Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. (...) This completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

A completeness theorem is established for logics with congruence endowed with general semantics (in the style of general frames). As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence (...) and general semantics. An example is provided showing that completeness is not always preserved by fibring ligics endowed with standard (non general) semantics. A categorial characterization of fibring is provided using coproducts and cocartesian liftings. (shrink)

The transference of preservation results between importing and unconstrained fibring is investigated. For that purpose, a new formulation of fibring, called biporting, is introduced, and importing is shown to be subsumed by biporting. In consequence, particular cases of importing, like temporalization, modalization and globalization are subsumed by fibring. Capitalizing on these results, the preservation of the finite model property by fibring is transferred to importing and then carried over to globalization.

Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive (...) levels. Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. (shrink)

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we (...) distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L D I etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, (possibly not normal) modal or intermediate logics, each complete for a class of (not necessarily frame) Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics (normal modal extensions of K) have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically. (shrink)

. The semantic collapse problem is perhaps the main difficulty associated to the very powerful mechanism for combining logics known as fibring. In this paper we propose cryptofibred semantics as a generalization of fibred semantics, and show that it provides a solution to the collapsing problem. In particular, given that the collapsing problem is a special case of failure of conservativeness, we formulate and prove a sufficient condition for cryptofibring to yield a conservative extension of the logics being combined. (...) For illustration, we revisit the example of combining intuitionistic and classical propositional logics. (shrink)

We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language both for classical and intuitionistic fragment), we then prove that in order (...) to express well-known properties like ‘speaks-for’ or ‘hand-off’, defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. (shrink)

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the (...) other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated. (shrink)

We study access control policies based on the says operator by introducing a logical framework called Fibred Security Language (FSL) which is able to deal with features like joint responsibility between sets of principals and to identify them by means of first-order formulas. FSL is based on a multimodal logic methodology. We first discuss the main contributions from the expressiveness point of view, we give semantics for the language (both for classical and intuitionistic fragment), we then prove that in order (...) to express well-known properties like 'speaks-for' or 'hand- off', defined in terms of says, we do not need second-order logic (unlike previous approaches) but a decidable fragment of first-order logic suffices. We propose a model-driven study of the says axiomatization by constraining the Kripke models in order to respect desirable security properties, we study how existing access control logics can be translated into FSL and we give completeness for the logic. (shrink)

This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...) formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete. (shrink)

:This article examines material economies of carbon fibre as a prosthetic form of masculinity. The paper advances three main arguments. Firstly, carbon fibre can be a site in which disability is overcome, an act of overcoming that is affected through masculinized technology. Secondly, carbon fibre can be a homosocial surface; that is, carbon fibre becomes both a surface extension of the self and a third-party mediator in homosocial relationships, a surface that facilitates intimacy between men in ways that devalue femininity (...) in both male and female bodies. Carbon fibre surfaces are material extensions of subjectivity, and carbon fibre surfaces are vectors of the cultural economies of masculine competition. Thirdly, the article gives an account of Oscar Pistorius as an example of the masculinization of carbon fibre, and the associated binding of a psychic attitude of misogyny and power to a form of violent and competitive masculine subjectivity. The paper unpacks the affects, economies and surfaces of “carbon fibre masculinity” and discusses Pistorius’ use of carbon fibre, homosociality and misogyny as forms of protest masculinity through which he unconsciously attempted to recuperate his gendered identity from emasculating discourses of disability. (shrink)

This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.

Modern applications of logic in mathematics, computer science, and linguistics use combined systems of different types of logic working together. This book develops a method for combining--or fibring--systems by breaking them into simple components which can be manipulated easily and recombined.

In a long-term transformation, that begins in Antiquity but takes a crucial turn in the Renaissance anatomies, the “fibre” becomes from around 1750 the operative building block and at the same time the first unifying principle of function-structure-complexes of organic bodies. It occupies the role that the cell takes up in the cell œconomies of the second third of the nineteenth century. In this paper, I will first discuss some key notions, technical analogies, and images that are related to “fibre”-concepts (...) from Andreas Vesalius to Albrecht von Haller and then focus on Charles Bonnet's and Denis Diderot's fibre œconomies. In Bonnet's and Diderot's fibre œconomies, the self-active, regulating properties of fibre-agents and their material structures, that reach from fibre bundles, tissues and membranes to apparati of organs, are united within the concrete whole of individual organized “systems” or “networks.”. (shrink)

Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither (...) the Barcan formula nor its converse hold. (shrink)

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems $\mathbf{L}_i, i \in I$, to form a new system $\mathbf{L}_I$. The methodology `fibres' the semantics $\mathscr{K}_i$ of $\mathbf{L}_i$ into a semantics for $\mathbf{L}_I$, and `weaves' the proof theory of $\mathbf{L}_i$ into a proof system of $\mathbf{L}_I$. There are various ways of doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different (...) systems, denoted by $\mathbf{L}^F_I, \mathbf{L}^D_I$ etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, modal or intermediate logics, each complete for a class of Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically. (shrink)

This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see (...) how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature. (shrink)

This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having (...) a fibred approach is discussed in the final section. (shrink)

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of (...) two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided. (shrink)

Recently, Dewar (2019) has suggested that one can apply the strategy of 'sophistication' - as exemplified by sophisticated substantivalism as a response to the diffeomorphism invariance of General Relativity - to gauge theories such as electrodynamics. This requires a shift to the formalism of fibre bundles. In this paper, I develop and defend this suggestion. Where my approach differs from previous discussions is that I focus on the metaphysical picture underlying the fibre bundle formalism. In particular, I aim to affirm (...) the physical reality of gauge properties. I argue that this allows for a local and separable explanation of the Aharonov-Bohm effect. Its puzzling features are explained by a form of holism inherent to fibre bundles. (shrink)

Lawvere hyperdoctrines give categorical algebraic semantics for intuitionistic predicate logic. Here we extend the hyperdoctrinal semantics to a broad variety of substructural predicate logics over the Typed Full Lambek Calculus, verifying their completeness with respect to the extended hyperdoctrinal semantics. This yields uniform hyperdoctrinal completeness results for numerous logics such as different types of relevant predicate logics and beyond, which are new results on their own; i.e., we give uniform categorical semantics for a broad variety of non-classical predicate logics. And (...) we introduce an analogue of Lawvere–Tierney topology and cotopology in the hyperdoctrinal setting, which gives a unifying perspective on different logical translations, in particular allowing for a uniform treatment of Girard’s exponential translation between linear and intuitionistic logics and of Kolmogorov’s double negation translation between intuitionistic and classical logics. In the hyerdoctrinal conception, type theories are categories, logics over type theories are functors, and logical translations between them, then, are natural transformations, in particular Lawvere–Tierney topologies and cotopologies on hyperdoctrines. The view of logical translations as hyperdoctrinal Lawvere–Tierney topologies and cotopologies has not been elucidated before, and may be seen as a novel contribution of the present work. From a broader perspective, this work may be regarded as taking first steps towards interplay between algebraic and categorical logics; it is, technically, a combination of substructural algebraic logic and hyperdoctrinal categorical logic, as the hyperdoctrinal completeness theorem is shown via the integration of the Lindenbaum–Tarski algebra construction with the syntactic category construction. As such this work lays a foundation for further interactions between algebraic and categorical logics. (shrink)

Women played a vital role in the American and British antislavery movements of the nineteenth century. Among other strategies, American women’s efforts included boycotting slave-produced goods and selling luxury items to raise money for the cause. Complicated by the nation’s diverse religious landscape, popular attitudes toward dress rendered some forms of consumer advocacy more effective than others. Fashionable antislavery fairs provided significant financial support for political campaigns. Meanwhile, Quaker Christians and some evangelical groups, which valued plain dress, promoted abstention from (...) all slave- produced goods and the genesis of an alternative free-labour cotton trade. Unlike the famous British boycotts of slave- produced sugar, American textile boycotts gained little support. This paper examines how the tension between American fashion and antifashion influenced the rise and fall of the free cotton movement. (shrink)

Although Wittgenstein is famously skeptical about the possibility of making substantial philosophical claims, he can be said to offer significant insights into the difference between inner and outer as well as the difference between self and other.1 He consistently reminds us that inner and outer are intimately connected instead of only causally related, as well as that the self—far from being a wholly independent entity—always already finds itself constituted by its relationships with others. In thus contesting the Cartesian view on (...) subjectivity, however, Wittgenstein may appear to simply reduce the inner to the outer and the self to the other.. (shrink)

Hypersequents are a natural generalization of ordinary sequents which turn out to be a very suitable tool for presenting cut-free Gentzent-type formulations for diverse logics. In this paper, an alternative way of formulating hypersequent calculi (by introducing meta-variables for formulas, sequents and hypersequents in the object language) is presented. A suitable category of hypersequent calculi with their morphisms is defined and both types of fibring (constrained and unconstrained) are introduced. The introduced morphisms induce a novel notion of translation between (...) logics which preserves metaproperties in a strong sense. Finally, some preservation features are explored. (shrink)

Women played a vital role in the American and British antislavery movements of the nineteenth century. Among other strategies, American women’s efforts included boycotting slave-produced goods and selling luxury items to raise money for the cause. Complicated by the nation’s diverse religious landscape, popular attitudes toward dress rendered some forms of consumer advocacy more effective than others. Fashionable antislavery fairs provided significant financial support for political campaigns. Meanwhile, Quaker Christians and some evangelical groups, which valued plain dress, promoted abstention from (...) all slave- produced goods and the genesis of an alternative free-labour cotton trade. Unlike the famous British boycotts of slave- produced sugar, American textile boycotts gained little support. This paper examines how the tension between American fashion and antifashion influenced the rise and fall of the free cotton movement. (shrink)

It is suggested that bifurcation of parallel fibres in the cerebellar cortex assists the spatiotemporal convergence of temporally dispersed and asomatotopic inputs to granule cells. This increases the number of combinations of inputs which can be compared for the purpose of sequence recognition.

. In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main (...) feature of these categories is the preservation, by morphisms, of meta-properties of the consequence relations, which allows, in several cases, to recover a logic by fibring of its fragments. The fibring in this categories is called meta−fibring. Several examples of well-known logics which can be recovered by meta-fibring its fragments (in opposition to fibring in the usual categories) are given. Finally, a general semantics for objects in Seq (and, in particular, for objects in Mcon) is proposed, obtaining a category of logic systems called Log. A general theorem of preservation of completeness by fibring in Log is also obtained. (shrink)

During the 1840s and 1850s the British embryologist and histologist Martin Barry (1802-1855) propounded a bold and original thesis about the microscopic structure of animal and vegetable tissue. He maintained that minute double spirals were virtually ubiquitous in the makeup of a wide range of structures. This paper considers how a claim of this kind was consonant with a romantic image of scientific creativity with which Barry identified. It describes his partially successful strategies to convince contemporaries of the veracity of (...) his claims. Major figures in the field, such as Richard Owen and Jan Evangelista Purkyně, affirmed that Barry's spirals were real objects in nature. Others, notably William Sharpey, became convinced that the spirals were mere artefacts and that Barry was deeply flawed as a scientific investigator. The ultimate rejection of his hypothesis had much to do with the moral repugnance that Barry's attempts to gain credit for a major discovery evoked among influential medical scientists. This negative assessment of Barry as an investigator reveals the lineaments of an alternative ethic of scientific practice. (shrink)

Fibre suspension has garnered considerable attention in turbulent flows that are used in many industries. Solid particles, such as dust particles, notably affect the turbulent flow field in a rotational frame. In assessing their impacts, the dusty turbulent flow for fibre suspensions needs to be studied in a frame of rotation that can be substantially applied in many industries. This study, therefore, aims to build a theoretical model for the energy motion of dusty turbulent flow of fibre suspensions in a (...) rotational frame. The turbulence momentum equation was considered to formulate the model in presence of dusty fluid rotating flow of fibre suspensions. The newly derived equation was derived in second-order correlation tensors Fi,j, Wi,j, Gi,j, Si,j, Xi,j, Yi,j, Qi,j, and Ri,j at any two points in the flow domain, where the tensors were expressed as space, time, and distance functions. The developed model is a considerable improvement because it takes into account all of the potential influential parameters that could affect the motion of turbulent energy, such as dust particles, suspending particles, and rotating frame. However, the impact of these parameters on turbulence energy motion must be evaluated in order to assess the performance of turbulence systems utilized in a variety of industries, such as paper manufacturing. The present theoretical development will contribute to open up experimental and numerical research opportunities for the advancement of the industry, science, and technology. (shrink)

DNA is packed as chromatin on several levels in the eukaryotic nucleus. Dissection of chromatin with nucleases produces three stable substructures: the nucleosome core particle, the chromatosome and the 30 nm fibre. Whilst the first two allow transcription, the 30 nm fibre is taken to be the first level of transcriptionally dormant chromatin and it has an important functional role in cell differentiation and epigenetic regulation. Its structure has been a subject of continuing discussion since native fibres cannot readily be (...) crystallized. This problem has recently been addressed by reconstitution of fibres on repeats of DNA sequences having nucleosome‐positioning properties and two different structures were reported.1,2The reconstitution results and their interpretations are compared in this review with experimental data from native chromatin and it is shown that the results of Robinson et al.2 conform well with the known structural features of native fibres and are a good first step towards understanding the structure of the fibre. BioEssays 30:1003–1009, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

L’ouvrage d’A. Wenger est la version remaniée de sa thèse de doctorat complétée par certains développements parus dans des revues spécialisées, Clio. Histoire, Femmes et Sociétés, Dix-huitième Siècle… La reprise de travaux antérieurs a entraîné parfois quelques redondances – sur l’onanisme ou la lectrice, par exemple – qu’une lecture plus attentive aurait pu éviter. Cette restriction est mineure au regard de l’intérêt de cette étude dont « l’objectif est de faire bouger les objets d’analyse t...

The Motoneurone and its Muscle Fibres presents a state-of-the-art summary of knowledge concerning the motoneurones, vital for innervating and commanding skeletal muscles. No muscle action would be possible without motoneurones. These cells are therefore absolutely essential for the execution of normal behaviour and for life support. It is their degeneration that leads to various kinds of motoneurone disease that are often ultimately lethal. However, the study of motoneurones is also important for general insights as to how neurones work, because the (...) motoneurone is probably the best understood kind of nerve cell so far in neuroscience. Motoneurones of the spinal cord were the first type of central nerve cell to be subjected to detailed physiological measurements, and much is known about how their activity is regulated by synapses from other central neurones. For most of the individual neurones within the central nervous system, the precise functional tasks are difficult to define. However, for motoneurones much is now known about their short- and long-term interactions with their main targets, the skeletal muscle fibres. Functions of neurones must be analyzed in relation to the response properties of their target cells. Therefore, this book deals with both, summarizing classical as well as recent knowledge concerning the motoneurone and its muscle fibres. This is the first time that so many aspects of this broad subject matter are treated in one comprehensive monograph. (shrink)

1. The current political scene in many countries is populated by polarised groups with sharply contrasting loyalties and beliefs implying that there are fundamental schisms between opposing groups....