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.

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)

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.

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.

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.

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.

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.

Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) unpublished results concerning neat reducts and amalgamation are given. . Several counterexamples which convey the gist of techniques used in this area are presented two of which are new It is known that the algebraic notion of amalgamation in a class of algebras corresponds to the metalogical notion of interpolation in the corresponding logic. Answers to open question in the recent paper [31] concerning both amalgamation and interpolation are summarized in tabular form at the end of this paper. This paper appears in two parts. The first part contains results on neat reducts. The present second part contains results relating the notion of neat embeddings to various amalgamation properties.1. (shrink)

Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and Pearce. In Example 2, uncountably many pairs of definitionally inequivalent theories are given such that their model categories are concretely isomorphic via bijections that preserve ultraproducts in the model categories up to isomorphism. Based on these results, we settle several conjectures of Barrett, (...) Glymour and Halvorson. (shrink)

This book features more than 20 papers that celebrate the work of Hajnal Andréka and István Németi. It illustrates an interaction between developing and applying mathematical logic. The papers offer new results as well as surveys in areas influenced by these two outstanding researchers. They also provide details on the after-life of some of their initiatives. Computer science connects the papers in the first part of the book. The second part concentrates on algebraic logic. It features a range of papers (...) that hint at the intricate many-way connections between logic, algebra, and geometry. The third part explores novel applications of logic in relativity theory, philosophy of logic, philosophy of physics and spacetime, and methodology of science. They include such exciting subjects as time travelling in emergent spacetime. The short autobiographies of Hajnal Andréka and István Németi at the end of the book describe an adventurous journey from electric engineering and Maxwell’s equations to a complex system of computer programs for designing Hungary’s electric power system, to exploring and contributing deep results to Tarskian algebraic logic as the deepest core theory of such questions, then on to applications of the results in such exciting new areas as relativity theory in order to rejuvenate logic itself. (shrink)

Introduced by Leon Henkin back in the fifties, the notion of neat reducts is an old venerable notion in algebraic logic. But it is often the case that an unexpected viewpoint yields new insights. Indeed, the repercussions of the fact that the class of neat reducts is not closed under forming subalgebras turn out to be enormous. In this paper we review and, in the process, discuss, some of these repercussions in connection with the algebraic notion of amalgamation. Some new (...) unpublished results concerning neat reducts and amalgamation are given. . Several counterexamples which convey the gist of techniques used in this area are presented two of which are new . It is known that the algebraic notion of amalgamation in a class of algebras corresponds to the metalogical notion of interpolation in the corresponding logic. Answers to open question in the recent paper [54] concerning both amalgamation and interpolation are summarized in tabular form at the end of this paper. This paper appears in two parts. The present first part contains results on neat reducts. The second part contains results relating the notion of neat embeddings to various amalgamation properties.1. (shrink)

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.

Este volumen recoge las lecciones del X Curso de Cultura hispanojudía y sefardí de la Universidad de Castilla-La Mancha, organizado por la Asociación de Amigos del Museo Sefardí (Toledo, Septiembre 2000) y consagrado al Pensamiento y Mística hispanojudía y sefardí. Las quince conferencias aquí reunidas ofrecen una perspectiva amplia, representativa y completa de los momentos, autores y temas más significativos tratados por pensadores y místicos sefardíes desde la Edad Media hasta nuestros días. Se aprecia una continuidad en los problemas y (...) una búsqueda constante de nuevas soluciones, adaptadas a las circunstancias de cada época. Es la primera vez que aparece en lengua castellana una visión global de esta rica faceta de la cultura hispanohebrea, que permite al lector acercarse a la evolución del pensamiento de los judíos originarios de Sefarad antes y después de 1492, tanto en su faceta filosófica con en su faceta mística (cábala). (shrink)

This study investigated how problem solvers get into and out of a state of impasse while solving difficult problems. 47 participants had to decipher the secret method behind 33 magic tricks while r...

This study examines processes through which social personae are conveyed by male Japanese students at a public university in Yokohama. Focusing on the frame-setting function of first person pronominals in contexts where there is no intra/inter speaker variation in the choice of FPP, this paper analyzes how speakers manage identity-associated discursive alignments related to a shared Okinawa prefecture background. The common experience of being from Okinawa prefecture and attending university far from home is the primary reason that these speakers are (...) close friends. However, analysis reveals speakers’ continual and active contention and re-formulation of this shared ‘Okinawan-ness’ and the personae to which it is linked. In particular, FPPs are implicated in speakers’ discussion of heterogeneity and/or local differences with respect to their Okinawa prefecture background. Strategic use of FPPs thus emerges as a salient tactic for speakers’ active negotiation of conversation relevant personae categories even in interactional contexts without variation. (shrink)

Multiple authorship is the universal solution to multi-tasking in the sciences. Without a team, each with their own set of expertise, and each involved mostly in complementary ways, a research project will likely not advance quickly, or effectively. Consequently, there is a risk that research goals will not be met within a desired timeframe. Research teams that strictly scrutinize their modus operandi select and include a set of authors that have participated substantially in the physical undertaking of the research, in (...) its planning, or who have contributed intellectually to the ideas or the development of the manuscript. Authorship is not an issue that is taken lightly, and save for dishonest authors, it is an issue that is decided collectively by the authors, usually in sync with codes of conduct established by their research institutes or national ministries of education. Science, technology and medicine publishers have, through independent, or sometimes coordinated efforts, also established their own sets of guidelines regarding what constitutes valid authorship. However, these are, for the greater part, merely guidelines. A previous and recent analysis of authorship definitions indicates that the definitions in place regarding authorship and its validity by many leading STM publishers is neither uniform, nor standard, despite several of them claiming to follow the guidelines as set forward by the International Committee of Medical Journal Editors or ICMJE. This disparity extends itself to ghost and guest authorship, two key authorship-related issues that are examined in this paper to assess the extent of discrepancies among the same set of STM publishers and what possible influence they might have on publishing ethics. (shrink)

According to estimates more than 400 biobanks currently operate across Europe. The term ‘biobank’ indicates a specific field of genetic study that has quietly developed without any significant critical reflection across European societies. Although scientists now routinely use this phrase, the wider public is still confused when the word ‘bank’ is being connected with the collection of their biological samples. There is a striking lack of knowledge of this field. In the recent Eurobarometer survey it was demonstrated that even in (...) 2010 two-thirds of the respondents had never even heard about biobanks. The term gives the impression that a systematic collection of biological samples can constitute a ‘bank’ of considerable financial worth, where the biological samples, which are insignificant in isolation but are valuable as a collection, can be preserved, analysed and put to ‘profitable use’. By studying the practices of the numerous already existing biobanks, the authors address the following questions: to what extent does the term ‘biobank’ reflect the normative concept of using biological samples for the purposes of biomedical research? Furthermore, is it in harmony with the so far agreed legal–ethical consensus in Europe or does it deliberately pull science to the territory of a new, ambiguous commercial field? In other words, do biobanks constitute a medico-legal fiction or are they substantively different from other biomedical research protocols on human tissues? (shrink)

Most departments in any field of science that have a sound academic basis have discussion groups or journal clubs in which pertinent and relevant literature is frequently discussed, as a group. This paper shows how such discussions could help to fortify the post-publication peer review movement, and could thus fortify the value of traditional peer review, if their content and conclusions were made known to the wider academic community. Recently, there are some tools available for making PPPR viable, either as (...) signed or anonymous comments, or in a hybrid format. Thus, limited platforms are currently in place to accommodate and integrate PPPR as a supplement to traditional peer review, allowing for the open and public discussion of what is often publicly-funded science. This paper examines ways in which the opinions that emerge from journal clubs or discussion groups could help to fortify the integrity and reliability of science while increasing its accountability. A culture of reward for good and corrective behavior, rather than a culture that protects silence, would benefit science most. (shrink)

In the present study, we explored the effects of high arousal on cognitive performance when facing a situation of risk. We also investigated how these effects are moderated by either positive or ne...

The diverse and paradoxical nature of globalization processes has given rise to new social constellations that shape transnational, national and local spaces. The historicity of identities, their past and present conditions, the changes they went through, the ways they influence the feeling of full membership in a community and the differentiation derived from cultural diversity and pluralism underscore the need for revisiting theoretical explorations. This paper addresses past and present social, cultural and religious processes in an era of transformations derived (...) from the complexity of today’s interconnected world and on the light of historical encounters. The need for revising the singularity of social and cultural trajectories and the religious trends gravitating in society is approached through snapshots of a twofold historical encounter: between Modernity and Latin America, and between Judaism and Modernity. Both express entrenched dilemmas of the binaries periphery-center and universal-particular. While one of them raised the issue of the dominant program of Modernity as a Western project, the other was entailed in the assumptions of one hegemonic religious constellation. (shrink)

This article takes the interlinkages between law and politics as its starting point. It analyzes recent changes in the legislative style of education governance in Sweden as not only a spec...

This article takes the interlinkages between law and politics as its starting point. It analyzes recent changes in the legislative style of education governance in Sweden as not only a species of crisis management, but also a long-term response to a series of tensions arising out of the push toward what has been identified as ‘juridification’ in many Western nations—the reliance on law and judicial means for addressing core moral predicaments, public policy questions, and political controversies. The article outlines the (...) notion of juridification at a theoretical level and highlights juridification processes and their possible ramifications on education. It argues that recent changes in the legislative style of education governance in Sweden not only reveal much about the commitments and implicit assumptions of modern regulatory and evaluative regimes, but also reflect the general impact of the rationalization of social and political life on the organization of government. The article provides a case with which to examine some of the theoretical underpinnings and implicit conceptual assumptions of modern regulatory and evaluative regimes as well as educational institutions’ relationships with the State. It shows that regulatory frameworks define the conceptualizations of what educational institutions do and thus of what actually gets done. (shrink)

TPPP/p25 is a recently discovered, unstructured protein involved in brain function. It is found predominantly in oligodendrocytes in normal brain but is enriched in neuronal and glial inclusions of Parkinson's disease and other synucleinopathies. Its physiological function seems to be the dynamic stabilization of microtubular ultrastructures, as well as the projections of mature oligodendrocytes and ciliary structures. We reappraise the earlier belief that TPPP/p25 is a brain‐specific protein. We have identified and cloned two shorter (N‐terminal‐free) homologs of TPPP/p25 that behave (...) differently from each other and from TPPP/p25. Two unique cell models have been established and used to study the effect of the unstructured protein on the energy metabolism and the formation of pathological aggregates. Our data suggest that the intracellular level of TPPP/p25 influences the cell differentiation, proliferation and the formation of protein aggregates, and consequently, the etiology of central nervous system diseases. (shrink)

This paper proposes an integrated account of the etiology of OCD that accommodates both dysfunctional cognitions and sensorimotor features of compulsive action. It is argued that cognitive/metacognitive theories do not aspire to address all obsessive-compulsive phenomenal properties and that empirical evidence concerning some of these requires the incorporation of motor deficits as an independent factor in a plausible conception of OCD. The difference in agency attribution between obsessive-compulsive persons and schizophrenia patients with delusions of control is also accounted for in (...) terms of bottom-up processes. (shrink)

The dominant philosophical conceptions of obsessive-compulsive behavior present its subject as having a deficiency, usually characterized as volitional, due to which she lacks control and choice in acting. Compulsions (mental or physical) tend to be treated in isolation from the obsessive thoughts that give rise to them. I offer a different picture of compulsive action, one that is, I believe, more faithful to clinical reality. The clue to (most) obsessive-compulsive behavior seems to be the way obsessive thoughts, which are grounded (...) in an irrational cognitive style in matters of risk, danger, and responsibility, motivate compulsions through bizarre means–end reasoning. I show that the patient with obsessive-compulsive disorder (OCD) is not weak and passive with regard to the compulsive act; rather, the act is voluntary and regarded by the patient as an instrument of control. I also defend the idea that OCD-related cognitions are either beliefs or mental states with relevantly similar functional roles. (shrink)

In this paper, by applying a feminist bioethical perspective, we identify a new form of medical paternalism that still shapes contemporary legal policies on human egg cryopreservation performed without medical reasons. The fear of negligent, careless women who opt to delay their pregnancy for mere convenience is a widely known gender biased stereotype. Nevertheless, the opinions and judgments of medical professionals on this issue have not yet been sufficiently explored by in-depth research. In this essay, therefore, first we look at (...) the broader bioethical, legal, and social aspects of human egg cryopreservation. In the second part of the paper we discuss a unique qualitative study conducted with professionals working at Hungarian IVF clinics. We argue, based on a bioethical analysis of the collected data, that when new reproduction technologies provide opportunities for women to widen their range of reproductive choices, the traditional forms of medical paternalism can be reinforced by gendered paternalism, as well. We identify several elements of gendered paternalism that characterized the attitudes of the IVF staff and discuss the professionals’ resistance to elective egg freezing and vitrification of eggs for the future. We conclude by suggesting directions for future policy. Although we focus on the Hungarian case in this paper, we are aware that similar attitudes can be observed in some other countries where this technology has become available and requested by women, but where they also face difficulties in their access to it. (shrink)

Gervain et al. discuss both behavioral and neurophysiological AGL studies that investigate rule and structure learning processes in infants. The paper provides an overview of all the major AGL paradigms used to date to investigate infant learning abilities at the level of morpho‐phonology and syntax from a very early age onwards. Gervain et al. also discuss the implications of the results for a general theory of natural language acquisition.

The paper explores the status of NATURE metaphors in Hungarian folk songs with respect to their representation and transmission of folk culture and worldview. Employing a Cultural Linguistic analysis, metaphors are observed from three perspectives: in relation to cultural schemas, generic-level conceptual metaphors, and experiential motivation. NATURE metaphors are to a large extent framed by cultural experience regarding their experiential basis, conceptual structure and relation with other cultural conceptualizations.

Gervain et al. discuss both behavioral and neurophysiological AGL studies that investigate rule and structure learning processes in infants. The paper provides an overview of all the major AGL paradigms used to date to investigate infant learning abilities at the level of morpho‐phonology and syntax from a very early age onwards. Gervain et al. also discuss the implications of the results for a general theory of natural language acquisition.