Recently the cosmological evolution of the universe has been considered where 3-dimensional spatial topology undergone drastic changes. The process can explain, among others, the observed smallness of the neutrino masses and the speed of inflation. However, the entire evolution is perfectly smooth from 4-dimensional point of view. Thus the raison d’être for such topology changes is the existence of certain non-standard 4-smoothness on R4 already at very early stages of the universe. We show that the existence of such (...) smoothness can be understood as a byproduct of the quantumness of the origins of the universe. Our analysis is based on certain formal aspects of the quantum mechanical lattice of projections of infinite dimensional Hilbert spaces where formalization reaches the level of models of axiomatic set theory. (shrink)

It is shown that data on the dissociation rate of deuterium obtained in an experiment at the Sudbury Neutrino Observatory provides evidence that the Continuous Spontaneous Localization wavefunction collapse model should have mass–proportional coupling to be viable.

A model for the structure of point-like fermions as tightly bound composite states is described. The model is based upon the premise that electromagnetism is the only fundamental interaction. The fundamental entity of the model is an object called the vorton. Vortons are semiclassical monopole configurations of electromagnetic charge and field, constructed to satisfy Maxwell's equations. Vortons carry topological charge and one unit each of two different kinds of angular momenta, and are placed in magnetically bound (...) pair states having angular momentum l=1/2. The topological charge prevents the mutual annihilation of the vorton pair. The helicity eigenstates of the vortons' intrinsic angular momenta form the basis for a set of internal quantum numbers for the pair which distinguish the different (point-like) pair states. Sixteen fourcomponent spinor states, eight leptonic and eight hadronic, are obtained. Eleven of these are identified with the quantum numbers of the experimentally known particles: e, ve, μ, vμ, τ, vτ; p, n, Λ, Λc, and b. Thus one new heavy lepton with its neutrino and three new quark states are predicted. Some possibilities for the extension of this model are discussed. (shrink)

An alternative neutrino oscillation process is presented as a counterexample for which the neutrino may have nil mass consistent with the standard model. The process is developed in a quantum trajectories representation of quantum mechanics, which has a Hamilton–Jacobi foundation. This process has no need for mass differences between mass eigenstates. Flavor oscillations and \ oscillations are examined.

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories (...) that are based on fundamentally different concepts of temporal evolution. (shrink)

We state the consistency problem of extensional partial set theory and prove two complementary results toward a definitive solution. The proof of one of our results makes use of an extension of the topological construction that was originally applied in the paraconsistent case.

If one builds a topological model, analogous to that of Moschovakis , over the product of uncountably many copies of the Cantor set, one obtains a structure elementarily equivalent to Krol's model . In an intuitionistic metatheory Moschovakis's original model satisfies all the axioms of intuitionistic analysis, including the unrestricted version of weak continuity for numbers.

Interpreting the diamond of modal logic as the derivative, we present a topological canonical model for extensions of K4 and show completeness for various logics. We also show that if a logic is topologically canonical, then it is relationally canonical.

We compute the effect of collapse models on neutrino oscillations. The effect of the collapse is to modify the evolution of the spatial part of the wave function and we will show that this indirectly amounts to a change on the flavor components. For the analysis we use the mass proportional CSL model, and perform the calculation to second order perturbation theory. As we will show, the CSL effect is very small—mainly due to the very small mass of (...) neutrinos—and practically undetectable. (shrink)

In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that (...) topological predictions can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone. (shrink)

We reformulate a key definition given by Wáng and Ågotnes to provide semantics for public announcements in subset spaces. More precisely, we interpret the precondition for a public announcement of ???? to be the “local truth” of ????, semantically rendered via an interior operator. This is closely related to the notion of ???? being “knowable”. We argue that these revised semantics improve on the original and offer several motivating examples to this effect. A key insight that emerges is the crucial (...) role of topological structure in this setting. Finally, we provide a simple axiomatization of the resulting logic and prove completeness. (shrink)

Beyond their linguistic and rhetorical uses, the mental epistemic verbs to knowand to believe reveal a basic conceptual system for human intentionality and the theory of representational mind. Numerous studies, particularly in the field of child development, have been devoted to the conditions under which knowledge and belief are acquired. Upstream of this empirical approach, this paper proposes a topological model of the conceptual structure underlying the linguistic use of to know and to believe. A cusp model (...) of catastrophe theory is chosen to model the formation of epistemic states. Its main characteristic is considering to believe as an intermediate state which lacks stability and presents the delayed effect of hysteresis. The attribution of mental states to the other (viewpoint of the third person) is obtained by the crossing of first and third person knowledge and belief, which gives rise to new categories (to know if and to falsely believe) and closes the system. Another merging of the beliefs of persons A and B, using the butterfly catastrophe, provides a model of interpersonal belief appreciated by an independent observer along a potential evolving from agreement to disagreement. (shrink)

This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent (...) class='Hi'>topological reconstruction of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness. (shrink)

In this highly original text, Christopher Steinsvold explores an alternative semantics for logics of rational belief. Topologies, as mathematical objects, are typically interpreted in terms of space; here topologies are re-interpreted in terms of an agent with rational beliefs. The topological semantics tells us that the agent can never, in principle, know everything; that the agent's beliefs can never be complete. -/- A number of completeness proofs are given for a variety of logics of rational belief. Beyond this, the (...) author explores the philosophical question of why our beliefs can never be complete, and considers the possibility that a totality of truths is a dialethia. -/- This work will be of interest to all philosophers interested in epistemology, and modal logicians as well. (shrink)

By using a language as accessible to as broad an audience as possible, in this paper we identify serious insufficiencies of the neutrino and quark hypotheses for the synthesis of the neutrons from protons and electrons inside stars according to the familiar reaction ${{\rm p}^+ + \bar {\nu} + {\rm e}^-\rightarrow {\rm n}}$ . We introduce, apparently for the first time, the hypothesis that the energy and spin needed for the synthesis of the neutron originate either from the environment (...) or from the ether conceived as a universal medium with very high energy density via an entity here called etherino, denoted with the letter “a” (from the Latin aether), carrying mass and charge 0, spin ${1\over 2}$ and 0.78 MeV energy according to the synthesis ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}}$ . We identify the compatibility ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}\rightarrow {\rm p}^+ + {\rm e}^- + \bar \nu}$ and the incompatibility condition ${{\rm p}^+ + {\rm a} + {\rm e}^-\rightarrow {\rm n}\rightarrow {\rm p}^+ + {\rm e}^- + \bar{{\rm a}}}$ of the neutrino and etherino hypotheses, the latter representing the possible return of missing features to the ether, without being necessarily in conflict with neutrino experiments. We review the new structure model of the neutron and hadrons at large with massive physical constituents produced free in the spontaneous decays as permitted by the covering hadronic mechanics. We show its compatibility with the standard model when interpreted as only providing the final Mendeleev-type classification of hadrons. We point out basically new clean energies predicted by the new model. We indicate new experiments confirming the above studies although in a preliminary form. Finally, we conclude with the proposal of new experiments suggested for the much needed search of new clean energies. (shrink)

The aim of this paper is to show that every topological space gives rise to a wealth of topological models of the modal logic S4.1. The construction of these models is based on the fact that every space defines a Boolean closure algebra (to be called a McKinsey algebra) that neatly reflects the structure of the modal system S4.1. It is shown that the class of topological models based on McKinsey algebras contains a canonical model that (...) can be used to prove a completeness theorem for S4.1. Further, it is shown that the McKinsey algebra MKX of a space X endoewed with an alpha-topologiy satisfies Esakia's GRZ axiom. (shrink)

In the modern scientific literature, there are many reports about the successful application of neural network technologies for solving complex applied problems, in particular, for modeling the urban real estate market. There are neural network models that can perform mass assessment of real estate objects taking into account their construction and operational characteristics. However, these models are static because they do not take into account the changing economic situation over time. Therefore, they quickly become outdated and need frequent updates. In (...) addition, if they are designed for a specific city, they are not suitable for other cities. On the other hand, there are several dynamic models taking into account the overall state of the economy and designed to predict and study the overall price situation in real estate markets. Such dynamic models are not intended for mass real estate appraisals. The aim of this article is to develop a methodology and create a complex model that has the properties of both static and dynamic models. Moreover, our comprehensive model should be suitable for evaluating real estate in many cities at once. This aim is achieved since our model is based on a neural network trained on examples considering both construction and operational characteristics, as well as geographical and environmental characteristics, along with time-changing macroeconomic parameters that describe the economic state of a specific region, country, and the world. A set of examples for training and testing the neural network were formed on the basis of statistical data of real estate markets in a number of Russian cities for the period from 2006 to 2020. Thus, many examples included the data relating to the periods of the economic calm for Russia, along with the periods of crisis, recovery, and growth of the Russian and global economy. Due to this, the model remains relevant with the changes of the international economic situation and it takes into account the specifics of regions. The model proved to be suitable for solving the following tasks: industrial economic analysis, company strategic and operational management, analytical and consulting support of investment, and construction activities of professional market participants. The model can also be used by government agencies authorized to conduct public cadastral assessment for calculating property taxes. (shrink)

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As a (...) result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making. (shrink)

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces-so-called "topological semantics". The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Attempts to introduce Gestalt theory into the realm of visual neuroscience are discussed on both theoretical and experimental grounds. To define the framework in which these proposals can be defended, this paper outlines the characteristics of a standard model, which qualifies as a received view in the visual neurosciences, and of the research into natural images statistics. The objections to the standard model and the main questions of the natural images research are presented. On these grounds, this paper (...) defends the view that Gestalt psychology and experimental phenomenology provide a contribution to the research into perception by the construction of phenomenological models for an ecologically meaningful interpretation of the empirical evidence and the hypothetical constructs of the natural image research within the visual neuroscience. A formal framework for the phenomenological models is proposed, wherein Gestalt theoretical principles and empirical evidence are represented in terms of topological properties and relationships, which account for the order and structures that make the environment accessible to observers at a relevant behavioural level. It is finally argued that these models allow us to evaluate the principles and the empirical evidence of various natures which are integrated from different fields into the research into perception, and in particular into visual neurosciences. (shrink)

In this paper we define the relation t of elementary extension of topological models in the language L t and show a Back and Forth criterion for t. We introduce some new operations on partial homeomorphisms preserving Back and Forth properties. Some properties of t are proved by the Back and Forth technique.

Dynamic topological logic combines topological and temporal modalities to express asymptotic properties of dynamic systems on topological spaces. A dynamic topological model is a triple 〈X ,f , V 〉, where X is a topological space, f : X → X a continuous function and V a truth valuation assigning subsets of X to propositional variables. Valid formulas are those that are true in every model, independently of X or f. A natural problem (...) that arises is to identify the logics obtained on familiar spaces, such as . It [9] it was shown that any satisfiable formula could be satisfied in some for n large enough, but the question of how the logic varies with n remained open.In this paper we prove that any fragment of DTL that is complete for locally finite Kripke frames is complete for . This includes DTL○; it also includes some larger fragments, such as DTL1, where “henceforth” may not appear in the scope of a topological operator. We show that satisfiability of any formula of our language in a locally finite Kripke frame implies satisfiability in by constructing continuous, open maps from the plane into arbitrary locally finite Kripke frames, which give us a type of bisimulation. We also show that the results cannot be extended to arbitrary formulas of DTL by exhibiting a formula which is valid in but not in arbitrary topological spaces. (shrink)

In this study, a hybrid model based on intelligent techniques is developed to predict the active power generated in a bioclimatic house by a low power wind turbine. Contrary to other researches that predict the generated power taking into account the speed and the direction of the wind, the model developed in this paper only uses the speed of the wind, measured mainly in a weather station from the government meteorological agency (MeteoGalicia). The wind speed is measured at (...) different heights, against the usual measurements in others researches, which uses the wind speed and the direction measured in a weather station on the wind turbine nacelle. The prediction is performed 30 minutes ahead, what ensures that the Building Management System knows the energy generated by the low power wind turbine 30 minutes before, and it can adapt the consumption of different equipment in the house to optimize the power use. The main objective is to allow the Building Management System to optimize the uses of energy, taking into account the predicted amount of energy that will be produced and the energy consumed in the house. The developed model uses a hybrid topology with four clusters to improve the prediction, achieving an error lower than 6.5% for Mean Absolute Error measured in a final test. To perform this test, part of the original dataset was isolated from the beginning of the training process to check the model with a dataset that is not used before, simulating the model as it is receiving new data. (shrink)

The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the (...) interactions among fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives. (shrink)

Should journalists resist business constraints they perceive as a threat to their professional integrity? This article suggests that the answer, at least sometimes, is yes. But in choosing a resistance strategy, journalists should not consider the "take this job and shove it" stance as the only option with moral integrity-or even as the best ethical option. This article develops a model of resistance strategies using the experiences of journalists at one newspaper to illustrate the range of options available for (...) resisting business constraints within a news organization. The types of strategies identified vary along the ethical dimensions of consideration of organizational, as well as professional, goals; and openness with regard to journalists' preference for professional goals. (shrink)

Should journalists resist business constraints they perceive as a threat to their professional integrity? This article suggests that the answer, at least sometimes, is yes. But in choosing a resistance strategy, journalists should not consider the "take this job and shove it" stance as the only option with moral integrity-or even as the best ethical option. This article develops a model of resistance strategies using the experiences of journalists at one newspaper to illustrate the range of options available for (...) resisting business constraints within a news organization. The types of strategies identified vary along the ethical dimensions of (a) consideration of organizational, as well as professional, goals; and (b) openness with regard to journalists' preference for professional goals. (shrink)

Starting from simple topological arguments due to Dirac on the classical rotational properties of extended rigid bodies, we abstract the concept of a finite-size spinor (FSS). The FSS is a concept distinct from both point spinors (e.g., electrons) and composite spinors (e.g., nuclei), and suggests a new model for baryons. The FSS offers a natural explanation of “threeness” for the quarks, excludes the existence of free quarks, denies the operational definition of quark spin statistics, and, moreover, leads to (...) the dual model of hadronic interactions. (shrink)

We present a novel, perspicuous framework for building iterated ultrapowers. Furthermore, our framework naturally lends itself to the construction of a certain type of order indiscernibles, here dubbed tight indiscernibles, which are shown to provide smooth proofs of several results in general model theory.

The generalizability crisis is compounded, or even partially caused, by a lack of specificity in psychological theories. Expanding the use of mechanistic models among psychologists is therefore important, but faces numerous hurdles. A cultural evolutionary approach can help guide and evaluate interventions to improve modeling efforts in psychology, such as developing standards and implementing them at the institutional level.

A link prediction model for weighted networks based on Dempster–Shafer evidence theory and the influence of common neighbours is proposed in this paper. First, three types of future common neighbours and their topological structures are proposed. Second, the concepts of endpoint weight influence, link weight influence, and high-strength node influence are introduced. Then, the similarity based on the impacts of current common neighbours and FCNs is defined, respectively. Finally, the two similarity indices are fused by the DS evidence (...) theory. This model effectively integrates multisource information and completely exploits the influence of all CCNs and FCNs on similarity. Experiments are performed on 9 real and 40 simulation-weighted datasets, and these findings are compared with several classic algorithms. Results show that the proposed method has higher precision than other methods, which can achieve good performance in link prediction in weighted networks. (shrink)

A Higgsless model for strong, electroweak and gravitational interactions is proposed. This model is based on the local symmetry group SU(3)×SU(2)L×U(1)×C,where C is the local conformal symmetry group. The natural minimal conformally invariant form of total Lagrangian is postulated. It contains all standard model fields and gravitational interaction. Using the unitary gauge and the conformal scale fixing conditions, we can eliminate all four real components of the Higgs doublet in this model. However, the masses of (...) vector mesons, leptons, and quarks are automatically generated and are given by the same formulas as in the conventional standard model. In this manner one gets the mass generation without the mechanism of spontaneous symmetry breaking and without the remaining real dynamical Higgs field. The gravitational sector is analyzed, and it is shown that the model admits in the classical limit the Einsteinian form of gravitational interactions. (shrink)

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact (...) solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...) point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

Topological developmental models with local (position of internodes) and global (branch lengths) characteristics are proposed to investigate the relationships between fundamental branching patterns of plants such as acrotony, mesotony, and basitony, including the coincidence of different patterns on the same plant. Modification of the basic acrotony during the development by means of, (1) the final expected main axis length results in either basitony or an extension of acrotony over a shortened main axis, (2) the final expected lateral branch length (...) yields either lateral unlimited sympodial branching or the absence of proximal branches. Combinations of these schemes can have variable quantitative expressions on main and lateral axes.As applications, progressive morphological changes introduced by monotonic variations of parameter values give an insight into the relationships between determinate and indeterminate growth, using Lycopersicon as an example. - A theoretical framework is proposed as a possible aid for formalizing plant typology. (shrink)

This article points out the challenges to current models for media ethics that arise from the private ownership of public media, and it proposes a new model that integrates Adam Smith's free-market theory and his system of moral reasoning. The model creates moral obligations to maintain the integrity of a system for anyone who profits from it. This model renews an appeal for the contemporary notion of transparency and is built on an analogy between the system of (...) the free market for creating wealth and the system of the free press for producing reliable market information. (shrink)

In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of van den Dries, and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF₀ given by Pierce and Pillay. Moreover, it provides a geometric alternative to (...) the axiomatizations obtained by Tressl and Guzy/Point in separate papers where the authors also build general schemes of axioms for some model complete theories of differential fields. We first characterize the existentially closed models of a given theory of differential topological fields and then, under an additional hypothesis of largeness, we show how to modify this characterization to get a general scheme of first-order axioms for the model companion of any large theory of differential topological fields. We conclude with an application of this lifting principle proving that, in existentially closed models of a large theory of differential topological fields, the jet-spaces are dense in their ambient topological space. (shrink)

'Mass terms', words like water, rice and traffic, have proved very difficult to accommodate in any theory of meaning since, unlike count nouns such as house or dog, they cannot be viewed as part of a logical set and differ in their grammatical properties. In this study, motivated by the need to design a computer program for understanding natural language utterances incorporating mass terms, Harry Bunt provides a thorough analysis of the problem and offers an original and detailed solution. An (...) extension of classical set theory, Ensemble Theory, is defined, and this provides the conceptual basis of a framework for the analysis of natural language meaning which Dr Bunt calls Two-level model-theoretic semantics. The validity of the framework is convincingly demonstrated by the formal analysis of a fragment of English including sentences with quantified and modified mass terms. Separate chapters of the book are devoted to an axiomatic definition of Ensemble Theory and a detailed discussion of its status as a mathematical formalism. (shrink)