived inconsistent behavior. Also, as perceived inconsistency is likely less problematic when a good relationship exists, we examine leader–member exchange as a contextual condition moderating the relationship between leader behavior and follower performance. We test our moderated mediation model in a multi-source study with 165 unique leader–follower dyads. As expected, leader narcissism was positively related to perceived inconsistent leader behavior, and this relationship was stronger for female leaders. Inconsistent leader behavior was negatively related to follower performance, but only when LMX was low. Our research highlights that perceived behavioral inconsistency can be problematic and—for female leaders—provides an explanation of the negative relation of leader narcissism with follower performance and of the inconsistencies in evaluations of narcissistic leaders’ effectiveness. (shrink)

Intensional logic has emerged, since the 1960' s, as a powerful theoretical and practical tool in such diverse disciplines as computer science, artificial intelligence, linguistics, philosophy and even the foundations of mathematics. The present volume is a collection of carefully chosen papers, giving the reader a taste of the frontline state of research in intensional logics today. Most papers are representative of new ideas and/or new research themes. The collection would benefit the researcher as well as the student. This book (...) is a most welcome addition to our series. The Editors CONTENTS PREFACE IX JOHAN VAN BENTHEM AND NATASHA ALECHINA Modal Quantification over Structured Domains PATRICK BLACKBURN AND WILFRIED MEYER-VIOL Modal Logic and Model-Theoretic Syntax 29 RUY J. G. B. DE QUEIROZ AND DOV M. GABBAY The Functional Interpretation of Modal Necessity 61 VLADIMIR V. RYBAKOV Logics of Schemes for First-Order Theories and Poly-Modal Propositional Logic 93 JERRY SELIGMAN The Logic of Correct Description 107 DIMITER VAKARELOV Modal Logics of Arrows 137 HEINRICH WANSING A Full-Circle Theorem for Simple Tense Logic 173 MICHAEL ZAKHARYASCHEV Canonical Formulas for Modal and Superintuitionistic Logics: A Short Outline 195 EDWARD N. ZALTA 249 The Modal Object Calculus and its Interpretation NAME INDEX 281 SUBJECT INDEX 285 PREFACE Intensional logic has many faces. In this preface we identify some prominent ones without aiming at completeness. (shrink)

The US neutrino community gathered at the Workshop on the Intermediate Neutrino Program at Brookhaven National Laboratory February 4-6, 2015 to explore opportunities in neutrino physics over the next five to ten years. Scientists from particle, astroparticle and nuclear physics participated in the workshop. The workshop examined promising opportunities for neutrino physics in the intermediate term, including possible new small to mid-scale experiments, US contributions to large experiments, upgrades to existing experiments, R&D plans and theory. The workshop was organized into (...) two sets of parallel working group sessions, divided by physics topics and technology. Physics working groups covered topics on Sterile Neutrinos, Neutrino Mixing, Neutrino Interactions, Neutrino Properties and Astrophysical Neutrinos. Technology sessions were organized into Theory, Short-Baseline Accelerator Neutrinos, Reactor Neutrinos, Detector R&D and Source, Cyclotron and Meson Decay at Rest sessions.This report summarizes discussion and conclusions from the workshop. (shrink)

Background: Issues concerning legislation and regulation with respect to the role of nurses in euthanasia and physician-assisted suicide gave the Minister for Health reason to commission a study of the role of nurses in medical end-of-life decisions in hospitals, home care and nursing homes.Aim: This paper reports the findings of a study of the role of nurses in euthanasia and physician-assisted suicide, conducted as part of a study of the role of nurses in medical end-of-life decisions. The findings for hospitals, (...) home care and nursing homes are described and compared.Method: A questionnaire was sent to 1509 nurses, employed in 73 hospitals, 55 home care organisations and 63 nursing homes. 1179 responses were suitable for analysis. The questionnaire was pilot-tested among 106 nurses, with a response rate of 85%.Results: In 37.0% of cases, the nurse was the first person with whom patients discussed their request for euthanasia or physician-assisted suicide. Consultation between physicians and nurses during the decision-making process took place quite often in hospitals and nursing homes and less frequently in home care situations . In some cases , nurses administered the euthanatics.Conclusions: The results show substantial differences between the intramural sector and the extramural sector , which are probably linked to the organisational structure of the institutions. Consultation between physicians and nurses during the decision-making process needs improvement, particularly in home care. Some nurses had administered euthanatics, although this task is by law exclusively reserved to physicians. (shrink)

This article provides ethical guidance on using race in health research as a variable or in defining the study population. To this end, a plain, non-exhaustive checklist is provided for researchers and research ethics committees, preceded by a brief introduction on the need for justification when using race as a variable or in defining a study population, the problem of exoticism, that distinctions pertain between race, ethnicity and ancestry, the problematic naming of races, and that race does not serve well (...) as a presumed biological construct in genetic research. (shrink)

This article reports the findings of a study into the role of Dutch nurses in the alleviation of pain and symptoms with a life-shortening intention, conducted as part of a study into the role of nurses in medical end-of-life decisions. A questionnaire survey was carried out using a population of 1509 nurses who were employed in hospitals, home care organizations and nursing homes. The response rate was 82.0%; 78.1% (1179) were suitable for analysis. The results show that in about half (...) of the cases (55.8%) nurses were involved in the decision making by the physician and that nurses were frequently (81.5%) involved in administering the medication. The authors' conclusion is that alleviation of pain and symptoms with a life-shortening intention represents a `grey' area, in which physicians and nurses act on the basis of personal ethical norms rather than legal rules, professional guidelines or shared moral values. (shrink)

Our goal was to explore self‐care practices among men who have sex with men in the context of Mpox in Brazil. This study used qualitative research methods, including interviews and thematic analysis, to collect and analyze data from male participants across the Brazilian territory. The narratives unveil men's perspectives on self‐care, risk reduction, and health beliefs during the Mpox pandemic. Our findings highlight a multifaceted approach to self‐care among men, encompassing hygiene, physical contact management, mask usage, skin lesion vigilance, and (...) adherence to official guidelines. Men's attitudes toward sexual behaviors emphasize the importance of reducing sexual partners, practicing safe sex, and combating misinformation through accurate information dissemination. The development of these behaviors and self‐care practices can be facilitated by nurses guided by Dorothea Orem's Self‐Care Theory, supported by patient‐centered care, with strategies to address and confront the stigma associated with the disease and provide emotional support. Thus, the study underscores the pivotal role of self‐care in mitigating infection risks, especially in the context of emerging infectious diseases. It acknowledges the impact of socio‐cultural factors and healthcare policies on men's preventive measures. However, it also recognizes limitations, such as potential bias due to stigma concerns and a nonrepresentative sample. Ultimately, the research advocates for tailored education, promotion of gender equity, and healthcare empowerment to effectively manage health risks in such contexts. (shrink)