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.

In order to modelize the reasoning of an intelligent agent represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this papers, we consider logic systems called L′T without this kind of constants but limited to the case where T is a finite poset. We prove a weak deduction theorem. We introduce also an algebraic semantics using Hey ting algebra with operators. To prove the completeness (...) theorem of the L′T system with respect to the algebraic semantics, we use the method of H. Rasiowa and R. Sikorski for first order logic. In the propositional case, a corollary allows us to assert that it is decidable to know “if a propositional formula is valid”. We study also certain relations between the L′T logic and the intuitionistic and classical logics. (shrink)

In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems the use of a set of constants constitutes a fundamental tool. We have introduced in [8] a logic system called equation image without this kind of constants but limited to the case that T is a finite poset. We have proved a completeness result for this system w.r.t. an algebraic semantics. We introduce in this paper (...) a Kripke-style semantics for a subsystem equation image of equation image for which there existes a deduction theorem. The set of “possible worldsr is enriched by a family of functions indexed by the elements of T and satisfying some conditions. We prove a completeness result for system equation image with respect to this Kripke semantics and define a finite Kripke structure that characterizes the propositional fragment of logic equation image. We introduce a reational semantics which has the advantage to allow an interpretation of the propositionnal logic equation image using only binary relations. We treat also the computational complexity of the satisfiability problem of the propositional fragment of logic equation image. (shrink)

In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this paper, we consider logic systems called L'T without this kind of constants but limited to the case where T is a finite poset. We study the tableau method for this system and we prove its completeness for a class of formulas with respect to an algebraic (...) semantics. (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)

This article focuses on the representation of female physical illness and disability in the works of two Arab women writers: Iraqi Alia Mamdouh’s Habbat al Naftalin [Mothballs] (1986) and Egyptian Salwa Bakr’s al ‘Arabah al Dhahabiyah la Tas‘ad ila al Sama’ [The Golden Chariot] (1991). It argues that the representation of female illness in these works centres upon the figure of the sick mother. Despite the limitations of this trope of illness, both novels offer a more complex illness narrative than (...) those of their Arab predecessors. By problematizing the representation of the sick woman/mother, both novels challenge the traditional role of the silent, sick female figure whose story remains outside the limits of representation. Finally, the article argues that this textual recuperation of the female suffering body is achieved through the employment of a mother— daughter plot which continues to represent the sick mother as socially and emotionally absent but which nevertheless renders her a central figure in the daughter’s narrative. (shrink)

This essay explores the material, phenomenological and political meaning of the Syrian corpse and the question of its dignity as represented in a series of media and visual outputs from 2011 to the present. The essay begins by arguing that the violence in Syria now targets the dead as much as the living. As such, the essay highlights the forms of ‘necroviolence’ that the Syrian corpse has been subjected to: mistreatment, erasure of markers of identity, denial of burial, mutilation and (...) ultimately an attempt to erase it from memory. The essay concludes by arguing that the Syrian corpse is not merely the passive subject or victim of ‘necroviolence’ but can also become the paradoxical agent of what we might call ‘postmortem resistance’. (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)

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 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)

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.

This article explains how we ordinary subjects of a state who are neither political leaders nor functionaries are responsible for outcomes that are properly attributed to that state and that took place during our adult lifetime. Its focus is on the connection we forge to those outcomes via our obedience alone. If our responsibility as subjects is justified, it would apply under all regime types including oppressive and authoritarian ones. The argument is that this responsibility can only be justified within (...) a minimal account of agency and a bare-bones account of responsibility. Thus, while we incur a burden of responsibility for the state via our obedience alone, that burden does not suffice to either blame us or extract remedies from us for state injustices. For us obedient subjects, however, it is important that we be cognizant of this burden as it marks the most minimal agency we exercise in the state. (shrink)

In his recent work, Jürgen Habermas signals the abandonment of his earlier claims to justify human rights and universalist morality. This paper explains the above shift, arguing that it is the inescapable result of his attempts in recent years to accommodate pluralism. The paper demonstrates how Habermas’s universal pragmatic justification of modern normative standards was inextricably tied to his consensus theory of validity. He was compelled by the structure of that argument to count on the current or future availability of (...) a unified framework within which all can potentially articulate their needs and interests. With his abandonment of the justification Habermas has rid discourse theory of this controversial assumption. In weakening its defense of human rights and universalist morality against the charge of ethnocentrism, he has strengthened his theory’s foothold in the lived pluralist world. Key Words: argumentation • ethnocentrism • Habermas • human rights • justification • legitimacy • pluralism • rational consensus • Rehg. (shrink)

Any living system possesses internal embedded description and exists as a superposition of different potential realisations, which are reduced in interaction with the environment. This reduction cannot be recursively deduced from the state in time present, it includes unpredictable choice and needs to be modelled also from the state in time future. Such non-recursive establishment of emerging configuration, after its memorisation via formation of reflective loop (sign-creating activity), becomes the inherited recursive action. It leads to increase of complexity of the (...) embedded description, which constitutes the rules of generative grammar defining possible directions of open evolutionary process. The states in time future can be estimated from the point of their perfection, which represents the final cause in the Aristotelian sense and may possess a selective advantage. The limits of unfolding of the reflective process, such as the golden ratio and the golden wurf are considered as the canons of perfection established in the evolutionary process. (shrink)

Any living system possesses internal embedded description and exists as a superposition of different potential realisations, which are reduced in interaction with the environment. This reduction cannot be recursively deduced from the state in time present, it includes unpredictable choice and needs to be modelled also from the state in time future. Such non-recursive establishment of emerging configuration, after its memorisation via formation of reflective loop (sign-creating activity), becomes the inherited recursive action. It leads to increase of complexity of the (...) embedded description, which constitutes the rules of generative grammar defining possible directions of open evolutionary process. The states in time future can be estimated from the point of their perfection, which represents the final cause in the Aristotelian sense and may possess a selective advantage. The limits of unfolding of the reflective process, such as the golden ratio and the golden wurf are considered as the canons of perfection established in the evolutionary process. (shrink)

(1997). Information processing as an intrinsic property of biological systems: Origin and dynamics of information. World Futures: Vol. 50, No. 1-4, pp. 571-581.

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non‐equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non‐equilibrium, the ratios of free and Mg‐bound adenylates, Mg2+ and membrane potentials are interdependent and can be computed. The adenylate status is balanced with the (...) levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non‐coupled to NAD+ reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self‐maintenance of metabolism. (shrink)

This book discusses the basic foundations of theoretical biology. Contrary to the objects of theoretical physics, the biological object contains a kind of ontological duality and refers to a fundamental wholeness of a living system. The rational interpretation of wholeness is considered by the author as a true basis for fundamental principles of development of theoretical biology and for understanding its link to physics, to psychology, and to semiotics. The rational holistic approach in application to theoretical biology can be substantiated (...) through the clarification of internal logic of organization and description of biological systems. This logic will provide an understanding of the place of life in the Universe. The main goal of this book is to introduce the view that in the potentially infinite system of human knowledge, a proper clarification of the place of Man in the Universe is possible only via understanding of the phenomenon of life. (Imprint: Nova Biomedical). (shrink)

(1992). The rituals of science: Comments on Abir‐Am (with response) Social Epistemology: Vol. 6, The Historical Ethnography of Scientific Rituals, pp. 373-387.

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.

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.

(1992). The rituals of science: Comments on Abir‐Am (with response) Social Epistemology: Vol. 6, The Historical Ethnography of Scientific Rituals, pp. 373-387.

This dissertation engages the following question: how, in the absence of an uncontroversial source of moral guidance, can liberals make political and moral claims across cultural divides? While committed to toleration, liberals cannot escape the compulsion to apply basic standards of equal individual human rights and liberties universally. Under postmetaphysical conditions, however, they no longer find credible arguments that assure them of the sources of these standards in "natural law," "human nature," or "practical reason." Aware that individual rights have their (...) provenance in modern "Western" history, liberals fear being intolerant when they apply these standards universally, and experience as a result a problem of cross-cultural judgement. ;In this project I engage in a sympathetic critique of Richard Rorty's, Jurgen Habermas's and John Rawls's attempts at addressing this problem and provide a fourth alternative that cannot be absorbed by any of their frameworks. Rorty offers liberals the comforts of ethnocentrism. He assures them that political and moral judgements are always made by someone from somewhere. For this comfort, however, he extracts the exorbitant ethical price of other-disregard. Habermas derives individual rights from the universal practice of argumentation. By relying on the overly exacting standard of "rational consensus," however, he limits the applicability of his answer to liberal secular contexts. In his free-standing answer, Rawls offers the promising standard of an "overlapping consensus." His overly static use of this concept, however, drains it of its promise. ;Drawing on each of these attempts as well as on Aristotle's Rhetoric, I offer the alternative of a political project of moral persuasion. Instead of seeking to address the problem of cross-cultural judgement by coup de plume, liberals' best hope is to obviate it in practice, by forging a global, minimally liberal, overlapping consensus. As moral persuaders liberals would intrude actively in nonliberal debates and would seek to convince nonliberals from within their various lights, of the worthiness of the commitment to the freedom and equality of persons. (shrink)

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.

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)