In this note we develop a method for constructing finite totally-ordered m-zeroids and prove that there exists a categorical equivalence between the category of finite, totally-ordered m-zeroids and the category of pseudo Łukasiewicz-like implicators.

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras, where * is a continuous t-norm. In this paper we investigate the (...) structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

A continuoxis t- norm is a continuous map * from [0, 1]² into [0,1] such that ([ 0,1], *, 1) is a commutative totally ordered monoid. Since the natural ordering on [0,1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and ([ 0,1], *, →, 1) becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras ([ 0,1], *, (...) →, 1), where * is a continuous t-norm. In this paper we investigate the structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [ 0,1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL- algebras, of Gödel algebras and of product algebras. (shrink)

We study the variety Var() of lattice-ordered monoids generated by the natural numbers. In particular, we show that it contains all 2-generated positively ordered lattice-ordered monoids satisfying appropriate distributive laws. Moreover, we establish that the cancellative totally ordered members of Var() are submonoids of ultrapowers of and can be embedded into ordered fields. In addition, the structure of ultrapowers relevant to the finitely generated case is analyzed. Finally, we provide a complete isomorphy invariant in (...) the two-generated case. (shrink)

Although ostensibly defending speculative philosophy, Reck is doubtful that any unprejudiced speculative philosophy can exist: "No matter how much a philosopher may strive for neutrality, his test for the true philosophy is always predicated on the assumptions that his conception of being presents being as it is and that the conceptions of being his rivals uphold are partial or false." In the pursuit of neutrality, Reck attempts a mere chronicle of the distinctive conceptions of being which he feels have animated (...) the various metaphysical traditions: "Realism holds that whatever is in any sense is real; idealism that mind and its content alone are real; materialism that matter and its patterns alone are real; and process philosophy that process and the factors in process are real." The historical development of each of the four types is presented in masterly fashion. This book truly stands head and shoulders over its nearest rival in the Metaphilosophical literature for the depth of historical comprehension, the brilliant but controlled use made of a wealth of scholarship. A graduate student reviewing for comprehensive exams could do worse than to use Reck’s book. Those systems motivated at least in part by the drive-to-synthesis are disqualified a priori of being viable alternatives, motivated by distinctive intuitions. Realism, further, is found to have an inherent difficulty: "The task for the realist is to explain how the different levels or kinds of being can be related in a hierarchically ordered cosmos. The task is nothing short of explicating the bond of being." When Leibniz tries to relate finite particulars through a "Supreme Monad," he is faulted for "veering dangerously" close to Monism. Sympathetic toward Realism, Reck suggests a modification of Leibniz’s theory: not a rendering of the relations between man and God less mechanical, but a reduction of the "first Monad" from being supreme to a finite particular, struggling, like us, to overcome the hindrances posed by his environment. Reck concedes that the cognitive use of speculative philosophy, even when it redefines its project as Metaphilosophy, may be "futile"; however, he underscores the aesthetic value of the various systems, as Santayana would, when we can "bracket" the question of existence or truth and simply contemplate these cultural masterpieces as pure "essences." "Happy are those students who can suspend their critical search for truth sufficiently to savor the aesthetic values the systems of philosophy contain!" Reck refrains from judging between rival theories because such a judgment is always delivered from a view of what one takes to exist; and the impulse to go beyond "essence" to "existence" is, as Santayana teaches, prompted by fear, pain, instinct, or necessity. Rather than being a disinterested wonder at what "is," this passion is an "irrational agency of animal faith." "Needless to add," writes Reck, "animal faith is no more trustworthy than God’s existence to guarantee the truth of knowledge." This view can raise problems for Reck’s "finite" god. The finite god he prefers is perhaps "strong" enough to provide enough interconnection between existing particulars to justify a "Metaphilosophical" science, if not a properly "Philosophical" one, in the traditional sense; Reck could point to his own successful Metaphilosophy as evidence that his "god" is at least this strong. But isn't even this finite god an existential belief which, as the basis for a criticism, compromises one’s neutrality and thus constitutes a flaw in one’s Metaphilosophical theory? Is it possible that a totally adequate Metaphilosophical theory, on Reck’s canons, could not save enough interconnection between particulars to justify even a Metaphilosophy, as well as a Philosophy?—P. M. (shrink)

The foundations of a theory of nonminimal coupling of matter and the gravitational field in the framework of Riemannian (or Riemann-Cartan) geometry are presented. In the absence of matter, the Einstein vacuum field equations hold. In order to allow for a Newtonian limit, the theory contains a new parameter l0 of dimension length. For systems with finite total mass, l0 is set equal to the Schwarzschild radius.

In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal (...) logic can be characterized by Kripke frames. Besides, the creation of non-classical modal logics puts the problem of characterization of finite matrices very far away from the original scope of Dugundji’s result. In this sense, we will show how to update Dugundji’s result in order to make precise the scope and the limits of many-valued matrices as semantic of modal systems. A brief comparison with the useful Chagrov and Zakharyaschev’s criterion of tabularity for modal logics is provided. (shrink)

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation of (...) cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes. (shrink)

Special groups [M. Dickmann, F. Miraglia, Special Groups : Boolean-Theoretic Methods in the Theory of Quadratic Forms, Memoirs Amer. Math. Soc., vol. 689, Amer. Math. Soc., Providence, RI, 2000] are a first-order axiomatization of the theory of quadratic forms. In Section 2 we investigate reduced special groups which are a lattice under their natural representation partial order ; we show that this lattice property is preserved under most of the standard constructions on RSGs; in particular finite RSGs and RSGs (...) of finite chain length are lattice ordered. We prove that the lattice property fails for the RSGs of function fields of real algebraic varieties over a uniquely ordered field dense in its real closure, unless their stability index is 1 . We show that Open Problem 1 has a positive answer for the RSG of the field Q . In the final section we explore the meaning of Open Problem 1 for formally real fields, in terms of their orders and real valuations; we introduce the notion of “parameter-rank” of a positive-primitive first-order formula of the language for special groups. (shrink)

The paper deals with pp formulas in the language of reduced special groups, and the question of when the validity of a pp formula on each finite subspace of a space of orderings implies its global validity [18]. A large new class of pp formulas is introduced for which this is always the case, assuming the space of orderings in question has finite stability index. The paper also considers pp formulas of the special type $b\in \Pi _{i=1}^{n}\,D\langle 1,a_{i}\rangle (...) $. Formulas of this type with n = 3 are the simplest sort of pp formula not covered by the result, and are also the source of the recent counterexamples in [9] and [19]. (shrink)

The most common way of proving decidability in propositional modal logic is to shew that the system in question has the finite model property. This is not however the only way. Gabbay in [4] proves the decidability of many modal systems using Rabin's result in [8] on the decidability of the second-order theory of successor functions. In particular [4, pp. 258-265] he is able to prove the decidability of a system which lacks the finite model property. Gabbay's system (...) is however complete, in the sense of being characterized by a class of frames, and the question arises whether there is a decidable modal logic which is not complete. Since no incomplete modal logic has the finite model property [9, p. 33], any proof of decidability must employ some such method as Gabbay's. In this paper I use the Gabbay/Rabin technique to prove the decidability of a finitely axiomatized normal modal propositional logic which is not characterized by any class of frames. I am grateful to the referee for suggesting improvements in substance and presentation.The terminology I am using is standard in modal logic. By aframeis understood a pair 〈W, R〉 in whichWis a class (of “possible worlds”) andR⊆W2. To avoid confusion in what follows, a frame will henceforth be referred to as aKripkeframe. By contrast, ageneral frameis a pair 〈,Π〉 in whichis a Kripke frame andΠis a collection of subsets ofWclosed under the Boolean operations and satisfying the condition that ifAis inΠthen so isR−1“A. A model on a frame (of either kind) is obtained by adding a functionVwhich assigns sets of worlds to propositional variables. In the case of a general frame we require thatV(p) ∈Π. (shrink)

The demand of many scientific areas for the usage of fractional partial differential equations to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations. (...) The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference method and standard finite difference technique, which are popular in the literature for solving engineering problems. (shrink)

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying (...) problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21]. (shrink)

Relativistic mean field theory with mesons σ, ω, π and ρ mediating interactions and nucleons as basic fermions has been very successful in describing nuclear matter and finite nuclei. However, in heavy-ion collisions, where the c. m. energy of two colliding nucleons will be in the hundreds of GeV region, nucleons are not expected to behave as point-like particles. Analyses of elastic pp and ¯pp scattering data in the relevant c. m. energy range show that the nucleon is a (...) composite object—a topological soliton or Skyrmion embedded in a condensed quark-antiquark ground state. Against this backdrop, we formulate an effective field theory model of nuclear matter based on the gauged linear σ-model where quarks are the basic fermions, but the mesons still mediate the interactions. The model describes the nucleon as a Skyrmion and produces a q¯q ground state analogous to a superconducting ground state. Quarks are quasi-particles in this ground state. When the temperature exceeds a critical value, the scalar field in the ground state vanishes, quarks become massless, and a chiral phase transition occurs leading to chiral symmetry restoration. We explore the possibility of a first order phase transition in this model by introducing suitable self-interactions of the scalar field. Internal structures of the Skyrmions are ignored, and they are treated as point-like fermions. (shrink)

We obtain an algorithm to compute finite coproducts of finitely generated Gödel algebras, i.e. Heyting algebras satisfying the prelinearity axiom =1. We achieve this result using ordered partitions of finite sets as a key tool to investigate the category opposite to finitely generated Gödel algebras . We give two applications of our main result. We prove that finitely presented Gödel algebras have free products with amalgamation; and we easily obtain a recursive formula for the cardinality of the (...) free Gödel algebra over a finite number of generators first established by A. Horn. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called (...) 4/3-problem without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

The subtle, almost ineffable, and ineffable cardinals were introduced in an unpublished 1971 manuscript of R. Jensen and K. Kunen. The concepts were extended to that of k-subtle, k-almost ineffable, and k-ineffable cardinals in 1975 by J. Baumgartner. In this paper we give a self contained treatment of the basic facts about this level of the large cardinal hierarchy, which were established by J. Baumgartner. In particular, we give a proof that the k-subtle, k-almost ineffable, and k-ineffable cardinals define three (...) properly intertwined hierarchies with the same limit, lying strictly above “total indescribability” and strictly below “arrowing ω”. The innovation here is presented in Section 2, where we take a distinctly minimalist approach. Here the subtle cardinal hierarchy is characterized by very elementary properties that do not mention closed unbounded or stationary sets. This development culminates in a characterization of the hierarchy by means of a striking universal second-order property of linear orderings. (shrink)

There are serious concerns about the commercialization of healthcare and adoption of the business approach in medicine. As market dynamics endanger established professional values, healthcare workers face more complicated ethical dilemmas in their daily practice. The aim of this study was to investigate the willingness of medical students to accept the assertions of commercialized healthcare and the factors affecting their level of agreement, factors which could influence their moral stance when market demands conflict with professional values. A cross-sectional study was (...) conducted in three medical schools in Turkey. The study population consisted of first-, third-, and sixth-year students, and 1,781 students participated in total. Students were asked to state if they agreed with the assertions of commercialized healthcare. Of all students, 87.2 per cent agreed with at least one of the assertions, and one-fifth of them agreed with more than half of the assertions. First-year students significantly agreed more with some assertions than third- and sixth-year students. Being female, having mid-level family income, choosing medicine due to idealistic reasons, and being in the third or sixth years of medical study increased the probability of disagreement. Also, studying in a medical school that included integrated lectures on health policies, rights related to health, and health inequities, along with early field visits, increased the probability of disagreement. This study suggests that agreement with the assertions of commercialized healthcare might be prevalent among students at a considerable level. We argue that this level of agreement is not compatible with best practice in professional ethics and indicates the need for an educational intervention in order to have physicians who give priority to patients’ best interests in the face of market demands. (shrink)

This paper presents an algorithm that, given a finite set E of pairs of second-order monadic terms, returns a finite set U of ‘substitution schemata’ such that a substitution unifies E iff it is an instance of some member of U . Moreover, E is unifiable precisely if U is not empty. The algorithm terminates on all inputs, unlike the unification algorithms for second-order monadic terms developed by G. Huet and G. Winterstein. The substitution schemata in U use (...) expressions which represent sets of terms that differ only in how many times designated strings of function constants follow themselves. The substitution schemata may contain unresolved ‘identity restrictions’; consequently, the members of U generally do not characterize all the unifiers of E in a completely explicit way. The algorithm is particularly useful for investigating the complexity of formal proofs. (shrink)

The aim of this paper is to characterize varieties of Heyting algebras with decidable theory of their finite members. Actually we prove that such varieties are exactly the varieties generated by linearly ordered algebras. It contrasts to the result of Burris [2] saying that in the case of whole varieties, only trivial variety and the variety of Boolean algebras have decidable first order theories.

As the subtitle indicates, this book intends to discuss Descartes’ attempt of laying a new foundation of knowledge. In a lively and critical interpretation of Descartes’ writings, especially of his Discours de la Méthode and of his Meditationes, and a competent use of the corresponding philosophical literature the success of this attempt of enlightenment and its shortcomings, identified with the Cartesian re-introduction of the traditional metaphysics, are explained in order to allow the author in a concluding discussion to present his (...) ideas of the necessary revision of Descartes philosophy. Presenting the I as the subject not only for the first time but in an unique way, and concentrating upon the problem of the self-originating human knowledge in an exemplary manner, Descartes is found to have become the founder of subjective philosophy. As knowledge of knowledge, philosophy is not concerned primarily with objects, but with knowledge and has self-foundation as its main task. So it has to start with human knowledge and to place the self as the fountain from which all knowledge proceeds. The demands of subjective philosophy dictate its method described in the Discours. The foundation of knowledge, which as such can only be true and certain knowledge, leads to enlightenment, i.e., to the rebellion against and to the great confrontation with the culture of the time, that is, with the guiding principles of understanding and evaluating the world of his society, and to the introduction of self-experience as the primary source of knowledge. Appointing human reason as the only leader of his intellectual life, Descartes determines the program and future order of his thoughts; the method, in the form of the four rules, has "correctly to direct his reason and to seek the truth in the sciences." It brings Descartes over the methodical doubt to the unquestionable and unsurpassed foundation of human knowledge, the absolute certitude of the self in the Cogito. His analysis of the poor, unprotected I, related to itself knowingly, is unique and of priceless philosophical value. However, the further stations of the philosophical way of Descartes who, unable to stand the ontological loneliness of this philosophically determined self-awareness, sacrificed the idea of scientific progress to a rational theology, cannot be followed. The claim of the metaphysician to be able to discover or, at least, to test every humanly possible knowledge in terms of the absolute knowledge, disintegrates in view of the progress of the new sciences. Not eternal, necessary truth, but the finite human I is the origin of subjective philosophy. The stability of rational relations does not lie in these relations themselves as if they were existing for themselves, but in the strict consequence of logical reason. "'God’ is... the title for the transcendental-philosophical background of consciousness, for the conditions to which the I-think is always already subjected." All contents which allegedly are already given in the infinite knowledge and can always be deduced from it, have to be produced and developed out of the first human knowledge by way of scientific research. Science which received its new foundation in subjective philosophy and is sought in the efforts of communication of the scientists, is not characterized by truth, but by certitude. "'Truth’ is the concern of metaphysics or better of religion. It is of the essence of such truth, not to be capable of demonstration. The absolutely true has no need to prove itself; it is entitled to faith." Differences between metaphysics and religion, and the nature and possible justification of such metaphysical and religious faith are regrettably not discussed.—M. S. (shrink)

In order for Herman Cappelen to argue in his Philosophy Without Intuitions that philosophers have been on the whole mistaken in thinking that we actually use intuitions much at all in our first-order philosophizing, he must attempt the task of characterizing what something must be, in order to be an intuition.My discussion here is focused on the latter half of the book concerning the “argument from philosophical practice. I am in wholehearted agreement with the first half’s thesis that the usage (...) of the term “intuition” is highly motley and of no methodological use. I truly sympathize with the frustration he evidently feels at wrangling with that task, because I’ve felt the same in my own project critiquing what I do take to be a fairly common practice in contemporary philosophy that we often gesture at when we speak of intuitions. For the literature on intuitions can be a total mess on even the most basic questions about what intuitions are: beliefs, or sui generis seemings? Special in .. (shrink)

A simple tool is provided to assist researchers in assessing contributions to a scientific publication, for ease in evaluating which contributors qualify for authorship, and in what order the authors should be listed. The tool identifies four phases of activity leading to a publication—Conception and Design, Data Acquisition, Analysis and Interpretation, and Manuscript Preparation. By comparing a project participant’s contribution in a given phase to several specified thresholds, a score of up to five points can be assigned; the contributor’s scores (...) in all four phases are summed to yield a total “contribution score”, which is compared to a threshold to determine which contributors merit authorship. This tool may be useful in a variety of contexts in which a systematic approach to authorial credit is desired. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown (...) to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

For a subset K ⊆ [0, 1], the notion of K-satisfiability is a generalization of the usual satisfiability in first order fuzzy logics. A set Γ of closed formulas in a first order language τ is K-satisfiable, if there exists a τ-structure such that ∥ σ ∥ ∈ K, for any σ ∈ Γ. As a consequence, the usual compactness property can be replaced by the K-compactness property. In this paper, the K-compactness property for Łukasiewicz first order logic is investigated. (...) Using the ultraproduct construction, it is proved that for any closed subset K and set Γ of closed formulas, Γ is K-satisfiable if and only if it is finitely K-satisfiable. (shrink)

Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be (...) extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

Involutive Stone algebras were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and (...) hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic that can be determined by a finite number of matrices. Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic. (shrink)

Church's simple theory of types is a system of higher-order logic in which functions are assumed to be total. We present in this paper a version of Church's system called PF in which functions may be partial. The semantics of PF, which is based on Henkin's general-models semantics, allows terms to be nondenoting but requires formulas to always denote a standard truth value. We prove that PF is complete with respect to its semantics. The reasoning mechanism in PF for partial (...) functions corresponds closely to mathematical practice, and the formulation of PF adheres tightly to the framework of Church's system. (shrink)

This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, (...) we show how to interpret the theory BTFA in Robinson's theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q. (shrink)

It is a fundamental intuition about truth that the conditions under which a sentence is true are given by what the sentence asserts. My aim in this paper is to show that this intuition captures the concept of truth completely and correctly. This is conceptual deflationism, for it does not go beyond what is asserted by a sentence in order to define the truth status of that sentence. This paper, hence, is a defense of deflationism as a conceptual account of (...) truth. This defense is developed in four stages. In the first stage I present a distinction between two types of deflationism, conceptual and metaphysical. This is the central stage of the argument and its main conclusion is that conceptual deflationism when joined with the principle of bivalence is inconsistent with metaphysical deflationism, that is, conceptual deflationism together with bivalence entails a non-deflationary metaphysical account of truth. In the second and third stages of the argument I argue that the totality of the Tarskian biconditionals, when interpreted as definitional biconditionals, offers a description of the nature of truth. In the fourth, and final, stage of the argument I advance a positive case for conceptual deflationism. I explain how the revision theory of truth provides this sort of deflationism with its best evidence: a clear demonstration of its consistency and a compelling argument for its material adequacy. (shrink)

Tuberculosis is caused by bacillus Mycobacterium tuberculosis. In this study, a mathematical model of tuberculosis is analyzed. The numerical behaviour of the considered model is analyzed including basic reproduction number and stability. We applied three numerical techniques to this model, i.e., nonstandard finite difference scheme, Runge–Kutta method of order 4, and forward Euler scheme. NSFD scheme preserves all the essential properties of the model. Acquired results corroborate that NSFD scheme converges for each step size. While the other two schemes (...) failed to preserve some properties of the model such as positivity and convergence. A graphical comparison presented in this study confirms the numerical stability of the NSFD technique shown here is maintained over a large area. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sexual Difference as Model: An Ethics for the Global FutureGail SchwabIn Éthique de la différence sexuelle (1984), Luce Irigaray targeted language and love—for her, inseparable from each other—as the two areas of focus for the elaboration of an ethics of sexual difference. The heterosexual couple seemed to have taken on a new, and somehow inappropriately central, importance in Irigaray’s thought in the early eighties; however, the projected mutations in (...) language and love theorized in Éthique did not exclusively concern the heterosexual relationship, even though many readers of Irigaray expressed just such reservations about the book. Éthique foregrounded the couple in the love relationship in order to rethink the philosophical basis of ethics in general, to develop new paradigms, beyond or outside of Western totalizing phallo- and logocentrism, for human relations—not only relations between women and men, but also, and perhaps even more importantly, relations among women and relations among men. Irigaray carried on this project in subsequent works, in Sexes et parentés (1987), which as the title explicitly indicates, opens up the ethical debate to familial and genealogical issues and broadens her focus to include children and the ethical basis of their relationships to parents and more generally to adults of both sexes, and in Sexes et genres à travers les langues (1990), a cross-cultural report on her empirical studies of gender differences in language usage, which sheds new light on the linguistic and communicational issues she had presented in Éthique and even before, in several seldom read and even more rarely analyzed works of the late seventies and early eighties. J’aime à toi (I Love to You) (1992) returns specifically to the more traditionally philosophical approach to the problems of language and love and their intertwining, and carries on the work projected in Éthique, but it goes much further in both the theoretical and the practical development of the concept of sexual difference as the foundation for a new ethics, a new culture of universal validity. J’aime à toi can be read as a follow-up to Éthique and as a founding text for the construction of an ethics of difference modeled on sexual difference, an ethics for the future of humanity in all of its diversity.Western Feminism and the Global FutureIrigaray is very much aware of the limits of the various Western political and academic feminisms, of the need to broaden their scope, both horizontally across cultures and vertically within specific cultures, before they can serve as the basis for a new ethics. Irigaray expresses the concern that Western feminists, rather than represent the exploited women of the world, may exploit them ideologically for their own personal or political purposes, at the risk of preventing them from coming to a feminism of their own making, appropriate to their own cultures and historical moments. “Certain women do implement power strategies—including the power of the media—but not solely for the benefit of the exploited women they use as an alibi. They thus run the risk of clouding the issues and [End Page 76] preventing their consciousness from being raised” [Irigaray, J’aime à toi 15]. 1 Irigaray calls this “egological” feminism (Dare I invent a new term here? Now we have “egofeminists” as well as “ecofeminists”...) and demonstrates its totally undemocratic orientation, despite its representative claims.Certain militants..., practicing direct democracy or an egological feminism, based on their own real, or imagined, needs and desires, rather than on those of all women, leave women subject to existing legislation. Indifferent to the rights necessary for all women—including the little girls of the present and the future, and the women of other cultures—they make decisions that perpetuate, and even aggravate, through unnecessary misunderstandings, the injustices done the female gender.[J’aime à toi 13]As a feminist, in general, it always pains me to read criticisms of feminism, even cogent and theoretically valid criticisms, and I am even now painfully aware of the political dangers of criticizing feminism myself in a public forum such as this one. However, if I have managed to learn anything from the works of Western feminists of color and from Third World feminists, it is... (shrink)

Clinical Ethics, Ahead of Print. ObjectiveThe purpose of this study was to assess if a relationship existed between audiologists’ perceptions of moral distress, occupational wellbeing, and patient-practitioner orientation.DesignThe Moral Distress Thermometer, Health and Safety Executive Management Standards Indicator Tool and Patient-Practitioner Orientation Scale was sent out to all audiologists registered with the professional body Audiology Australia.Study sample: A total of 43 audiologists completed the questionnaires.ResultsUsing a multiple linear regression model there was no evidence of a relationship between patient-practitioner orientation and (...) either moral distress or occupational wellbeing. However, an association between higher moral distress and lower occupational wellbeing was demonstrated. The occupational wellbeing subscales of ‘managerial support’, ‘peer support’, ‘relationships’, ‘role’, and ‘change’ were strongly associated with poorer scores on moral distress.ConclusionFor our sample of audiologists, ethical conflict appeared to be linked to reduced job satisfaction. There is a need to consider ways of providing supportive organisational structures in which ethical conflicts can be openly discussed and negotiated in order to improve occupational wellbeing in the profession. (shrink)

The k-provability for an axiomatic system A is to determine, given an integer k 1 and a formula in the language of A, whether or not there is a proof of in A containing at most k lines. In this paper we develop a unification-theoretic method for investigating the k-provability problem for Parikh systems, which are first-order axiomatic systems that contain a finite number of axiom schemata and a finite number of rules of inference. We show that the (...) k-provability problem for a Parikh system reduces to a unification problem that is essentially the unification problem for second-order terms. By solving various subproblems of this unification problem , we solve the k- probability problem for a variety of Parikh systems, including several formulations of Peano arithmetic. Our method for investigating the k-provability problem employs algorithms that compute and characterize unifiers. We give some examples of how these algorithms can be used to solve complexity problems other than the k-provability problem. (shrink)

We investigate and extend the notion of a good approximation with respect to the enumeration ${({\mathcal D}_{\rm e})}$ and singleton ${({\mathcal D}_{\rm s})}$ degrees. We refine two results by Griffith, on the inversion of the jump of sets with a good approximation, and we consider the relation between the double jump and index sets, in the context of enumeration reducibility. We study partial order embeddings ${\iota_s}$ and ${\hat{\iota}_s}$ of, respectively, ${{\mathcal D}_{\rm e}}$ and ${{\mathcal D}_{\rm T}}$ (the Turing degrees) into (...) ${{\mathcal D}_{\rm s}}$ , and we show that the image of ${{\mathcal D}_{\rm T}}$ under ${\hat{\iota}_s}$ is precisely the class of retraceable singleton degrees. We define the notion of a good enumeration, or singleton, degree to be the property of containing the set of good stages of some good approximation, and we show that ${\iota_s}$ preserves the latter, as also other naturally arising properties such as that of totality or of being ${\Gamma^0_n}$ , for ${\Gamma \in \{\Sigma,\Pi,\Delta\}}$ and n > 0. We prove that the good enumeration and singleton degrees are immune and that the good ${\Sigma^0_2}$ singleton degrees are hyperimmune. Finally we show that, for singleton degrees a s < b s such that b s is good, any countable partial order can be embedded in the interval (a s, b s). (shrink)

Academic ethical values, having the well-deserved place by nursing and other scientific fields, and developing of the nursing science are proportionate to obeying the academic ethical values and internalizing those values. This study was carried out to determine the nurse academicians’ attitudes related to ethical values and related factors. The descriptive research was carried out between the dates of May and June 2017. The scope of the research consisted of nurse academicians working for two universities in Turkey and the sample (...) of the study consisted of 103 nurse academicians who had accepted to participate in the research. Data were collected by using “Descriptive Characteristics Information Form” and “Academic Ethics Values Scale”. Ethical considerations: Ethic approval from the institution, the Training and Research Hospital Noninvasive Clinical Studies Ethics Committee at the University of İzmir Katip Çelebi, and written approval from the owner of the scale were taken in order to carry out the study. The average age of the participants was 35.7 ± 9.6, 95% of them were female, and 51.5% of them were working as research assistants. The nurse academicians’ total item point average was 177,99 ± 11,01 and the attitudes of nurse academicians towards academic ethical values were positively. When the sub-dimension item point averages of the scale were examined, the lowest item point average was determined for the sub-dimension of “Scientific Research” as the highest item point average were being determined for the sub-dimension of “Teaching Process”. In this study that the participants’ attitudes towards academic ethical values were found meaningful at a high level, it was seen that academic assignment and age were important factors for the nurse academicians’ attitudes towards the colleagues and the teaching process. (shrink)

Totality states of affairs (Russell's 'general facts') are defended against Martin's criticisms. Although higher-order, they are not 'abstract in Quine's sense. If space-time is the whole of being, and if it can be seen as a vast conjunction of states of affairs, then the state of affairs that this is the totality of lower-order states of affairs is not additional to, but completes, space-times. If totality states of affairs are admitted, then there seems no need for any further negative states (...) of affairs additional to totality states of affairs. (shrink)

This text constitutes a reflection on politics, women, feminism and the future in the current global crisis. The civilizing crisis is total, universal and unstoppable. Here we try to sketch some ideas of what I think is really at stake: the definition of subject, person and rights, the idea of the future desirable society, and the foundations and regulation of social life, the concept of good life. In the context of an escalating global crisis and the growing feeling of being (...) in transition to nowhere, the question of whether the arrival of this new order will resist our rights is vital, ethical and politically fundamental. This document tries to collaborate with the process of answering it. The order of the world to come is being built today, in increasingly adverse conditions for the rights and freedoms of women and it is important to anticipate the reflection on some of its foreseeable consequences. (shrink)

Hume seems to argue unconvincingly against the infinite divisibility of finite regions of space. I show that his conclusion is entailed by respectable metaphysical principles which he held. One set of principles entails that there are partless (unextended) things. Another set entails that these cannot be ordered so that an infinite number of them compose a finite interval.

We formulate and analyze the dynamics of an influenza pandemic model with vaccination and treatment using two preventive scenarios: increase and decrease in vaccine uptake. Due to the seasonality of the influenza pandemic, the dynamics is studied in a finite time interval. We focus primarily on controlling the disease with a possible minimal cost and side effects using control theory which is therefore applied via the Pontryagin’s maximum principle, and it is observed that full treatment effort should be given (...) while increasing vaccination at the onset of the outbreak. Next, sensitivity analysis and simulations (using the fourth order Runge-Kutta scheme) are carried out in order to determine the relative importance of different factors responsible for disease transmission and prevalence. The most sensitive parameter of the various reproductive numbers apart from the death rate is the inflow rate, while the proportion of new recruits and the vaccine efficacy are the most sensitive parameters for the endemic equilibrium point. (shrink)

Rationale, aims and objectives To compare the pharmacotherapeutic approaches to diabetic hypertension of family physicians (FPs) and general practitioners (GPs). Methods A retrospective prescription-based study was conducted in 15 out of a total of 20 health centres, involving 115 primary care physicians – 77 FPs and 38 GPs, representing 74% of the primary care physicians of Bahrain. Prescriptions were collected during May and June 2000 to comprise a study population of 1266 diabetic-hypertensive patients. Results As monotherapy, angiotensin-converting enzyme (ACE) inhibitors (...) (37.9%) and β-blockers (38.3%) were the most commonly prescribed classes of antihypertensives by FPs and GPs, respectively. Calcium channel blockers (CCBs) were ranked third by both categories of physicians. For two-drug combinations, a β-blocker and an ACE inhibitor was the combination of choice for both physician categories. Patients managed by the FPs were more likely to receive a β-blocker–CCB combination (17.4 vs. 14.9%) or a diuretic–ACE inhibitor combination (16.7 vs. 11.4%) and less likely to receive a β-blocker–diuretic combination (11.8 vs. 16.7%) than those managed by the GPs. The proportion of patients receiving antihypertensive combinations was 40.6 and 38.5% for FPs and GPs, respectively. While the GPs prescribed CCB as a monotherapy to the elderly most often, the FPs choice was a β-blocker. Diuretics were less preferred by both FPs and GPs. β-Blocker–ACE inhibitor was again the most preferred combination of both FPs and GPs. FPs prescribed CCB–β-blocker combinations more often than GPs (P = 0.01), whereas CCB–ACE inhibitor combinations were less preferred (P = 0.09). A trend towards excessive use of short-acting nifedipine as monotherapy for elderly patients, both by FPs and by GPs, was noticed. Glibenclamide, alone or in combination with metformin, was the foremost antidiabetic drug prescribed by FPs and GPs. Middle-aged (45–64 years) patients seen by GPs were more likely to receive glibenclamide than those treated by FPs (P = 0.001) and less likely to receive gliclazide (P = 0.01). Combinations of a β-blocker with either glibenclamide or insulin were prescribed considerably more often by GPs.Conclusions Within the same practice setting, a substantial difference was observed between FPs and GPs in terms of preference for different classes of drugs in the management of diabetic hypertension. The compliance of both FPs and GPs was suboptimal; overall, the compliance of the FPs was closer to the recommended guidelines, however. Educational programmes should specifically address these inadequacies in order to improve the quality of health care. (shrink)

Hypotrichous ciliates extensively process genomic DNA during their life cycle. Processing occurs after cell mating, beginning with multiple rounds of DNA replication to form polytene chromosomes. Thousands of transposonlike elements are then excised from the chromosomes and destroyed, and thousands of short, internal eliminated sequences (IESs) are excised from coding and noncoding parts of genes and destroyed. IES removal from a gene is accompanied by splicing of the remaining chromosomal DNA segments to form a transcriptionally competent gene. For some genes (...) these DNA segments are in a scrambled order and are ligated into a genetically correct order at the time of IES removal. Next the polytene chromosomes are cut up band‐by‐band and all genes are excised from the chromosomes as short, linear molecules averaging 2.2 kbp (in Oxytricha nova). Gene excision is accompanied by destruction of all nongenic DNA, which, together with the transposonlike elements and IESs, accounts for ∼95% of the total sequence complexity of the genome in O. nova. Telomeric sequences are added to the excised gene‐sized DNA molecules. Finally, the gene‐sized molecules are replicated several times to form the macronucleus of the organism. (shrink)

Gonseth's primary concern in this volume, as in his earlier study of space, is the methodology of philosophical investigation. How does the philosopher achieve thoroughness without introducing arbitrariness? His method of dialectical synthesis is aptly illustrated by focusing on a privileged example, the problem of time. Common language analysis of "time" words, his initial concern, gives a preliminary sketch of a solution by making explicit the intuitive view of time implicit in language. Language, however, is unintelligible apart from experience, while (...) experience, in turn, entails an openness to the deeper understanding made possible through mathematics and physics. Yet neither of these is self-sufficient. A time order can be axiomatized, but the interpretation of this axiomatic system involves the intersection of a theoretical horizon and a phenomenal horizon. Similarly, the more precisely the physicist attempts to measure coincidences and durations the more dependent he becomes on theoretical knowledge and on a personal evaluation of the total situation. Neither Bergson's stress on subjective time nor the positivists' objectification of time can properly interrelate intuitive, mathematical, and physical time. A dialectical synthesis clarifies and integrates the subjective and objective aspects of time. This challenging book invites philosophers of all persuasions to re-examine their own implicit assumptions on the nature and method of philosophy.—E. M. M. (shrink)