A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous E = mc² . The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.

A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.

We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...) accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND. (shrink)

We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.

Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local (...) deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open. (shrink)

In 1978, Yu. F. Borisov presented an axiom system using a few basic assumptions and four explicit axioms, the fourth being a formulation of the relativity principle; and he demonstrated that this axiom system had (up to choice of units) only two models: a relativistic one in which worldview transformations are Poincaré transformations and a classical one in which they are Galilean. In this paper, we reformulate Borisov’s original four axioms within an intuitively simple, but strictly formal, first-order logic framework, (...) and convert his basic background assumptions into explicit axioms. Instead of assuming that the structure of physical quantities is the field of real numbers, we assume only that they form an ordered field. This allows us to investigate how Borisov’s theorem depends on the structure of quantities. We demonstrate (as our main contribution) how to construct Euclidean, Galilean, and Poincaré models of Borisov’s axiom system over every non-Archimedean field. We also demonstrate the existence of an infinite descending chain of models and transformation groups in each of these three cases, something that is not possible over Archimedean fields. As an application, we note that there is a model of Borisov’s axioms that satisfies the relativity principle, and in which the worldview transformations are Euclidean isometries. Over the field of reals it is easy to eliminate this model using natural axioms concerning time’s arrow and the absence of instantaneous motion. In the case of non-Archimedean fields, however, the Euclidean isometries appear intrinsically as worldview transformations in models of Borisov’s axioms and neither the assumption of time’s arrow, nor the rejection of instantaneous motion, can eliminate them. (shrink)

We present three natural but distinct formalisations of Einstein’s special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.

ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than (...) 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics. (shrink)

This is the second part of the paper [Part I] which appeared in the previous issue of this journal.

Injury to the central or peripheral nervous system is often associated with persistent pain. After ischemic injury to the spinal cord, rats develop severe mechanical allodynia-like symptoms, expressed as a pain-like response to innocuous stimuli. In its short-lasting phase the allodynia can be relieved with the [gamma]-aminobutyric acid (GABA)-B receptor agonist baclofen, which also reverses the hyperexcitability of dorsal horn interneurons to mechanical stimuli. Furthermore, there is a reduction in GABA immunoreactivity in the dorsal horn of allodynic rats. Clinical neuropathic (...) pain of peripheral and central origin often cannot be relieved by opiates at doses that do not cause side effects. The loss of sensitivity to opiates may be associated with the up-regulation of endogenous antiopioid substances, such as the neuropeptide cholecystokinin (CCK). CCK and its receptor (CCK-R) protein is normally not detectable in rat dorsal root ganglion cells. After peripheral nerve section, both CCK and CCK-R are up-regulated in the dorsal root ganglia. Furthermore, CI 988, an antagonist of the CCK-B receptor, chronically coadministered with morphine, reduces autotomy, a behavior that may be a sign of neuropathic pain following peripheral nerve section. Thus, opiate insensitivity may be due to the release of CCK from injured primary afferents. Similarly, in the chronic phase of the spinal ischemic model of central pain, the allodynia-like symptom is not relieved by systemic morphine, but is significantly reversed by the CCK-B antagonist. Consequently, up-regulation of CCK and CCK-R in the CNS may also underlie opiate drug insensitivity following CNS injury. Thus, dysfunction of central inhibition involving GABA and endogenous opioids may be a factor underlying the development of sensory abnormalities and/or pain following injury to neural tissue. (shrink)

This book collects the work of leading scholars on Alain Badiou and G.W.F. Hegel, creating a dialogue between, and a critical appraisal of, these two central figures in European philosophy.

Jian Zhou,* Weiqiang Ju,* Xiaopeng Yuan, Xiaofeng Zhu, Dongping Wang, Xiaoshun HeOrgan Transplant Center, First Affiliated Hospital, Sun Yat-sen University, Guangzhou, People's Republic of China *These authors contributed equally to this work: Hyperosmolar nonketotic hyperglycemic coma is a serious, rare complication induced by methylprednisolone pulse therapy for acute rejection after orthotopic liver transplantation. Herein, we report an unusual case of a 58-year-old woman who experienced acute rejection at 30 months after OLT, only one case in which HNKHC resulted in MP (...) pulse therapy for acute rejection in all 913 recipients in our center. The general morbidity of HNKHC was 1.09‰ in this study. HNKHC is characterized by rapid onset, rapid progression, and a lack of specific clinical manifestations. High-dose MP management was a clear risk factor. The principle of treatment included rapid rehydration, low-dose insulin infusion, and correcting disorders of electrolytes and acidosis. In conclusion, clinicians considering MP pulse therapy after OLT should be alert to the occurrence of HNKHC. Keywords: liver transplantation, complications, hyperosmolar nonketotic hyperglycemic coma, methylprednisolone pulse therapy, principle of treatment. (shrink)

When fcc single crystals with high-symmetry crystal orientations are deformed to moderate strains by rolling, tension or channel die compression, long dislocation boundaries inclined to the extension axis form. Similarly, long dislocation boundaries are often found in grains embedded in polycrystals deformed in the same manner. These extended planar boundaries are characteristically - 30-40° from the extension direction and contain the transverse specimen axis. The objective of the present article is to demonstrate that EPBs formed during plane strain deformation are (...) parallel to equivalent slip planes, a pair of hypothetical slip systems used for analyses of the strain and crystal rotation components in place of the larger number of physical slip systems. The coincidence of EPBs and equivalent slip plane inclinations is shown to account for persistent observations of EPBs in the angle range - 30-40° from the rolling direction, in rolled single crystals of various initial orientations. The tendency of EPBs towards tilt or twist boundary character can also be rationalized on the basis of the equivalent slip system concept and consideration of the dislocation types available to be incorporated into EPBs. (shrink)

This study investigated the differences between past and future temporal discounting in terms of neural activity in relation to temporal distance. Results show that brain regions are engaged differently in past and future temporal discounting. This is likely because past temporal discounting requires memory reconstruction, whereas future temporal discounting requires the processing of uncertainty about the future. In past temporal discounting, neural activity differed only when preferences were made between rewards received one hour prior and rewards received further in the (...) past. The peak amplitudes of P2 and P3 varied as the temporal distance increased from 2 weeks to 50 years. In future temporal discounting, neural activity differed only when preferences were evaluated between two delayed rewards. The delay conditions and had a significant influence on P2 and N2. Findings indicate the existence of different decision-making systems operating in past and future temporal discounting. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:VIOLENCE AND NONVIOLENCE IN HINDU RELIGIOUS TRADITIONS Francis X. Clooney, SJ. Boston College Outline I.Violence, Sacrifice and Ritual 1. Some basic attitudes toward the killing of animals 2.Resolving the problem of sacrificial violence by internalization 3.Substitutions 4.Renunciation and nonviolence: an elite pathway 5.Violence andnonviolenceinrelation to vegetarianism: Hans Schmidt's theses?. Traditional Hindu Theorizations of Violence in Mimamsa Ritual Theory and Vedanta Theology 1. The ritual analysis (at Mimamsa Sutra 1.1.2) (...) of the Shyena rite which is performed in order to harm enemies 2.The Vedanta analysis (at Uttara Mimamsa Sutra 3.1.25) of ritual violence in relation to the prohibition of violence??. Violence in the Life of the State HOFrancis X. Clooney, S.J. 1. The royal power to punish (danda) 2.The synthesis of the ideals of brahmin and king a..The distribution and management of violence in the Laws ofManu (1st century CE) b. Policy toward warfare in the Arthashastra of Kautilya 3.The collapse of the brahmanical synthesis—and the emergence of a (seemingly) more nonviolent Hinduism 4.A comment on Gandhi (1 869-1948) and the contemporary emergence of post-Gandhian Hindu perspectives IV.Alternate Views from Outside the Sanskritic Tradition 1. Tamil Wisdom on Violence and Nonviolence: a.Tirukkural (c. 2nd century CE) b.Cilappatikaram (5th century CE) 2.Blood and Goddesses 3.From a Village Perspective a. Some Trouble with Cows b.Mahasweta Devi and the Literary Exposure of Violence V.The Question of a Christian Perspective on the Hindu Treatment of Violence and Religion: Are Victims Necessary? Some Presuppositions: • The following reflections, complex as they are, are governed by a reluctance to simplify Hindu teaching. I seek to avoid the view that the Hindu traditions had only one view of violence and nonviolence. • I use the term "Hindu" loosely and as a shorthand, without claiming that there is a single Hindu tradition, or a single creed shared by all Hindus, or a single attitude toward violence. But neither do I claim that there are simply many traditions without any common elements which justify the appellation "Hindu." • I am reluctant to idealize the Hindu traditions as if nonviolence must necessarily be taken as the epitome ofHindu thought. India's traditions are complex, and require complex treatment. • A serious artificiality of this paper is that I treat Hinduism without simultaneously lookinginto Buddhist andJain materials, though both were traditions with important and enduring commitments to nonviolence. Particularly with respect to the renunciant, marginal components of traditions, one ought not to make overly neat or decisive distinctions Violence and Nonviolence in Hindu Religious Traditions 1 1 1 between the Hindu, Buddhist, and Jain theories and practices related to violence and nonviolence. • I attempt to give preference to indigenous discussions ofissues related to violence and nonviolence; the context and mode of thinking are important, notjust the conclusions drawn. I therefore avoid simply mining Hindu texts for an answer to a contemporary question, "What is the Hindu attitude toward violence and nonviolence?" • In most ofwhat follows we must distinguish contexts where "violence" indicates "physical action which causes pain to some living being," from contexts where "violence" indicates "an intention, rooted in anger or malice, to hurt someone." I use the word "violence" for both in order to highlight the complex issues of distinction involved. In considering the Sanskrit formulations, one likewise has to distinguish himsa as "causing pain" from himsa as "intending to harm." • It is often difficult to date ancient texts, and even when one narrows down a date—within 200-300 years—its significance still depends on other, often equally broadly stated dates. Nevertheless, I do offer dates throughout, as summarized here: •ancient Vedic sacrificial practices, from before 1200 BCE •Vedic ritual analyses and reformulations of sacrifices as ritualized acts, in the Brahmanas, from after 1000 BCE •the Upanishadic exploration of the deeper meanings of ritual and interiorized alternatives to ritual, from after 900 BCE •the Buddha, c. 500 BCE •key texts in the theorization of royal power, The Laws of Manu (beginning of Common Era) and Arthashastra (c. 150 CE) •the Tamil wisdom text Tirukkural (100 CE) •Goddess texts as evidenced in Sanskrit formulations, from after 500 CE... (shrink)

There are good reasons for envisioning a global discourse about God, premised necessarily agreed upon perfections considered to be by definition proper to God, and for thinking through the implications of our understanding of God for morality. Philosophically, it makes sense to hold that claims about omnipotence, omniscience, and other superlative perfections are indeed maximal, and define “God” wherever the terminology of divine persons is taken up. Religiously too, it makes sense to assert that a deity possessed of perfections is (...) not just the deity of one’s own tribe or religion, but also the deity of the whole world, whether acknowledged as such or not. This essay delves into the larger set of rich complexities by three moves. First, I look into a single extended historical case of the extension of the discourse about God beyond the Christian West, the discourse on God proffered by Western Jesuit missionaries in India from the sixteenth to twentieth centuries. Second, I place next to that Jesuit learning the instance of a famed Hindu theologian’s discourse on God, God’s perfections, and their moral implications. Third, I briefly step back and assess the dangers and fruitful prospects inherent in thinking about God and morality in an interreligious context. (shrink)

The microstructures of cryogenically ball-milled Cu were investigated by high-resolution electron microscopy. It was found that the grain-size reduction is a dislocation-controlled continuous process which consists of the formation of small-angle grain boundaries , a gradual increase in misorientations as a result of accumulation of more dislocations and, finally, the formation of large-angle GBs. The GBs were generally curved, wavy or faceted, and heavily strained, which are typical characteristics of nanostructured materials. In addition, extrinsic dislocations were found in many GBs, (...) indicating that most are in a high-energy non-equilibrium configuration, which is consistent with observations in equal-channel angular pressing processed Cu, Ni, and Al-Mg, repetitive corrugation and straightening processed Cu and room-temperature ball-milled Cu. These results support a still-disputed concept that GBs in nanostructured metals processed by severe plastic deformation are mostly in non-equilibrium states. (shrink)