Although Fuzzy logic and Fuzzy Mathematics is a widespread subject and there is a vast literature about it, yet the use of Fuzzy issues like Fuzzy sets and Fuzzy numbers was relatively rare in time concept. This could be seen in the Fuzzy time series. In addition, some attempts are done in fuzzing Turing Machines but seemingly there is no need to fuzzy time. Throughout this article, we try to change this picture and show why it is helpful to consider (...) the instants of time as Fuzzy numbers. In physics, though there are revolutionary ideas on the time concept like B theories in contrast to A theory also about central concepts like space, momentum… it is a long time that these concepts are changed, but time is considered classically in all well-known and established physics theories. Seemingly, we stick to the classical time concept in all fields of science and we have a vast inertia to change it. Our goal in this article is to provide some bases why it is rational and reasonable to change and modify this picture. Here, the central point is the modified version of “Unexpected Hanging” paradox as it is described in "Is classical Mathematics appropriate for theory of Computation".This modified version leads us to a contradiction and based on that it is presented there why some problems in Theory of Computation are not solved yet. To resolve the difficulties arising there, we have two choices. Either “choosing” a new type of Logic like “Para-consistent Logic” to tolerate contradiction or changing and improving the time concept and consequently to modify the “Turing Computational Model”. Throughout this paper, we select the second way for benefiting from saving some aspects of Classical Logic. In chapter 2, by applying quantum Mechanics and Schrodinger equation we compute the associated fuzzy number to time. These, provides a new interpretation of Quantum Mechanics.More exactly what we see here is "Particle-Fuzzy time" interpretation of quantum Mechanics, in contrast to some other interpretations of Quantum Mechanics like " Wave-Particle" interpretation. At the end, we propound a question about the possible solution of a paradox in Physics, the contradiction between General Relativity and Quantum Mechanics. (shrink)

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

This paper provides a philosophical analysis of the Price equation and its role in evolutionary theory. Traditional models in population genetics postulate simplifying assumptions in order to make the models mathematically tractable. On the contrary, the Price equation implies a very specific way of theorizing, starting with assumptions that we think are true and then deriving from them the mathematical rules of the system. I argue that the Price equation is a generalization-sketch, whose main purpose is to (...) provide a unifying framework for researchers, helping them to develop specific models. The Price equation plays this role because, like other scientific principles, shows features as abstractness, unification and invariance. By underwriting this special role for the Price equation some recent disputes about it could be diverted. (shrink)

We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

Hall [(2007), Philosophical Studies, 132, 109–136] offers a critique of structural equations accounts of actual causation, and then offers a new theory of his own. In this paper, I respond to Hall’s critique, and present some counterexamples to his new theory. These counterexamples are then diagnosed.

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...) be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (shrink)

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and (...) Eckart potentials. (shrink)

We study the relative strength of the two axioms Every Pell equation has a nontrivial solution Exponentiation is total over weak fragments, and we show they are equivalent over IE1. We then define the graph of the exponential function using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol #, where # = x[log2y]. We prove the recursion laws of exponentiation in the corresponding fragment.

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be (...) verified with observation data. (shrink)

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...) century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.

Locus equations contain an economical set of hidden (i.e., not directly observable in the data) parameters of speech that provide an elegant way of characterizing the ubiquitous context-dependent behaviors exhibited in speech acoustics. These hidden parameters can be effectively exploited to constrain the huge set of context-dependent speech model parameters currently in use in modern, mainstream speech recognition technology.

The new mathematical connection of De Donder’s differential entropy production with the differential changes of thermodynamic potentials (Helmholtz free energy, enthalpy, and Gibbs free energy) was obtained through the linear sequence of equations (direct, straightforward path), in which we use rigorous thermodynamic definitions of the partial molar thermodynamic properties. This new connection uses a global approach to the problem of reversibility and irreversibility, which is vital to global learners’ view and standardizes the linking procedure for thermodynamic potentials (Helmholtz free energy, (...) enthalpy, and and Gibbs free energy)—preferably to the sensing learners. It is shown that De Donder’s differential entropy production in an isolated composite system is equal to the differential change in total entropy and that De Donder’s equation agrees with Clausius’ inequality. The useful work of the irreversible process is discussed, which with the decrease of irreversibility tends towards the hypothetical maximum useful work of the reversible process. (shrink)

There exist two conjectures for constraint satisfaction problems of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities satisfied by its polymorphisms clone, together with the natural uniformity on (...) it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core. (shrink)

We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational (...) axiomatization for these dynamic relation algebras. The completenessresult uses techniques from modal logic. We also lookat the variety generated by the class of dynamic relation algebras and note that there exist nonrepresentable algebras in this variety, ones which cannot be construedas spaces of relations. These results are also proved for an extension to a signature containing atomic tests and union. (shrink)

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, $W\gamma _{ik} = - G_{ik} + \tfrac{1}{2}g_{ik} g^{mn} G_{mn} - k(T_{ik} - \tfrac{1}{2}g_{ik} g^{mn} T_{mn} )$ together with the covariant Hilbert-gauge condition, $(\gamma _i^h - \tfrac{1}{2}\delta _i^k g^{mn} \gamma _{mn} )_{;k} = 0$ where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions γ ik(z)with (...) g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,Δp(Δg*)2(Δx)3≥h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k +γ k. (shrink)

A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.

The history of the publication of the gravitational field equations of general relativity in November 1915 by Einstein and Hilbert is briefly reviewed. An analysis of the internal structure and logic of Hilbert's theory as expounded in extant proofs and in the published version of his relevant paper is given with respect to the specific question what information would have been found on a missing piece of Hilbert's proofs. The existing texts suggest that the missing piece contained the explicit form (...) of the Riemann curvature scalar in terms of the Ricci tensor as a specification of the axiomatically underdetermined Lagrangian in Hilbert's action integral. An alternative reading that the missing piece of the proofs already may have contained the Einstein tensor, i.e. an explicit calculation of the gravitational part of Hilbert's Lagrangian is argued to be highly implausible. (shrink)

This paper uses duality to elaborate Slutzky equations of risks in quasi-linear decision models extended by independent background risks. Wealth, substitution and total effects are characterized in terms of mean-variance preferences. It is shown that both Pratt and Zeckhauser’s proper risk aversion and Kimball’s standard risk aversion are sufficient for negative substitution effects.

To find exact traveling wave solutions to nonlinear evolution equations, we propose a method combining symmetry properties with trial polynomial solution to nonlinear ordinary differential equations. By the method, we obtain some exact traveling wave solutions to the Burgers-KdV equations and a kind of reaction-diffusion equations with high order nonlinear terms. As a result, we prove that the Burgers-KdV equation does not have the real solution in the form a 0+a 1tan ξ+a 2tan 2 ξ, which indicates that some (...) types of the solutions to the Burgers-KdV equation are very limited, that is, there exists no new solution to the Burgers-KdV equation if the degree of the corresponding polynomial increases. For the second equation, we obtain some new solutions. In particular, some interesting structures in those solutions maybe imply some physical meanings. Finally, we discuss some classifications of the reaction-diffusion equations which can be solved by trial equation method. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. Afterwards we (...) give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. (shrink)

In classifications of vocabulary knowledge, vocabulary size and depth have often been separately conceptualized (Schmitt, 2014). Although size and depth are known to be substantially correlated, it is not clear whether they are a single construct or two separate components of vocabulary knowledge (Yanagisawa & Webb, 2020). This issue has not been addressed extensively in the literature and can be better examined using structural equation modeling (SEM), with measurement error modeled separately from the construct of interest. The current study (...) reports on conventional and Bayesian SEM approaches (e.g., Muthén & Asparouhov, 2012) to examine the factor structure of the size and depth of second language vocabulary knowledge of Japanese adult learners of English. A total of 255 participants took five vocabulary tests. One test was designed to measure vocabulary size in terms of the number of words known, while the remaining four were designed to measure vocabulary depth in terms of word association, polysemy, and collocation. All tests used a multiple-choice format. The size test was divided into three subtests according to word frequency. Results from conventional and Bayesian SEM show that a correlated two-factor model of size and depth with three and four indicators, respectively, fit better than a single-factor model of size and depth. In the two-factor model, vocabulary size and depth were strongly correlated (r =.945 for conventional SEM and.943 for Bayesian SEM with cross loadings), but they were distinct. The implications of these findings are discussed. (shrink)

Structural equation modelling (SEM) is outlined and compared with two non-linear alternatives, artificial neural networks and ''fast and frugal'' models. One particular non-linear decision-making situation is discussed, that exemplified by a lexicographic semi-order. We illustrate the use of SEM on a dataset derived from 539 volunteers' responses to questions about food-related risks. Our conclusion is that SEM is a useful member of the armoury of techniques available to the student of human judgement: it subsumes several multivariate statistical techniques and (...) permits their flexible combination, and it provides robust goodness-of-fit statistics and is available in (generally) easy-to-use computer packages. Although the number of tasks for which SEM provides a persuasive psychological model is small, it is very useful in identifying the important variables and their inter-relations that contribute to task performance, and thus can constitute a valuable intermediate staging point between raw data and a fully fledged psychological theory. (shrink)

Applying the resolution–scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Itô process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker–Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrödinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we identify a generalization to time dependent (...) problems in any number of dimensions. The Itô process is then driven by a function which is identified as establishing the link between non-differentiable dynamics and standard quantum mechanics. This is the basis for the scale relativistic interpretation of standard quantum mechanics and, in the case of applications to chaotic systems, it leads us to identify quantum-like states as characterizing the entire system rather than the motion of its individual constituents. (shrink)

Journal of Mathematical Logic, Ahead of Print.

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

Equational Boolean Relation Theory concerns the Boolean equations between sets and their forward images under multivariate functions. We study a particular instance of equational BRT involving two multivariate functions on the natural numbers and three infinite sets of natural numbers. We prove this instance from certain large cardinal axioms going far beyond the usual axioms of mathematics as formalized by ZFC. We show that this particular instance cannot be proved in ZFC, even with the addition of slightly weaker large cardinal (...) axioms, assuming the latter are consistent. (shrink)

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

The article is guided by two main research questions: First, do the Equator Principles (EPs), a voluntary CSR-initiative in the project finance sector, and the recently published working paper of the Thun Group of Banks adequately address the U.N. Guiding Principles on Business and Human Rights or do they fall behind the ‘Ruggie framework’? Second, is the demand for human rights due diligence sufficient to classify the EPs as a positive and leverage-based concept of CSR (à la Wettstein and Wood) (...) or is this requirement still a feature of a negative and impact-based concept of CSR? In case it is a negative and impact-based concept of CSR, the question comes up which further steps should be taken by financial institutions to fulfill their positive and leverage-based responsibilities. The article argues that positive and leverage-based responsibilities for multinational companies exist – due to the moral nature of human rights and due to the political authority of multinational companies – and that the current (Ruggie-like) requirements for human rights due diligence are not adequate for a positive and leverage-based concept of CSR. Further measures should be taken by multinational companies – and especially (Equator) banks which possess a high leverage-influence over their clients – to not only ensure the respect for human rights, but also the on-the-ground protection and realization of human rights. (shrink)

In their important work on locus equations, Sussman and his colleagues have helped to simplify the theoretical problem of how human listeners identify place of articulation contrasts among consonants, but much work remains before this problem is solved.

A number of recent discussions have argued that George Price's equationfor representing evolutionary change is a powerful and illuminatingtool, especially in the context of debates about multiple levels ofselection. Our paper dissects Price's equation in detail, and comparesit to another statistical tool: the calculation and comparison ofaverage fitnesses. The relations between Price's equation and equationsfor evolutionary change using average fitness are closer than issometimes supposed. The two approaches achieve a similar kind ofstatistical summary of one generation of change, (...) and they achieve thisvia a similar loss of information about the underlying fitnessstructure. (shrink)

This study shows how precise simple analytical solutions for the generalized Dirac equation with repulsive vector and attractive energy-dependent Lorentz scalar potentials, position-dependent mass potential, and a tensor interaction term can be obtained within the framework of both similarity transformation and the asymptotic iteration methods. These methods yield a significant improvement over existing approaches and provide more plausible and applicable ways in explaining the pseudospin symmetry’s breaking mechanism in nuclei.