In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish some relations between mixed logic and minimal, intuitionistic and classical logics. We present at the end a sequent calculus version for this logic.

A numeral system is an infinite sequence of different closed normal -terms intended to code the integers in -calculus. Barendregt has shown that if we can represent, for a numeral system, the functions Successor, Predecessor, and Zero Test, then all total recursive functions can be represented. In this paper we prove the independancy of these three particular functions. We give at the end a conjecture on the number of unary functions necessary to represent all total recursive functions.

We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.

In 1990 J-L. Krivine introduced the notion of storage operators. They are $\lambda$ -terms which simulate call-by-value in the call-by-name strategy and they can be used in order to modelize assignment instructions. J-L. Krivine has shown that there is a very simple second order type in AF2 type system for storage operators using Gödel translation of classical to intuitionistic logic. In order to modelize the control operators, J-L. Krivine has extended the system AF2 to the classical logic. In his system (...) the property of the unicity of integers representation is lost, but he has shown that storage operators typable in the system AF2 can be used to find the values of classical integers. In this paper, we present a new classical type system based on a logical system called mixed logic. We prove that in this system we can characterize, by types, the storage operators and the control operators. (shrink)

In this paper, we extend the system AF2 in order to have the subject reduction for the $betaeta$-reduction. We prove that the types with positive quantifiers are complete for models that are stable by weak-head expansion.

In 1990, J.L. Krivine introduced the notion of storage operator to simulate, in $lambda$-calculus, the 'call by value' in a context of a 'call by name'. J.L. Krivine has shown that, using Gödel translation from classical into intuitionistic logic, we can find a simple type for storage operators in AF2 type system. In this present paper, we give a general type for storage operators in a slight extension of AF2. We give at the end (without proof) a generalization of this (...) result to other types. (shrink)

In 1990, J. L. Krivine introduced the notion of storage operator to simulate “call by value” in the “call by name” strategy. J. L. Krivine has showed that, using Gödel translation of classical into intuitionistic logic, one can find a simple type for the storage operators in AF2 type system. This paper studies the ∀-positive types and the Gödel transformations of TTR type system. We generalize by using syntactical methods Krivine's theorem about these types and for these transformations. We give (...) a proof of this result in the case of the type of recursive integers. (shrink)

The storage operators were introduced by J.L. Krivine ([6]); they are closed λ-terms which, for some fixed data type (the integers for example), allow to simulate “call by value” while using “call by name”. J.L. Krivine showed that such operators can be typed, in the type system, using Gödel's translation from classical to intuitionistic logic ([8]).This paper studies the existence of storage operators which give a normal form as result (strong storage operators) for recursive and iterative representation of data in (...) λ-calculus. We obtain the following result:We can find typed strong storage operators for the recursive representations of data type, but that is not the case for the iterative representations of an infinite data type.We give the proof of this result in the case of integers. (shrink)

In this paper, we define a realizability semantics for the simply typed $lambdamu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the computational behavior of some closed typed terms. We also prove a completeness result of our realizability semantics using a particular term model.

In this paper, we present three methods to give the value of a classical integer in $\lambda\mu$ -calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the corresponding Church integer. The third method is the M. Parigot's method which uses the J.L. Krivine's storage operators.

In this paper, we present an extension of λμ-calculus called λμ++-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

In this paper, we present an extension of $lambdamu$-calculus called $lambdamu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

In 1990, J. L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In the present paper we define for every λ-term S which realizes the successor function on Church integers the notion of S-storage operator. We prove that every storage operator is an S-storage operator. But the converse is not always true.

In 1990, J.L. Krivine introduced the notion of storage operator to simulate 'call by value' in the 'call by name' strategy. J.L. Krivine has shown that, using Gödel translation of classical into intuitionitic logic, we can find a simple type for the storage operators in AF2 type system. This paper studies the $forall$-positive types (the universal second order quantifier appears positively in these types), and the Gödel transformations (a generalization of classical Gödel translation) of TTR type system. We generalize, by (...) using syntaxical methods, the J.L. Krivine's Theorem about these types and for these transformations. We give a proof of this result in the case of the type of recursive integers. (shrink)

In this paper, we present the -calculus which at the typed level corresponds to the full classical propositional natural deduction system. The Church–Rosser property of this system is proved using the standardisation and the finiteness developments theorem. We also define the leftmost reduction and prove that it is a winning strategy.

We give a direct, purely arithmetical and elementary proof of the strong normalization of the cut-elimination procedure for full (i.e., in presence of all the usual connectives) classical natural deduction.

We prove the strong normalization of full classical natural deduction by using a translation into the simply typed λμ-calculus. We also extend Mendler’s result on recursive equations to this system.

Storage operators have been introduced by J. L. Krivine in [5] they are closed λ-terms which, for a data type, allow one to simulate a "call by value" while using the "call by name" strategy. In this paper, we introduce the directed λ-calculus and show that it has the usual properties of the ordinary λ-calculus. With this calculus we get an equivalent--and simple--definition of the storage operators that allows to show some of their properties: $\bullet$ the stability of the set (...) of storage operators under the β-equivalence (Theorem 5.1.1); $\bullet$ the undecidability (and semidecidability) of the problem "is a closed λ-term t a storage operator for a finite set of closed normal λ-terms?" (Theorems 5.2.2 and 5.2.3); $\bullet$ the existence of storage operators for every finite set of closed normal λ-terms (Theorem 5.4.3); $\bullet$ the computation time of the "storage operation" (Theorem 5.5.2). (shrink)

In this paper we consider a type system with a universal type $omega$ where any term (whether open or closed, $beta$-normalising or not) has type $omega$. We provide this type system with a realisability semantics where an atomic type is interpreted as the set of $lambda$-terms saturated by a certain relation. The variation of the saturation relation gives a number of interpretations to each type. We show the soundness and completeness of our semantics and that for different notions of saturation (...) (based on weak head reduction and normal $beta$-reduction) we obtain the same interpretation for types. Since the presence of $omega$ prevents typability and realisability from coinciding and creates extra difficulties in characterizing the interpretation of a type, we define a class ${mathbb U}^+$ of the so-called positive types (where $omega$ can only occur at specific positions). We show that if a term inhabits a positive type, then this term is $beta$-normalisable and reduces to a closed term. In other words, positive types can be used to represent abstract data types. The completeness theorem for ${mathbb U}^+$ becomes interesting indeed since it establishes a perfect equivalence between typable terms and terms that inhabit a type. In other words, typability and realisability coincide on ${mathbb U}^+$. We give a number of examples to explain the intuition behind the definition of ${mathbb U}^+$ and to show that this class cannot be extended while keeping its desired properties. (shrink)

Matti Häyry presents a new ethical theory that he calls “conflict-responsive need-based negative utilitarianism.”1 In this commentary, I present my critical observations on his main points against the more general background of utilitarianism and theories of value.

In this paper, we critically consider the analogy between “infodemic” and “pandemic”, i.e. the spread of fake news about COVID-19 as a medial virus and the infection with the biological virus itself from the perspective of cultural evolutionary theory (CET). After confronting three major shortcomings of the ‘infodemic’ concept, we use CET as a background framework to analyze this phenomenon. To do so, we summarize which bi-ases are crucial for transmission in terms of cultural selection and how transmission is restricted (...) by filter bubbles or echo chambers acting as TRIMS (transmission isolating mechanisms) post “infection”, which isolate false from trustworthy scientific information in the context of the Corona pandemic. This is followed by a demonstration of the threat to biological fitness posed by the effects of an infection with fake news, which leads to a reduced willingness to vaccinate and follow health measures. We identify fake news on Covid as pseudoscience, trying to immunize itself from external influences. We then address the question of how to combat the infodemic. Since debunking strategies, such as warnings by fact-checking, have proven relatively ineffective in combating fake news, the inoculation theory from psychology might offer an alternative solution. Through its underlying ‘prebunking strategy’, which educates individuals about the risks and tactics of fake news prior to a potential infection, they could be ‘immunized’ in advance, similar to a virological vaccination. Although we recognize that the pandemic/infodemic analogy is in fact far from perfect, we believe that CET could provide a theoretical underpinning in order to give much more semantic depth to the concept ‘infodemic’. (shrink)

BackgroundObtaining informed consent for participation in genomic research in low-income settings presents specific ethical issues requiring attention. These include the challenges that arise when providing information about unfamiliar and technical research methods, the implications of complicated infrastructure and data sharing requirements, and the potential consequences of future research with samples and data. This study investigated researchers’ and participants’ parents’ experiences of a consent process and understandings of a genome-wide association study of malaria involving children aged five and under in Mali. (...) It aimed to inform best practices in recruiting participants into genomic research.MethodsA qualitative rapid ethical assessment was undertaken. Fifty-five semi-structured interviews were conducted with the parents of research participants. An additional nine semi-structured interviews were conducted with senior research scientists, research assistants and with a member of an ethics committee. A focus group with five parents of research participants and direct observations of four consent processes were also conducted. French and translated English transcripts were descriptively and thematically coded using OpenCode software.ResultsParticipants’ parents in the MalariaGEN study had differing understandings of the causes of malaria, the rationale for collecting blood samples, the purposes of the study and the kinds of information the study would generate. Genomic aspects of the research, including the gene/environment interaction underlying susceptibility or resistance to severe malaria, proved particularly challenging to explain and understand.ConclusionsThis study identifies a number of areas to be addressed in the design of consent processes for genomic research, some of which require careful ethical analysis. These include determining how much information should be provided about differing aspects of the research and how best to promote understandings of genomic research. We conclude that it is important to build capacity in the design and conduct of effective and appropriate consent processes for genomic research in low and middle-income settings. Additionally, consideration should be given to the role of review committees and community consultation activities in protecting the interests of participants in genomic research. (shrink)

In these days, there is an increasing technological development in intelligent tutoring systems. This field has become interesting to many researchers. In this paper, we present an intelligent tutoring system for teaching mathematics that help students understand the basics of math and that helps a lot of students of all ages to understand the topic because it's important for students of adding and subtracting. Through which the student will be able to study the course and solve related problems. An evaluation (...) of the intelligent tutoring systems was carried out and the results were encouraging. (shrink)

In recent decades, non-representational approaches to mental phenomena and cognition have been gaining traction in cognitive science and philosophy of mind. In these alternative approach, mental representations either lose their central status or, in its most radical form, are banned completely. While there is growing agreement that non-representational accounts may succeed in explaining some cognitive capacities, there is widespread skepticism about the possibility of giving non-representational accounts of cognitive capacities such as memory, imagination or abstract thought. In this paper, I (...) will critically examine the view that there are fundamental limitations to non-representational explanations of cognition. Rather than challenging these arguments on general grounds, I will examine a set of human cognitive capacities that are generally thought to fall outside the scope of non-representational accounts, i.e. numerical cognition. After criticizing standard representational accounts of numerical cognition for their lack of explanatory power, I will argue that a non-representational approach that is inspired by radical enactivism offers the best hope for developing a genuine naturalistic explanatory account for these cognitive capacities. (shrink)

This paper expands Rami Ali’s dissolution of the gamer’s dilemma (Ethics Inf Technol 17:267-274, 2015). Morgan Luck’s gamer’s dilemma (Ethics Inf Technol 11(1):31-36, 2009) rests on our having diverging intuition when considering virtual murder and virtual child molestation in video games. Virtual murder is seemingly permissible, when virtual child molestation is not and there is no obvious morally relevant difference between the two. Ali argues that virtual murder and virtual child molestation are equally permissible/impermissible when considered under different modes of (...) engagement. To this end, Ali distinguishes between story-telling gameplay and simulation games, discussing both in depth. I build on the dissolution by looking into competitive gameplay in order to consider what the morally relevant difference between virtual murder and virtual child molestation might be when competing in a video game. I argue that when competitors consent to participate in a competition, the rules of the competition supersede everyday moral intuitions. As such, virtual competitions ought to represent such consent from virtual characters. Virtual children cannot be represented as giving consent to be molested because (1) children cannot be represented as giving sexual consent, and (2) consent to be possibly molested cannot be given. This creates a morally relevant difference between murder and molestation. By fully addressing competitive gameplay, I answer Luck’s worry that Ali’s dissolution is incomplete (Ethics Inf Technol 20:157-162, 2018). (shrink)

We claim that, as it stands, the Deutsch–Wallace–Everett approach to quantum theory is conceptually incoherent. This charge is based upon the approach’s reliance upon decoherence arguments that conflict with its own fundamental precepts regarding probabilistic reasoning in two respects. This conceptual conflict obtains even if the decoherence arguments deployed are aimed merely towards the establishment of certain ‘emergent’ or ‘robust’ structures within the wave function: To be relevant to physical science notions such as robustness must be empirically grounded, and, on (...) our analysis, this grounding can only plausibly be done in precisely the probabilistic terms that lead to conceptual conflict. Thus, the incoherence problems presented necessitate either the provision of a new, non-probabilistic empirical grounding for the notions of robustness and emergence in the context of decoherence, or the abandonment of the Deutsch–Wallace–Everett programme for quantum theory. (shrink)

Embodied and extended cognition is a relatively new paradigm within cognitive science that challenges the basic tenet of classical cognitive science, viz. cognition consists in building and manipulating internal representations. Some of the pioneers of embodied cognitive science have claimed that this new way of conceptualizing cognition puts pressure on epistemological and ontological realism. In this paper I will argue that such anti-realist conclusions do not follow from the basic assumptions of radical embodied cognitive science. Furthermore I will show that (...) one can develop a form of realism that reflects rather than just accommodates the core principles of non-representationalist embodied cognitive science. (shrink)

This article offers an account of the responsibility that individuals bear by virtue of their national belonging alone. Via their national pride, the living connect themselves actively with select actions performed by others who might long be dead. They imagine themselves as having won past wars, built ancient empires and the like. This same feat of their imagination imposes on them a responsibility for the bad outcomes that were brought about through their imagined exploits. Their national responsibility for the "sins (...) of the fathers" however lends itself only to the kinds of responses that these living agents can demand of themselves. While their national responsibility can be captured by either the vocabulary of guilt or that of shame, the latter turns out to be more promising as it better accounts for the strong hold that the national idea has on contemporary political thinking. (shrink)

This article aims to study the intersection between critical realism and complexity theories through the existing literature on complex systems via an engagement with Luhmann’s autopoiesis. With reference to the philosophies of substance and persistence, I build on previous critical realist scholarship and provide an explanation for what the literature has only noted as the limitations and potentials of autopoiesis for complex systems thinking and its compatibility with Critical Realism. By highlighting how Luhmann’s autopoiesis is not a trans-immanent/ perdurantist-exdurantist system, (...) I show first how a trans immanent system through the method of calibration entails a complex causation involving objects in the environment of systems and not just within their boundaries. Second, I explain how a trans-immanent system fits with CR via the Morphogenetic Régulation framework by exploring the theme of crisis in terms of the movement from inadequate to adequate understanding of objects. (shrink)

Karim Fathi liefert erstmalig einen Überblick über die unterschiedlichen Diskurse und Strategien der Komplexitätsbewältigung auf der Ebene von Teams, Organisationen und Gesellschaften. Unter der Leitdifferenz kommunikativer Komplexitätsbewältigung untersucht er Fragen wie: Welche Strategien und Methoden ergeben sich im Umgang mit komplexen, vieldimensionalen und unvorhersehbaren Problemen? Wie können Kommunikationsprozesse so gestaltet werden, dass sie höhere kollektive Intelligenz ermöglichen? Sein universell anwendbarer Ansatz unterstützt komplexe Problemlöseprozesse auf allen Ebenen und fördert transdisziplinäres Denken in Zeiten globalen strukturellen Wandels.

This article offers an account of the responsibility that individuals bear by virtue of their national belonging alone. Via their national pride, the living connect themselves actively with select actions performed by others who might long be dead. They imagine themselves as having won past wars, built ancient empires and the like. This same feat of their imagination imposes on them a responsibility for the bad outcomes that were brought about through their imagined exploits. Their national responsibility for the “sins (...) of the fathers” however lends itself only to the kinds of responses that these living agents can demand of themselves. While their national responsibility can be captured by either the vocabulary of guilt or that of shame, the latter turns out to be more promising as it better accounts for the strong hold that the national idea has on contemporary political thinking. (shrink)

There are growing bodies of evidence demonstrating the benefits of equity, diversity, and inclusion on academic and organizational excellence. In turn, some editors have stated their desire to improve the EDI of their journals and of the wider scientific community. The Royal Society of Chemistry established a minimum set of requirements aimed at improving EDI in scholarly publishing. Additionally, several resources were reported to have the potential to improve EDI, but their effectiveness and feasibility are yet to be determined. In (...) this commentary we suggest six approaches, based on the Royal Society of Chemistry set of requirements, that journals could implement to improve EDI. They are: adopt a journal EDI statement with clear, actionable steps to achieve it; promote the use of inclusive and bias-free language; appoint a journal’s EDI director or lead; establish a EDI mentoring approach; monitor adherence to EDI principles; and publish reports on EDI actions and achievements. We also provide examples of journals that have implemented some of these strategies, and discuss the roles of peer reviewers, authors, researchers, academic institutes, and funders in improving EDI. (shrink)

This is a clear and original investigation of God's nature and existence. First of all, it considers (among other things) two of God's traditional properties: being all-knowing and being all-powerful. It argues he cannot possess these properties. But, it argues this is in accord with him being worthy of worship. Secondly, it introduces the notion of evil being "overridden". It argues he has to bring about other free living things and it is plausible they have to be liable to experience (...) evil due to their conditions. But, it argues the evil in this world is "overridden". Thirdly, it considers the principal arguments for the claim he does not exist. (They refer to the evil in the world.) It argues they do not establish sufficient grounds for this claim. Finally, it considers some well-known arguments for the claim he exists. It argues they face difficulties. It sets out other arguments: eg, some arguments to increase any degree of belief one has that God can exist. It includes a number of Appendices: God's sovereignty; Are there sufficient grounds for the claim that, very probably, God does not exist?; Theodicy and some theodicies; Some further remarks on God and time; Some further remarks on a living thing which possesses the power to do this or that freely;... It covers as a whole the principal parts of the Philosophy of Religion. It unifies these parts to a significant degree. It proceeds regularly by way of formal and clear arguments. (shrink)

The professions have focused considerable attention on developing codes of conduct. Despite their efforts there is considerable controversy regarding the propriety of professional codes of ethics. Many provisions of professional codes seem to exacerbate disputes between the profession and the public rather than providing a framework that satisfies the public''s desire for moral behavior.After examining three professional codes, we divide the provisions of professional codes into those provisions which urge professionals to avoid moral hazard, maintain professional courtesy and serve the (...) public interest. We note that whereas provisions urging the avoidance of moral hazard are uncontroversial, the public is suspicious of provisions protecting professional courtesy. Public interest provisions are controversial when the public and the profession disagree as to what is in the public interest. Based on these observations, we conclude with recommendations regarding the content of professional codes. (shrink)

A small but growing number of studies have aimed to understand, assess and reduce existential risks, or risks that threaten the continued existence of mankind. However, most attention has been focused on known and tangible risks. This paper proposes a heuristic for reducing the risk of black swan extinction events. These events are, as the name suggests, stochastic and unforeseen when they happen. Decision theory based on a fixed model of possible outcomes cannot properly deal with this kind of event. (...) Neither can probabilistic risk analysis. This paper will argue that the approach that is referred to as engineering safety could be applied to reducing the risk from black swan extinction events. It will also propose a conceptual sketch of how such a strategy may be implemented: isolated, self-sufficient, and continuously manned underground refuges. Some characteristics of such refuges are also described, in particular the psychosocial aspects. Furthermore, it is argued that this implementation of the engineering safety strategy safety barriers would be effective and plausible and could reduce the risk of an extinction event in a wide range of possible scenarios. Considering the staggering opportunity cost of an existential catastrophe, such strategies ought to be explored more vigorously. (shrink)

Econophysics is a new and exciting cross-disciplinary research field that applies models and modelling techniques from statistical physics to economic systems. It is not, however, without its critics: prominent figures in more mainstream economic theory have criticized some elements of the methodology of econophysics. One of the main lines of criticism concerns the nature of the modelling assumptions and idealizations involved, and a particular target are ‘kinetic exchange’ approaches used to model the emergence of inequality within the distribution of individual (...) monetary income. This article will consider such models in detail, and assess the warrant of the criticisms drawing upon the philosophical literature on modelling and idealization. Our aim is to provide the first steps towards informed mediation of this important and interesting interdisciplinary debate, and our hope is to offer guidance with regard to both the practice of modelling inequality, and the inequality of modelling practice. _1_ Introduction _1.1_ Econophysics and its discontents _1.2_ Against burglar economics _2_ Modelling Inequality _2.1_ Mainstream economic models for income distribution _2.2_ Econophysics models for income distribution _3_ Idealizations in Kinetic Exchange Models _3.1_ Binary interactions _3.2_ Conservation principles _3.3_ Exchange dynamics _ 4 _ Fat Tails and Savings _ 5 _ Evaluation. (shrink)

A fundamental tenet of Paul Feyerabend’s pluralistic view of science has it that theory proliferation, that is, the availability of theoretical alternatives, is of crucial importance for the detection of anomalies in established theories. Paul Hoyningen-Huene calls this the Anomaly Importation Thesis, according to which anomalies are imported, as it were, into well-established theories from competing alternatives. This article pursues two major objectives: (a) to work out the systematic details of Feyerabend’s ideas on theory proliferation and anomaly import as they (...) are presented in his early publications and his Against Method and (b) to compare Feyerabend’s ideas on theory proliferation and anomaly import with corresponding features in Popper’s critical rationalist philosophy of science. As it turns out, neither the Principle of Proliferation nor the Anomaly Importation Thesis are necessarily incompatible with critical rationalism. In spite of Feyerabend’s general anti-Popperian attitude, I argue that theoretical pluralism can be seen as an advancement of the critical rationalist philosophy and that critical rationalism provides good arguments for pluralism. (shrink)

The `problem of time' is a cluster of interpretational and formal issues in the foundations of general relativity relating to both the representation of time in the classical canonical formalism, and to the quantization of the theory. The purpose of this short chapter is to provide an accessible introduction to the problem.