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)

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 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)

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)

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)

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)

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)

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)

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)

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.

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.

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.

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)

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)

I review the present status of the problem of initial conditions for inflation and describe several ways to solve this problem for many popular inflationary models, including the recent generation of the models with plateau potentials favored by cosmological observations.

The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the application of a term/function to any other term/function, including itself. The calculus can be seen as a formal theory with certain pre-established axioms and inference rules, which can be interpreted by models. Dana Scott proposed the first non-trivial model of the extensional lambda (...) calculus, known as $ D_{\infty }$, to represent the $\lambda $-terms as the typical functions of set theory, where it is not allowed to apply a function to itself. Here we propose a construction of an $\infty $-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case $D_{\infty }$, and we see that the Scott topology does not provide enough information about the relationship between higher homotopies. This motivates a new line of research focused on the exploration of $\lambda $-models with the structure of a non-trivial $\infty $-groupoid to generalize the proofs of term conversion to higher-proofs in $\lambda $-calculus. (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)

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)

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)

Cosmological inflation is widely considered an integral and empirically successful component of contemporary cosmology. It was originally motivated by its solution of certain so-called fine-tuning problems of the hot big bang model, particularly what are known as the horizon problem and the flatness problem. Although the physics behind these problems is clear enough, the nature of the problems depends on the sense in which the hot big bang model is fine-tuned and how the alleged fine-tuning is problematic. (...) Without clear explications of these, it remains unclear precisely what problems inflationary theory is meant to be solving and whether it does in fact solve them. I analyze the structure of these problems and consider various interpretations that may substantiate the alleged fine-tuning. On the basis of this analysis I argue that at present there is no unproblematic interpretation available for which it can be said that inflation solves the big bang model’s alleged fine-tuning problems. (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)

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)

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)

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 paper sets out some new skeleton mathematically-couched models for dealing with supervenience in some, if not all, its many guises. Our models are based around a naïve invocation of a ‘topology’ induced on object sets by property sets. We have two aims: one is to provide an overview of supervenience with enough rigour and detail to act as a self-contained introduction to the subject; and the other is to set out our new approach—but without getting too bogged down in (...) excessive mathematical, or indeed philosophical, niceties—so that it can be used as a foundation for further work. Throughout we have scattered examples and comments to help clarify the points we make. The early sections use our topological approach to recast what appears elsewhere in the literature. And in the latter sections of the paper, we introduce some new ideas and techniques which help in exploring the general structures underpinning supervenience. (shrink)

A topological class logic is an infinitary logic formed by combining a first-order logic with the quantifier symbols O and C. The meaning of a formula closed by quantifier O is that the set defined by the formula is open. Similarly, a formula closed by quantifier C means that the set is closed. The corresponding models are a topological class spaces introduced by Ćirić and Mijajlović (Math Bakanica 1990). The completeness theorem is proved.

We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed (...) in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed. (shrink)

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as (...) more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( (...) \sqsubseteq \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

Cosmology is usually understood as an observational science, where experimentation plays no role. It is interesting, nevertheless, to change this perspective addressing the following question: what should we do to create a universe, in a laboratory? It appears, in fact, that this is, in principle, possible according to at least two different paradigms; both allow to circumvent singularity theorems, i.e. the necessity of singularities in the past of inflating domains which have the required properties to generate a universe similar to (...) ours. The first of them is substantially classical, and is built up considering solitons which collide with surrounding topological defects, generating an inflationary domain of space–time. The second is, instead, partly quantum and considers the possibility of tunnelling of past-non-singular regions of spacetime into an inflating universe, following a well-known instanton proposal. We are, here, going to review some of these models, as well as highlight possible extensions, generalizations and the open issues (as for instance the detectability of child universes and the properties of quantum tunnelling processes) that still affect the description of their dynamics. In doing so we will remark how the works on this subject can represent virtual laboratories to test the role that fundamental principles of physics (particularly, the interplay of quantum and general relativistic realms) played in the formation of our universe. (shrink)

A three-variable biochemical prototype involving two enzymes with autocatalytic regulation proposed by Decroly and Goldbeter (1987) is analyzed using a topological approach. A two-branched manifold, a so-called template, is thus identified. For certain control parameter values, this template is a horseshoe template with a global torsion of two half-turns. This implies that the bifurcation diagram can be described using the usual sequences associated with a unimodal map with a differentiable maximum as well as exemplified by the logistic map. Moreover, (...) a type-I intermittency associated with a saddle-node bifurcation is exhibited. The dynamics from a single time series are also investigated to determine whether it is possible to investigate the dynamics of this biochemical model from the measure of a single concentration. (shrink)

Using nonstandard methods, we generalize the notion of an algebraic primitive element to that of an hyperalgebraic primitive element, and show that under mild restrictions, such elements can be found infinitesimally close to any given element of a topological field.

The ring‐shaped ATPase machine, cohesin, regulates sister chromatid cohesion, transcription, and DNA repair by topologically entrapping DNA. Here, we propose a rigid scaffold model to explain how the cohesin regulators Pds5 and Wapl release cohesin from chromosomes. Recent studies have established the Smc3‐Scc1 interface as the DNA exit gate of cohesin, revealed a requirement for ATP hydrolysis in ring opening, suggested regulation of the cohesin ATPase activity by DNA and Smc3 acetylation, and provided insights into how Pds5 and Wapl (...) open this exit gate. We hypothesize that Pds5, Wapl, and SA1/2 form a rigid scaffold that docks on Scc1 and anchors the N‐terminal domain of Scc1 (Scc1N) to the Smc1 ATPase head. Relative movements between the Smc1‐3 ATPase heads driven by ATP and Wapl disrupt the Smc3‐Scc1 interface. Pds5 binds the dissociated Scc1N and prolongs this open state of cohesin, releasing DNA. We review the evidence supporting this model and suggest experiments that can further test its key principles. (shrink)

Given an abstract logic L = L(Q i ) i ∈ I generated by a set of quantifiers Q i , one can construct for each type τ a topological space S τ exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set $S_T = \{(S_\tau, \pi^\tau_\sigma)\mid\sigma, \tau \in T, \sigma \subset \tau\}$ is an inverse topological system whose bonding mappings π τ σ are naturally (...) determined by the reduct operation on structures. We relate the compactness of L to the topological properties of S T . For example, if I is countable then L is compact iff for every τ each clopen subset of S τ is of finite type and S τ is homeomorphic to $\underset{lim}S_T$ , where T is the set of finite subtypes of τ. We finally apply our results to concrete logics. (shrink)

Construction cost estimation is one of the essential processes in construction management. Project cost is a complex engineering problem due to various factors affecting the construction industry. Accurate cost estimation is important in construction management and significantly impacts project performance. Artificial intelligence models have been effectively implemented in construction management studies in recent years owing to their capability to deal with complex problems. In this research, extreme gradient boosting is developed as an advanced input selector algorithm and coupled with three (...) AI models, including random forest, artificial neural network, and support vector machine for cost estimation. Datasets were gathered based on a survey conducted on 90 building projects in Iraq. Statistical indicators and graphical methods were used to evaluate the developed models. Several input predictors were used, and XGBoost highlighted inflation as the most crucial parameter. The results indicated that the best prediction was attained by XGBoost-RF using six input parameters, with r-squared and the mean absolute percentage error equal to 0.87 and 0.25, respectively. The comparison results revealed that all AI models showed good prediction performance when applied to datasets affected by more than two parameters. The outcomes of this research revealed an optimistic strategy that can help decision makers select the influencing parameters in the early phases of project management. Also, developing a prediction model with high precision results can assist the project’s estimators in decreasing the errors in the cost estimation process. (shrink)