We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of (...) the four classes of trees mentioned above. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms (...) of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analysing first order definable and undefinable paths in trees. (shrink)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. (...) We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for (...) class='Hi'>linear or partial orders conflicts with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

Abstract : The main goal in this work to find the general solution for some kind of linear second order homogenous differential equations with variable coefficients which have the general form , by using the substitution ,which transform form the above equation to Riccati equation .

Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's intuitionistic theorems (...) in the traditional monograph "Introduction to Metamathematics". We analyze four different translations of intuitionistic logic into linear logic and compare their proofs using a linear logic based prover with focusing. In order to enhance the set of problems in our library, we apply the three provability-preserving translations to the propositional benchmarks in the ILTP Library. Finally, we generate a comprehensive set of reachability problems for Petri nets and encode such problems as linear logic sequents, thus enlarging our collection of problems. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' (...) temporal logic of linear discrete time with gaps follows. (shrink)

A major question in sensory science is how a sensation of magnitude F (such as loudness) depends upon a sensory stimulus of physical intensity I (such as a sound-pressure-wave of root-mean-square sound-pressure-level). An empirical just-noticeable sensation difference (∆F)_j at F_j specifies a just-noticeable intensity difference (∆I)_j at I_j. Classically, intensity differences accumulate from a stimulus-detection threshold I_th up to a desired intensity I. The corresponding sensation differences likewise accumulate up to F(I) from F(I_th ), the non-zero sensation (as suggested by (...) hearing studies) at I_th. Consequently, sensation growth F(I) can be obtained through classic Fechnerian integration, in which some empirically-based relation for the Weber Fraction, ∆I⁄I, is combined with either Fechner’s Law ∆F=B or Ekman’s Law (∆F⁄F)=g. The number of steps in I is equated to the number of steps in F; an infinite series ensues, whose higher-order terms are traditionally ignored (Fechnerian integration). But also, remarkably, so are the integration bounds I_th and F(I_th ). Here, we depart from orthodoxy by including those bounds. Bounded Fechnerian integration is first used to derive hypothetical sensation-growth equations for which the differential ∆F(I)=F(I+∆I)-F(I) does indeed return either Fechner’s Law or Ekman’s Law respectively. One relation emerges: linear growth of sensation F with intensity I. Subsequently, 24 sensation-growth equations F(I) that the author had derived using bounded Fechnerian integration (12 equations for the Weber Fraction (∆I⁄I), each combined with either Fechner’s Law or with Ekman’s Law) are scrutinized for whether their differentials F(I+∆I)-F(I) return the respective Fechner’s Law or Ekman’s Law, particularly in the previously-unexamined limits (∆I⁄I)≪1 and (∆I⁄I)→0. Classic claims made by Luce and Edwards (1958) are then examined, viz., that three popular forms of the Weber Fraction, when combined with Fechner’s Law, produce sensation-magnitude equations that subsequently return the selfsame Fechner’s Law. When sensation-growth equations are derived here using bounded Fechnerian integration, Luce and Edwards (1958) prove to be wrong. (shrink)

In this paper, a solenoid based linearly movable armature system is designed using robust control theory in order to improve the performance of the system. Reference track method is the best performance analysis for position control systems. Among the robust controllers, H infinity mixed-sensitivity and Mixed H 2 /H∞ with Regional Pole Placement Controllers are used to improve the performance of the system. Comparison of the proposed controllers for tracking a reference displacement signals (step and sine wave) and a promising (...) simulation result have been obtained. (shrink)

In what respects is Western civilization superior or inferior to its rivals? In raising this question we are addressing a particularly strong form of the problem of relativism. For in order to compare civilizations one with another we would need to be in possession of a framework that is neutral and objective, a framework based on principles of evaluation which would be acceptable, in principle, to all human beings. Morality will surely provide one axis of such a framework (and we (...) note in passing that believers in Islam might quite reasonably claim that their fellow-believers are characteristically more moral than are many in the West). Criteria such as material wellbeing, too, will need to play a role, as also will happiness or pleasure (and again we note that it is not clear a priori that there is more happiness in the West than there is among the citizens of other civilizations). Since, however, these axes of evaluation do not run in tandem, we cannot expect to be able to formulate some single criterion which would enable us to rank civilizations in a simple unilinear order. Even happiness (pace some proponents of the utilitarian philosophy) comes in different types, and to count in the civilization stakes the happiness involved would presumably need to be of the right kind. Thus it is not clear that happiness derived from, say, taking drugs or torturing small animals is going to be able to count in favor of a civilization as much as, say, happiness derived from reading poetry or planting corn. Hence, for these and other reasons, we will have to deal with a multidimensional framework, in which some civilizations may excel along some axes but do badly on others. A further problem turns on the fact that there is no such relation as better than. Rather, when A is better than B then this is always in some respect C. Yet even when we compare one thing with another in some given respect we are not always dealing with a simple linear order. This is because the relation ‘being better than in respect C’ is not in every case transitive.. (shrink)

What the world needs now is another theory of vagueness. Not because the old theories are useless. Quite the contrary, the old theories provide many of the materials we need to construct the truest theory of vagueness ever seen. The theory shall be similar in motivation to supervaluationism, but more akin to many-valued theories in conceptualisation. What I take from the many-valued theories is the idea that some sentences can be truer than others. But I say very different things to (...) the ordering over sentences this relation generates. I say it is not a linear ordering, so it cannot be represented by the real numbers. I also argue that since there is higher-order vagueness, any mapping between sentences and mathematical objects is bound to be inappropriate. This is no cause for regret; we can say all we want to say by using the comparative truer than without mapping it onto some mathematical objects. From supervaluationism I take the idea that we can keep classical logic without keeping the familiar bivalent semantics for classical logic. But my preservation of classical logic is more comprehensive than is normally permitted by supervaluationism, for I preserve classical inference rules as well as classical sequents. And I do this without relying on the concept of acceptable precisifications as an unexplained explainer. The world does not need another guide to varieties of theories of vagueness, especially since Timothy Williamson (1994) and Rosanna Keefe (2000) have already provided quite good guides. I assume throughout familiarity with popular theories of vagueness. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's (...) Collapsing Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .

The major point in [1] chapter 2 is the following claim: “Any formalized system for the Theory of Computation based on Classical Logic and Turing Model of Computation leads us to a contradiction.” So, in the case we wish to save Classical Logic we should change our Computational Model. As we see in chapter two, the mentioned contradiction is about and around the concept of time, as it is in the contradiction of modified version of paradox. It is natural to (...) try fabricating the paradox not by time but in some other linear ordering or the concept of space. Interestingly, the attempts to have similar contradiction by the other concepts like space and linear ordering, is failed. It is remarkable that, the paradox is considered either Epistemological or Logical traditionally, but by new considerations the new version of paradox should be considered as either Logical or Physical paradox. Hence, in order to change our Computational Model, it is natural to change the concept of time, but how? We start from some models that are different from the classical one but they are intuitively plausible. The idea of model is somewhat introduced by Brouwer and Husserl [3]. This model doesn’t refute the paradox, since the paradox and the associated contradiction would be repeated in this new model. The model is introduced in [2]. Here we give some more explanations. (shrink)

I describe a way of handling comparative adjectives "a is P-er than b", in terms of degrees "a has P to degree d". I defend this approach against attacks due to C J F Williams in an article in the same issue of *Analysis*, by tracing his objections to the assumption that degrees must be linearly ordered. Since this abstract is written years later, I can mention that some of the ideas were taken further in my Hypercomparatives. Synthese 111, 1997, (...) 97-114 . (shrink)

This paper argues that processes in the sensible realm can be in accord with reason in the Timaeus, since rationality is understood here as being based on regularity, which is conferred onto processes by time. Plato uses two different temporal structures in the Timaeus, associated with the contrast there drawn between Greek and Egyptian approaches to history. The linear order of before and after marks natural processes as rational and underlies the Greek treatment of history. By contrast, a bidirectional (...) temporal structure is the basis for the Egyptian approach to historical processes: present actions are not only determined by preceding ones in the past, but can also be influenced by the future (plans, aims). This latter temporal structure is shown to be necessary for learning from history, which makes human actions more regular. (shrink)

Bayne and Carter argue that the mode of consciousness induced by psychedelic drugs does not fit squarely within the traditional account of modes as levels of consciousness, and favor instead a multi-dimensional account according to which modes of consciousness differ along several dimensions—none of which warrants a linear ordering of modes. We discuss the assumption that psychedelic drugs induce a single or paradigmatic mode of consciousness, as well as conceptual issues related to Bayne and Carter’s main argument against the (...) traditional account. Finally, we raise a set of questions about the individuation of dimensions selected to differentiate modes of consciousness that could be addressed in future discussions of the multi-dimensional account. (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)

The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known paradoxes (...) in judgement aggregation and we pinpoint the reasoning steps that trigger the inconsistencies. Moreover, we extend the map of possibility and impossibility results in judgement aggregation by discussing the case of substructural logics. In particular, we show that there exist fragments of linear logic for which general possibility results can be obtained. (shrink)

We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the (...) practical and scientific issues that we face in our daily lives, and we need careful study to enable us to avoid losses. For this, the linear programming method was used, which is one of the research methods. Processes, where the problem data is converted into a linear mathematical model for which the optimal solution achieves the desired goal. Since these models are linear models, we can solve them using the direct simplex method and its modifications, but the specificity that these models enjoy has enabled scholars and researchers to find special methods that help us in obtaining the optimal solution. Whatever the method used, the goal is to determine the number of units transferred from any material from production centers to consumption centers, or to allocate a machine or person to do a job so that the cost or time is as short as possible. These issues were addressed according to classical logic, but the ideal solution was a specific value appropriate to the conditions in which the data was collected and does not take into account the changes that may occur in the work environment. In order to obtain results that are more accurate and enjoy a margin of freedom, we present in this book a study of transport issues and neutrosophic allocation issues and some methods for solving them. By neutrosophic issues we mean These are the problems in which the data are neutrosophic values, i.e. the required quantities and the available quantities. (shrink)

The aim of this article is to depict as accurately as possible the ideological conflict between liberal democracy and an insidious present-day version of communism, namely cultural socialism. Obviously, it is not easy to describe the essential relationships between two complex phenomena that evolve nonlinearly within a hypercomplex environment. The ideological systems of liberal democracy and cultural socialism involve both objective and subjective facts, material and immaterial components, neutral and emotion-laden aspects, deliberate and unintentional behaviors, linear and nonlinear effects, (...) and planner-dependent and observer-dependent events. They affect each other and also fall under the influence of different non-political factors that characterize the Euro-Atlantic societies. In order to cope with the complexity of this research object we adopt the methodological dualism and a praxeological approach. The system of discursive liberal democracy can be seen – from a praxeological perspective – as a spontaneous order generated and maintained by three classes of attractors: the attractors of democracy (inclusion, political equality, high level of political participation, and majority rule), the attractors of liberalism (rule-governed political agency and the right to reasonable self-determination), and the attractors of public rationality (publicness, objectivity, verifiability, and revisability). Liberal democracy subsists in any society only if a sufficient number of its members reproduce the corresponding attractors in their political (and non-political) conduct. It is important to note that it is much easier to reproduce the attractors of democracy than the attractors of liberalism and rationality. Maybe because of that the socialists strive to undermine the system of liberal democracy by perverting – in the first instance – the standards of (public) rationality. One of the most important ingredient of cultural socialism is so-called "political correctness", by means of which people are prevented from expressing genuinely and politely certain beliefs or doubts in the public sphere even if they profess the standards of objectivity, verifiability, and revisability. Under the pressure of political correctness the attractors of public rationality tend to wither, the liberal dimension of the political system disappears too, and democracy becomes a sheer tyranny. Choosing a form of political organization is not a scientific, but a socio-political matter. It is not the job of social scientists to recommend or impose political goals in general and a specific political system in particular. However, inasmuch as some goals are set, social scientists can indicate the most appropriate means of meeting them. If the Euro-Atlantic societies still value liberal democracy and want to preserve it, it is important to teach them how to reproduce its attractors and to counteract the pernicious effects of cultural socialism. (shrink)

We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment needed for their (...) formalization, and even simplify their logical formulation. (shrink)

A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided (...) it can be axiomatized with Horn sentences. The existence of free models is a useful intermediate result. The independence Property is also a tool to decide that a sentence cannot be deduced. We illustrate this with the case of the classical Caratheodory theorem for Pasch-Peano geometries. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic multi-objective programming (...) problem at end of this paper. (shrink)

The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are somewhat limited in predicting possible neurodevelopmental issues. They rely on linear models and assumptions of normality for physical growth data – obscuring key statistical information about possible neurodevelopmental risk in growth data that actually has accelerated, non-linear rates-of-change and variability encompassing skewed (...) distributions. Here, we use new analytics to profile growth data from 36 newborn babies that were tracked longitudinally for 5 months. By switching to incremental (velocity-based) growth charts and combining these dynamic changes with underlying fluctuations in motor performance – as the transition from spontaneous random noise to a systematic signal – we demonstrate a method to detect very early stunting in the development of voluntary neuromotor control and to flag risk of neurodevelopmental derail. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of (...) choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

This study investigated the perception of how methods of entrepreneurial education predict the level of economic security in the Southern Senatorial District of Cross River State. It was guided by two research questions and two hypotheses, tested at a significant level of 0.05. The research design was a survey. The study had 350 participants. A 40-item "Entrepreneurship Education and Economic Security Questionnaire" (EEESQ) was validated by five experts from the University of Calabar and used in data collection. The EEESQ was (...) pilot tested on 30 respondents who were not a part of the study sample. In order to evaluate the consistency of the EEESQ, Cronbach Alpha statistics were used, and they yielded reliability values of 0.84 and 0.80 for the independent and dependent variables, respectively. Three hundred and fifty respondents responded to the instrument, which was administered. In order to find the answers to the study questions and test the hypotheses, data were analyzed using linear regression analysis at the significant level of .05. The study discovered that experiential and transdisciplinary teaching strongly predict economic security. It was recommended that educators at various stages should introduce students to real-world scenarios when teaching entrepreneurship education. (shrink)

How should your opinion change in light of an epistemic peer's? We show that the pooling rule known as "upco" is the unique answer satisfying some natural desiderata. If your revised opinion will impact your other views by Jeffrey conditionalization, then upco is the only standard pooling rule that ensures the order in which peers are consulted makes no difference. Popular alternatives like linear pooling, geometric pooling, and harmonic pooling cannot boast the same. In fact, no alternative can that (...) possesses four minimal properties these proposals all share. (shrink)

There have been innumerable attempts to characterize personal identity either in terms of psychological continuity or in terms of the linear and self-referential process of reproduction of one's self. I will defend the thesis according to which personal identity emerges mainly as a process of transcendence of one's own "minimal self". It is precisely by means of this critical distancing from his self, I contend, that the individual learns to see himself under a new perspective as far as to (...) experience his self as a surprise. Amazed at his own self, he lives a reawakening which leads him to a transformation of his way of living. This transcendence of the self cannot take place self-referentially but only through the force of an example provided by another person. Such act neither aims at the annihilation of the individual, nor does it contrast with self-love. It is in conlict merely with what Harry Frankfurt calls "selfindulgence". The idea of a transcendence of the self is already to be found in Plato, who fostered the overcoming of and puriication from amathia (in the sense of a "not knowing but pretending to know") and from an excessive love of oneself. Indeed, these latter would be the two grave diseases which render formless the soul of a human being, for they stand in the way of the cura sui. The same theme will reappear in Max Scheler's phenomenological reduction, which endeavours to bracket egocentrism (construed as excessive love of oneself) in order to give a form to the personal identity. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)

Unlike other writing systems that are readily classifiable as alphabetic or syllabic in their structure, the Indic Devanagari script (of which Hindi is an example) has properties of both syllabic and alphabetic writing systems. Whereas Devanagari consonants are written in a linear left-to-right order, vowel signs are positioned nonlinearly above, below, or to either side of the consonants. This fact results in certain words in Hindi for which, in a given syllable, the vowel precedes the consonant in writing but (...) follows it in speech. The current research exploited this property of the script to examine when the disparity between spatial and temporal sequenc- ing would incur a processing cost and the implications of the findings from naming speed, accuracy, and writing order for the level at which words in Devanagari are segmented. The results support a partly phonemic and partly syllabic level of segmentation, consistent with the structural hybridity of the script. (shrink)

There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a (...) little, or not at all. There are far fewer proposals for how to proceed in these cases, and those there are have undesirable features. I begin by considering four proposals and arguing that they don't work. Then I'll describe my own proposal, which is intended to cover the situation in which we want to pool the individual opinions in order to ascribe an opinion to the group considered as an agent in its own right. (shrink)

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). (...) It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

The concept of time-travel is a modern idea which combines the imaginary signification of rational domination, the imaginary signification of technological omnipotence, the imaginary concept of eternity and the imaginary desire for immortality. It is a synthesis of central conceptual schemata of techno-science, such as the linearity and homogeneity of time, the radical separation of subjectivity from the world, the radical separation of the individual from his/her social-historical environment. The emergence of this idea, its spread during the 20th century as (...) a major theme of science fiction literature alongside its dissemination as a scientific hypothesis, its popularity with both the public and the scientific community, are indications of the religious role of techno-science. It is my opinion, finally, that, as a chimera, time-travel is non-feasible and impossible. In order to support my claims, I will briefly outline the origins of the time-travel concept and its epistemological and metaphysical/ontological conditions. If these conditions prove to be absurd, the logical impossibility of time-travel will have been demonstrated. (shrink)

There are two important ways in which, when dealing with documents, we go beyond the boundaries of linear text. First, by incorporating diagrams into documents, and second, by creating complexes of intermeshed documents which may be extended in space and evolve and grow through time. The thesis of this paper is that such aggregations of documents are today indispensable to practically all complex human achievements from law and finance to orchestral performance and organized warfare. Documents provide for what we (...) can think of as a division of intellectual, instructional, and deontic labour, allowing plans, orders, and obligations to be enmeshed together in a way that often involves the use of diagrammatic elements, as for example in a musical score. (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that (...) the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that (...) the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions (...) are required, and mathematical criteria were derived to design molecular models capable of pattern generation. The classical embryological feature of proportion regulation can be incorporated into the models. The conditions are mathematically necessary for the simplest two-factor case, and are likely to be a fair approximation in multi-component systems in which activation and inhibition are systems parameters subsuming the action of several agents. Gradients, symmetric and periodic patterns, in one or two dimensions, stable or pulsing in time, can be generated on this basis. Our basic concept of autocatalysis in conjunction with lateral inhibition accounts for self-regulatory biological features, including the reproducible formation of structures from near-uniform initial conditions as required by the logic of the generation cycle. Real tissue form, for instance that of budding Hydra, may often be traced back to local curvature arising within an initially relatively flat cell sheet, the position of evagination being determined by morphogenetic fields. Shell theory developed for architecture may also be applied to such biological processes. (shrink)

abstract Postdiction effects are phenomena in which a stimulus influences the appearance of events taking place before it. In metacontrast masking, for instance, a masking stimulus can ren- der a target stimulus shown before the mask invisible. This and other postdiction effects have been considered incompatible with a simple explanation according to which (i) our perceptual experiences are delayed for only the time it takes for a distal stimulus to reach our sensory receptors and for our neural mechanisms to process (...) it, and (ii) the order in which the processing of stimuli is completed corresponds with the apparent temporal order of stimuli. As a result, the theories that account for more than a single postdiction effect reject at least one of these theses. This paper presents a new framework for the tim- ing of experiences—the non-linear latency difference view—in which the three most dis- cussed postdiction effects—apparent motion, the flash-lag effect, and metacontrast masking—can be accounted for while simultaneously holding theses (i) and (ii). This view is grounded in the local reentrant processes, which are known to have a crucial role in perception. Accordingly, the non-linear latency difference view is both more parsimonious and more empirically plausible than the competing theories, all of which remain largely silent about the neural implementation of the mechanisms they postulate. (shrink)

Philosophers of dispositionalism deny the Humean account of causality in terms of constant conjunction, contiguity, temporal priority and contingency. And some of them go further to explain the causal relation not between events or objects, but between properties, in terms of reciprocity, simultaneity, ubiquity, intentionality and holism. But their exposition seems to remain fragmented even though they try to make use of the notions of intentionality and holim. I would inquire reasons why it is piecemeal, by analysing that they employ (...) these notions of intentionality and holism which has been constructed within the dualistic tradition. If one wants to make the dispositional project to be powerful, she should look for the notions of intentionality and holism which are free of the dualistic traits and which have been constructed in the tradition of naturalism. The concept of integrationality may be a candidate for such a task. This conception was coined in Zhongyong under the name of cheng in that there is nothing without cheng, and was developed in one of Sok-hon Ham's thesis that any entity in the world contains "seed" within it to realize objectives shared by all involved. Humans are privileged and distinct from other natures, but there is continuity between them. An example of the integrationality applied to the case of humans would be that realization of myself and realizations of all others are one and not two. I would summarize notions of "cheng" and "seed" by offering the integrationality thesis, that is, that there is integrationality in any entity like dispositions such that the integrationality is a power to realize the embedded objective of it in the context where it interacts with all others. I would claim that integrationality is a metaphysical basis for a way of human thinking, by arguing that it is a necessary part of presupposition for our understanding of the world without which the world is not intelligible. The notion of integrationality is involved empirically as well as conceptually. Empirically, there are numerous reports from physics, biology and information science, which provide with a clue which may well be taken to show the ubiquitous integrationality. But some conceptual considerations would also indicate necessarily toward the same direction. These would include various theses of ontology, epistemology, disposition, modality, naturalized intentionality, fitting and topics like these. I will investigate some of them in order to justify my claim of this paper. (shrink)

Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change through experiences: taste for Mozart changes through listening to it, sympathy for another player through observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework for defining, (...) analysing and comparing rival models of change. I show that seemingly basic postulates on modelling change together have strong implications, like irrelevance of the order in which someone has his experiences and ‘linearity’ of change. This is a step towards placing the modelling of change on solid axiomatic grounds and enabling non-arbitrary incorporation of change into economic models. (shrink)

The foundation of a building connects the main body superstructure to the ground. Every form of foundation and footing have a unique application in a given location for a certain weather condition. Understanding the foundation work is crucial for carrying out building activities. Due to the variety of structures they support, foundations are frequently built in different subsoil conditions and are exposed to static loads. The proper evaluation of soil-bearing capacity is fundamental to the construction of various buildings. One of (...) the quick, easy, and affordable ways to determine soil carrying capacity is the plate load test. The effect of subsoil conditions on the test results is assessed and analyzed in thorough parametric investigations. An overview of axial static and dynamic plate load testing will be given in this study. This article presents detailed processes and schematics. In an effort to highlight the differences and shared characteristics of the results, computational test results of the static load plate test and the dynamic load plate test are contrasted. A load cell, a steel plate, a hydraulic actuator mounted on a big truck to apply a load, a load cell to measure the load, and one or more linear variable displacement transformers to measure the vertical displacements make up the test setup. The maximum thrust load that should be applied to a fixed or stationary actuator when it is not moving is known as a "static load depending on the actuator's static load capacity, we can determine what a safe load is. The maximum thrust load that should be applied to the actuator while it is moving is known as a dynamic load. Dynamic load capacity refers to how much force an actuator can exert when driven and extending or retracting. With each method's benefits and drawbacks considered, it can be determined that using them in various situations and agreeing to the confrontation of these tests for the purpose of comparing results is the best course of action in order to have a base that satisfies the construction standards. (shrink)

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting (...) it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (= ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). (shrink)

The article fits into the debate regarding space, time and nature in dialogue with the world lived by subjects that build up themselves or are built as mythological heroes, source of speech and spacial concrete practices. It's a poorly explored field in Geography that recently approaches to the cultural dynamic debate, to the symbolic field and also to their spacialization processes. The aim is to discuss the possibility of understanding in the present time about the space organization processes related to (...) the society's previous moments, in a space/time dialectics which articulate the present and past times in a complex and non linear way. Methodologically, starting from a literature review about the theme, the present study was linked to the field and documental research about migration to the vicinal ways of Transamazônica Highway (BR-230 Highway), the creation of the "Centro Espírita União do Vegetal", a religion that arises in the Amazon and set up its headquarters in Brasília and the construction of Brasilia as a modern metropolis without a past. The conclusion points at the possibility of space/time nexuses linking the Myth of Nature to the Creation of Heroes, constantly appropriated and with new meanings, in order to support speeches and new actions dialectically throughout the Brazilian contemporaneous space. (shrink)

In 1596, in the Mysterium Cosmographicum, a twenty-five-year-old Johannes Kepler rashly banished lines from the universe. They “scarcely admit of order,” he wrote, and God himself could have no use for them in this “well-ordered universe.” Twenty-five years later, though, Kepler had come to repent the temerity of his youth. “O male factum!” he lamented in a 1621 second edition of the Mysterium – “O what a mistake” it was to dismiss lines, for linearity is revealed in those most perfect (...) and divine motions – the revolutions of the heavenly orbs. Why did Kepler come to lament the rashness of his youth? The answer lies deep in the details of Kepler’s discovery of elliptical orbits in 1605. Kepler struggled to find an empirically adequate description and physically plausible explanation of Mars’s path through the heavens. He realized, though, that his originally spherical notion of location and direction were insufficient to reconcile descriptions and explanations of the planet’s motion. Crucially inspired by the “magnetic philosophy” of William Gilbert, Kepler adopted an oriented conception of space, which finally allowed a plausible mechanism to be constructed for elliptical motion – the true path of the planet. Yet, this oriented space required the stipulation of straight lines. Without straight lines, even God could not construct the planets’ elliptical orbits. (shrink)

This paper describes an AFOSR-supported basic research program that focuses on developing a new framework for combining hard with soft data in order to improve space situational awareness. The goal is to provide, in an automatic and near real-time fashion, a ranking of possible threats to blue assets (assets trying to be protected) from red assets (assets with hostile intentions). The approach is based on Conceptual Spaces models, which combine features from traditional associative and symbolic cognitive models. While Conceptual Spaces (...) are revolutionary, they lack an underlying mathematical framework. Several such frameworks have attempted to represent Conceptual Spaces, but by far the most robust is the model developed by Holender. His model utilizes integer linear programming in order to obtain an overall similarity value between observations and concepts that support the formation of hypotheses. This paper will describe a method for building Conceptual Spaces models for threats that utilizes ontologies as a means to provide a clear semantic foundation for this inferencing process; in particular threat ontologies and space domain ontologies are developed and employed in this approach. A space situational awareness use-case is presented involving a kinetic kill scenario and results are shown to assess the performance of this fusion-based inferencing framework. (shrink)