We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide (...) regular grammar logics with converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. The translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. It is practically relevant because it makes it possible to use a decision procedure for the guarded fragment in order to decide (...) regular grammar logics with converse. The class of regular grammar logics includes numerous logics from various application domains. A consequence of the translation is that the general satisfiability problem for every regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Other logics that can be translated into GF2 include nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed-point operators. (shrink)

In this paper we study elimination of imaginaries in some classes of pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries once we add sorts for the quotient groups $\Gamma /\Delta $ for each definable convex subgroup $\Delta $, and sorts for the quotient groups $\Gamma /(\Delta + \ell \Gamma )$ where $\Delta $ is a definable convex subgroup and $\ell \in \mathbb {N}_{\geq (...) 2}$. We refer to these sorts as the quotient sorts. For the dp-minimal case we obtain a complete elimination of imaginaries if we also add constants to distinguish the cosets of $\ell \Gamma $ in $\Gamma $, where $\ell \in \mathbb {N}_{\geq 2}$. (shrink)

We investigate the definability in monadic ∑11 and monadic Π11 of the problems REGk, of whether there is a regular subgraph of degree k in some given graph, and XREGk, of whether, for a given rooted graph, there is a regular subgraph of degree k in which the root has degree k, and their restrictions to graphs in which every vertex has degree at most k, namely REGkk and XREGkk, respectively, for k ≥ 2 . Our motivation partly (...) stems from the fact that REGkk and XREGkk are logspace equivalent to CONN and REACH, respectively, for k ≥ 3, where CONN is the problem of whether a given graph is connected and REACH is the problem of whether a given graph has a path joining two given vertices. We use monadic first - order reductions, monadic ∑11 games and a recent technique due to Fagin, Stockmeyer and Vardi to almost completely classify whether these problems are definable in monadic ∑11 and monadic Π11, and we compare the definability of these problems. (shrink)

It has been proved that total generalized variation can better preserve edges while suppressing staircase effect. In this paper, we propose an effective hybrid regularization model based on second-order TGV and wavelet frame. The proposed model inherits the advantages of TGV regularization and wavelet frame regularization, can eliminate staircase effect while protecting the sharp edge, and simultaneously has good capability of sparsely estimating the piecewise smooth functions. The alternative direction method of multiplier is employed to solve the new model. (...) Numerical results show that our proposed model can preserve more details and get higher image visual quality than some current state-of-the-art methods. (shrink)

Bird’s Ultimate Argument sought to show that Armstrong’s N relationships involving categorical universals can’t entail nomic regularities. In N’s place Bird offered the non-categorical SR relation. Two kinds of objection have been raised: either Bird’s own alternative metaphysics fails in just the same way as Armstrong’s or the target of Bird’s argument may anyway have a way out of the problem. My aim is to reclaim the victory for Bird. I argue that the responses in defence of Armstong’s N relationships (...) fail to acknowledge that Bird was explicitly concerned with Armstrong’s commitment to a categoricalist view of universals. Moreover, Bird’s alternative account does not suffer the same problem since his metaphysics of properties is essentialist. Nevertheless, Bird’s account does need elaborating on to explainwhySR relationships entail their regularities. I offer Schaffer’s Axiomatic Solution as a candidate for this purpose. (shrink)

The key to this study lies in my own identity as a researcher who specializes in the fifteenth century and Franciscan reforms, especially the confrontation in eastern Central Europe between the theory of the via media based on a return to the Martianian Constitutions, and the Observance sub vicariis brought by Giovanni of Capistrano when he crossed the Alps in 1451.2 The major aspect of this is a view on the “pre-history” of the Libellus ad Leonem, which was written in (...) 1513 by Paolo Giustiniani and Pietro Quirini in preparation of the Fifth Lateran Council. This “pre-history” concerns a century of transformations of the links between the Observant reforms, humanist culture and the.. (shrink)

The majority of the currently flourishing theories of actual causation are located in a broadly counterfactual framework that draws on structural equations. In order to account for cases of symmetric overdeterminiation and preemption, these theories resort to rather intricate analytical tools, most of all, to what Hitchcock has labeled explicitly nonforetracking counterfactuals. This paper introduces a regularity theoretic approach to actual causation that only employs material conditionals, standard Boolean minimization procedures, and a stability condition that regulates the behavior of (...) causal models under model expansions. Notwithstanding its lightweight analytical toolbox, this regularity theory performs at least as well as the structural equations accounts with their heavy appliances. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to (...) prove the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

ABSTRACT A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent: 1. B is regular; 2. the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B; 3. B is isomorphic to a bilattice of the form L 1 · L 2 where (...) L 1 and L 2 are bounded lattices. We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation. (shrink)

In this paper, we define the regular and totally regular single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular single valued neutrosophic hypergraphs. We also extend work on completeness of single valued neutrosophic hypergraphs.

This paper proposes a coevolutionary scenario on the origins of compositionality and word order regularity in human language, and illustrates it using a multi-agent, behavioral model. The model traces a `bottom-up' process of syntactic development; artificial agents, by iterating local orders among lexical items, gradually build up basic constituent word order(s) in sentences. These results show that structural features of language (e.g. syntactic categories and word orders) could have coevolved with lexical items, as a consequence of general learning (...) mechanisms (e.g. pattern extraction and sequential learning) initially not language-specific. Keywords: Computer simulation; language origin; coevolution; compositionality; word order regularity. (shrink)

Cardinality arguments against regular probability measures aim to show that no matter which ordered field ℍ we select as the measures for probability, we can find some event space F of sufficiently large cardinality such that there can be no regular probability measure from F into ℍ. In particular, taking ℍ to be hyperreal numbers won't help to guarantee that probability measures can always be regular. I argue that such cardinality arguments fail, since they rely on the (...) wrong conception of the role of numbers as measures of probability. With the proper conception of their role we can see that for any event space F, of any cardinality, there are regular hyperreal-valued probability measures. (shrink)

How regular do mechanisms need to be, in order to count as mechanisms? This paper addresses two arguments for dropping the requirement of regularity from the definition of a mechanism, one motivated by examples from the sciences and the other motivated by metaphysical considerations regarding causation. I defend a broadened regularity requirement on mechanisms that takes the form of a taxonomy of kinds of regularity that mechanisms may exhibit. This taxonomy allows precise explication of the degree and location (...) of regular operation within a mechanism, and highlights the role that various kinds of regularity play in scientific explanation. I defend this regularity requirement in terms of regularity’s role in individuating mechanisms against a background of other causal processes, and by prioritizing mechanisms’ ability to serve as a model of scientific explanation, rather than as a metaphysical account of causation. It is because mechanisms are regular, in the expanded sense described here, that they are capable of supporting the kinds of generalizations that figure prominently in scientific explanations. (shrink)

Nondeterministic exponential time complexity bounds are established for recognizing true propositional formulas with partially ordered quantifiers on propositional variables.

Assume $\langle \aleph_0, \aleph_1 \rangle \rightarrow \langle \lambda, \lambda^+ \rangle$ . Assume M is a model of a first order theory T of cardinality at most λ+ in a language L(T) of cardinality $\leq \lambda$ . Let N be a model with the same language. Let Δ be a set of first order formulas in L(T) and let D be a regular filter on λ. Then M is $\Delta-embeddable$ into the reduced power $N^\lambda/D$ , provided that every (...) $\Delta-existential$ formula true in M is true also in N. We obtain the following corollary: for M as above and D a regular ultrafilter over $\lambda, M^\lambda/D$ is $\lambda^{++}-universal$ . Our second result is as follows: For $i < \mu$ let Mi and Ni be elementarily equivalent models of a language which has cardinality $\leq \lambda$ . Suppose D is a regular filter on λ and $\langle \aleph_0, \aleph_1 \rangle \rightarrow \langle \lambda, \lambda^+ \rangle$ holds. We show that then the second player has a winning strategy in the $Ehrenfeucht-Fra\ddot{i}ss\acute{e}$ game of length λ+ on $\prod_i M_i/D$ and $\prod_i N_i/D$ . This yields the following corollary: Assume GCH and λ regular (or just $\langle \aleph_0, \aleph_1 \rangle \rightarrow \langle \lambda, \lambda^+ \rangle$ and 2λ = λ+). For L, Mi and Ni be as above, if D is a regular filter on λ, then $\prod_i M_i/D \cong \prod_i N_i/D$. (shrink)

Traditionally, philosophers have cashed out the distinction between law-like and accidental regularities sharply: a regularity is either law-like, and thereby necessary, or accidental. However, Mitchell and Lange have drawn attention to the fact that some law-like regularities come in different degrees of necessity. For instance, the regularity expressed by “all electrons are negatively charged” has a greater degree of necessity than the one expressed by “all mammals are warm-blooded”, even if both of them are true. Moreover, Mitchell argues that the (...) dichotomy between accidental and necessary regularities is unable to capture the complexity of the causal structure of the world. Building on this, I argue that regularities do not only come in different degrees of necessity, but also have different formal features and ontological features. All these features matter in order to make sense of the causal complexity of the world. Accordingly, I propose a new conceptual framework to analyze regularities according to three mutually independent levels of analysis: formal features, degree of necessity, and ontological grounds. This new framework can make sense of different degrees of necessity, and it naturally accommodates a wide variety of scientifically-relevant regularities including those typically associated with laws of nature, biological mechanisms, and dispositional properties. (shrink)

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

Giovanni Sambin has recently introduced the notion of an overlap algebra in order to give a constructive counterpart to a complete Boolean algebra. We propose a new notion of regular open subset within the framework of intuitionistic, predicative topology and we use it to give a representation theorem for overlap algebras. In particular we show that there exists a duality between the category of set-based overlap algebras and a particular category of topologies in which all open subsets are (...) regular. (shrink)

In this paper, we define the regular and totally regular bipolar single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular bipolar single valued neutrosophic hypergraphs. We extend work on completeness of bipolar single valued neutrosophic hypergraphs.

In this book I have tried to develop an analysis of the concept of an empirical law, an analysis that differs in many ways from the alternative analyse's found in contemporary literature dealing with the subject. 1 am referring especially to two well-known views, viz. the regularity and necessity views, which have given rise to many interesting papers and books within the philosophy of science. In developing my own views, it very soon became clear to me that the mere restatement (...) of these alternative views, followed by a discussion of their defects and an explanation of my own view, would not suffice to show what 1 regard as basically unsound in these views. If we seriously consider the well-known difficulties facing the regularity view, we have to consider the possibility that the time has arrived to stop our attempts to solve, by means of patch-work additions, the fundamental problem of empirical laws within the traditional context of logical positivist doctrines. I have tried to find a solution which is based on a different philosophical context, the main incentive being that the discouraging results of the customary attempts to solve the problem might have been the outcome of the fundamental philosophical setting within which the problem had been formulated and within which everyone looked for a solution. The problem of empirical laws is not a problem existing by its own rights - it is shaped by an underlying point of view or theoretical framework. For this reason I have started with a brief sketch of the logical positivist context. However, I want to stress the fact that my intention was not to offer an historical exposition, but an exposition which becomes meaningful when related to the subsequent arguments concerning empirical laws. The notion of direct or theory-free observation has been taken as the fundamental characteristic of the logical positivist point of view. This view has been further characterised by means of five theses, among which is the thesis that observational terms are isolated or theory-independent units of extensional meaning. These terms are then supposed to be the starting-points of meaning and the end-points of confirmation, and these very characteristics mark the privileged position such terms have in a logical positivist philosophy. The post-positivist view, on the other hand, is characterised by the opposing notion of theory-loaded observation. This notion leads to other conclusions which radically oppose some of the theses of logical positivism. The notion of theory- loaded observation itself, although often clearly stated, has not yet been systematically elucidated, and I have made an attempt to do this in ch. I after my sketch of the logical positivist context. This seemed to me to be necessary in order to make my post-positivist point of view as clear as possible, before tackling the problem of empirical law itself. I have paid special attention to the lawlikeness of concepts and their confirmation and falsification. These epistemological issues are followed by a separate examination of Goodman's riddle in ch. II, because it lies somewhere between the lawlikeness of concepts and the lawlikeness of laws. If Goodman's riddle is taken as a serious problem, as I think it should, it is primarily a problem of concept or theory formation and not a problem of induction. In ch. III the regularity view has been examined and the well-known difficulties related to such a view are considered, assuming the knowledge gained in ch. I. This has led to some interesting results, especially in connection with the analysis of counterfactuals and the confirmation of 'normal' singular conditionals, to which I return in the last chapter. Three different views of the necessity view are briefly stated and investigated in ch. IV. RESCHER'S view is, I think, close to mine, which has been developed in ch. V. However, there are fundamental epistemological differences between our views. In the last chapter I have given my own analysis of the concept of an empirical law, which should not be taken as a synthesis of a regularity and a necessity view, but as opposed to both. It is, as far as particulars may count, the result of an analysis of the concepts 'regularity' and 'necessity'. I have tried to argue that the greatest shortcoming of the regularity view lies in the fact that the proponents of such a view have not been really concerned with the concept of 'regularity' itself. They usually take this concept to be intuitively clear enough to serve as basis for their analysis. Their attacks upon the necessity view are based on the reproach that 'necessity' is a very obscure concept, and that it should, therefore, be avoided in the philosophy of science. We could, however, reproach them in a similar way, since the concept of 'regularity' is anything but clear. One may say that an empirical law formulates a 'regularity in nature', but we can only do justice to the function a law has in science, if we are ready to view this regularity as a necessary connection, which does not exist in an observer-independent reality, but in a theoretically co-constituted empirical world. This investigation does not pretend to answer all questions concerning empirical laws. It should, therefore, not be regarded as complete, but neither should the arguments and suggestions be regarded as completely free from ambiguity. Much remains to be done in order to offer a generally acceptable theory and better understanding. (shrink)

We present Woodin's proof that if there exists a measurable Woodin cardinal δ, then there is a forcing extension satisfying all $\Sigma _{2}^{2}$ sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in V δ . We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary (...) embedding j: V → M with critical point $\omega _{1}^{V}$ such that M is countably closed in the forcing extension. (shrink)

This paper investigates the quantifier "there exist unboundedly many" in the context of first-order arithmetic. An alternative axiomatization is found for Peano arithmetic based on an axiom schema of regularity: The union of boundedly many bounded sets is bounded. We also obtain combinatorial equivalents of certain second-order theories associated with cuts in nonstandard models of arithmetic.

Leuridan (2010) argued that mechanisms cannot provide a genuine alternative to laws of nature as a model of explanation in the sciences, and advocates Mitchell’s (1997) pragmatic account of laws. I first demonstrate that Leuridan gets the order of priority wrong between mechanisms, regularity, and laws, and then make some clarifying remarks about how laws and mechanisms relate to regularities. Mechanisms are not an explanatory alternative to regularities; they are an alternative to laws. The existence of stable regularities in (...) nature is necessary for either model of explanation: regularities are what laws describe and what mechanisms explain. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a distributional semantic model, here exemplified by bidirectional encoder representations from transformers (BERT), represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping between CHICKEN (as an animal) and CHICKEN (as a meat) similar to that which maps between (...) LOBSTER (as an animal) to LOBSTER (as a meat)?” We did so using the LRcos model, which combines a logistic regression classifier of different categories (e.g., animal vs. meat) with a measure of cosine similarity. We found that (a) the model was sensitive to the shared structure within a given regular relationship; (b) the shared structure varies across different regular relationships (e.g., animal/meat vs. location/organization), potentially reflective of a “regularity continuum;” (c) some high-order latent structure is shared across different regular relationships, suggestive of a similar latent structure across different types of relationships; and (d) there is a lack of evidence for the aforementioned effects being explained by meaning overlap. Lastly, we found that both components of the LRcos model made important contributions to accurate responding and that a variation of this method could yield an accuracy boost of 10% in answering sense analogy questions. These findings enrich previous theoretical work on regular polysemy with a computationally explicit theory and methods, and provide evidence for an important organizational principle for the mental lexicon and the broader conceptual knowledge system. (shrink)

This article reconstructs the history of medical research in East Africa (Kenya, Tanganyika, Uganda), laying out the lies, rumours, and oppressive techniques that made research such a fraught enterprise during the colonial era. The focus is on the beginning stages of medical research: researchers' arrivals, villagers' responses, the gathering of subjects and consent. New archival and oral sources gathered in East Africa illuminate the research encounter and reintegrate the perspective of villagers cum subjects. Data from the 1950s shows that upon (...) arrival in a village, researchers regularly lied in order to avoid sensitive topics and sidestep potential opposition. Misinformation fuelled villagers' fears, skepticism and rumours of blood stealing researchers. When it came to gathering subjects, researchers were rarely involved in the challenging work of enticing villagers to participate, preferring to rely on chiefs. Chiefs, however, often relied on heavy‐handed and ethically questionable techniques. The article concludes by looking at the much‐discussed concept of group consent, and showing that historically a chief never had the authority to consent on behalf of villagers. (shrink)

The attempt to provide a faithful mapping from distal shape space to proximal state space in terms of a higher order relationship defined over proximal similarity space stumbles on the context sensitivity of higher order relationships. Proportional analogy problems using quadruples of figures illustrate that for a number of interesting perceptual problems, the number of relevant dimensions cannot be reduced.

We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces the (...) integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

Our theme is that not every interesting question in set theory is independent of ZFC. We give an example of a first order theory T with countable D(T) which cannot have a universal model at ℵ1 without CH; we prove in ZFC a covering theorem from the hypothesis of the existence of a universal model for some theory; and we prove--again in ZFC--that for a large class of cardinals there is no universal linear order (e.g. in every (...) class='Hi'>regular $\aleph_1 < \lambda < 2^{\aleph_0}$). In fact, what we show is that if there is a universal linear order at a regular λ and its existence is not a result of a trivial cardinal arithmetical reason, then λ "resembles" ℵ1--a cardinal for which the consistency of having a universal order is known. As for singular cardinals, we show that for many singular cardinals, if they are not strong limits then they have no universal linear order. As a result of the nonexistence of a universal linear order, we show the nonexistence of universal models for all theories possessing the strict order property (for example, ordered fields and groups, Boolean algebras, p-adic rings and fields, partial orders, models of PA and so on). (shrink)

Let be an o-minimal structure expanding a real closed field R. We show that any definable set in Rn can be stratified into cells, whose defining functions are smooth Lipschitz continuous functions with constant 2n3/2, which have additional regularity conditions on the derivatives of higher order.

The thesis focuses on a quite recent research field lying in between Descriptive Set Theory and Automata Theory (for infinite objects). In both areas, one is often concerned with subsets of the Cantor space or of its homeomorphic copies. In Descriptive Set Theory, such subsets are usually stratified in topological hierarchies, like the Borel hierarchy, the Wadge hierarchy and the difference hierarchy; in Automata Theory, such sets are studied in terms of regularity, that is, the property of being recognised by (...) an automaton or, equivalently, of being expressible in Monadic Second-Order Logic. This double point of view leads to many interesting questions about the interplay and relationship between topological complexity and regularity. While we have a complete picture of what happens in the case of automata on words, the case of automata on trees is still a terra incognita. Some results have already been obtained for particular classes of languages, like Buchi languages, deterministic languages, ¨ and unambiguous languages. In this thesis we instead drop any restriction and prove some new results concerning arbitrary regular tree languages which belong to low levels of the Borel hierarchy and of the Wadge hierarchy. (shrink)

We consider semi‐algebraic sets and properties of these sets that are expressible by sentences in first‐order logic over the reals. We are interested in first‐order properties that are invariant under topological transformations of the ambient space. Two semi‐algebraic sets are called topologically elementarily equivalent if they cannot be distinguished by such topological first‐order sentences. So far, only semi‐algebraic sets in one and two‐dimensional space have been considered in this context. Our contribution is a natural characterisation of topological (...) elementary equivalence of regular closed semi‐algebraic sets in three‐dimensional space, extending a known characterisation for the two‐dimensional case. Our characterisation is based on the local topological behaviour of semi‐algebraic sets and the key observation that topologically elementarily equivalent sets can be transformed into each other by means of geometric transformations, each of them mapping a set to a first‐order indistinguishable one. (shrink)

Learning in natural environments is often characterized by a degree of inconsistency from an input. These inconsistencies occur, for example, when learning from more than one source, or when the presence of environmental noise distorts incoming information; as a result, the task faced by the learner becomes ambiguous. In this study, we investigate how learners handle such situations. We focus on the setting where a learner receives and processes a sequence of utterances to master associations between objects and their labels, (...) where the source is inconsistent by design: It uses both “correct” and “incorrect” object‐label pairings. We hypothesize that depending on the order of presentation, the result of the learning may be different. To this end, we consider two types of symbolic learning procedures: the Object‐Label (OL) and the Label‐Object (LO) process. In the OL process, the learner is first exposed to the object, and then the label. In the LO process, this order is reversed. We perform experiments with human subjects, and also construct a computational model that is based on a nonlinear stochastic reinforcement learning algorithm. It is observed experimentally that OL learners are generally better at processing inconsistent input compared to LO learners. We show that the patterns observed in the learning experiments can be reproduced in the simulations if the model includes (a) an ability to regularize the input (and also to do the opposite, i.e., undermatch) and (b) an ability to take account of implicit negative evidence (i.e., interactions among different objects/labels). The model suggests that while both types of learners utilize implicit negative evidence in a similar way, there is a difference in regularization patterns: OL learners regularize the input, whereas LO learners undermatch. As a result, OL learners are able to form a more consistent system of image‐utterance associations, despite the ambiguous learning task. (shrink)

Separated decision-making for maintenance and spare ordering is unrealistic in the industry, so this paper aims to optimize them together. A joint policy of inspection-based preventive maintenance and spare ordering considering two modes of spare ordering, namely, a regular order and an emergency order, is proposed for single-unit systems using a three-stage failure process. If the system is recognized to be in the minor defective stage, the original inspection interval is shortened and a regular order (...) is placed. However, replacement is undertaken preventively or correctively if the severe defective stage is identified or a failure occurs. Depending on the system state and the state of the regular ordered spare when replacement is needed, all possible scenarios are considered to construct optimization model I. The decision variables are the optimal inspection interval and the times of shortening the original inspection interval. Additionally, model II on the basis of an assumption that the spare is always ordered at time 0 is also developed. The results from a numerical example illustrated the applicability and the effectiveness of model I compared to model II, and the irregular inspection policy is validated to be cost-saving compared to the regular inspection policy. (shrink)

Rhythmic entrainment is the formation of regular, predictable patterns in time and/or space through interactions within or between systems that manifest potential symmetries. We contend that this process is a major source of symmetries in specific systems, whether passive physical systems or active adaptive and/or voluntary/intentional systems, except that active systems have more control over accepting or avoiding rhythmic entrainment. The result of rhythmic entrainment is a simplification of the entrained system, in the sense that the information required to (...) describe it is reduced. Entrainment can be communicated, passing information from one system to another. The paradigm is a group of jazz percussionists agreeing on a complex musical progression. The process of rhythmic entrainment is complementary to that of symmetry breaking, which produces information. The two processes account for much, if not all, of the complexity and organization in the universe. Rhythmic entrainment can be more or less spontaneous, with the completely spontaneous form being uncontrollable. A balance between the two forms can produce a more robust system, requiring less energy to maintain, whether in physical, biological or social systems. We outline some applications in physics, chemistry, biology, measurement and communication, ending with the especially interesting case of social and economic order. First though, we must introduce some basic principles. (shrink)

This thesis is divided into three parts, the first and second ones focused on combinatorics and classification problems on discrete and geometrical objects in the context of descriptive set theory, and the third one on generalized descriptive set theory at singular cardinals of countable cofinality.Descriptive Set Theory (briefly: DST) is the study of definable subsets of Polish spaces, i.e., separable completely metrizable spaces. One of the major branches of DST is Borel reducibility, successfully used in the last 30 years to (...) solve and compare many classification problems. One of our goals is the classification of knots, very familiar and tangible objects in everyday life, which also play an important role in modern mathematics. The study of knots and their properties is known as knot theory. Our plan is to gain insight into knots using discrete objects, such as linear and circular orders. This approach was already exploited in [6]. The first part of this work is therefore devoted to countable linear orders and the study of the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results. We also expand our research to the case of circular orders.Another objective of this first part is to extend the notion of convex embeddability on countable linear orders. We provide a family of quasi-orders of which embeddability is a particular case as well. We study these quasi-orders from a combinatorial point of view and analyse their complexity with respect to Borel reducibility. Furthermore, we extend the analysis of these quasi-orders to the set of uncountable linear orders.The second part of the project deals with classification problems on knots and $3$ -manifolds. The goal here is to apply the results obtained in the first part to the study of proper arcs and knots, establishing lower bounds for the complexity of some natural relations between these geometrical objects. We also obtain some combinatorial results which are particularly interesting when we restrict to the set of wild proper arcs and wild knots, classes which haven’t received much attention so far. These parts are included in the two preprints [4, 5] in collaboration with my supervisor Alberto Marcone, Luca Motto Ros (University of Torino), and Vadim Weinstein (University of Oulu).The second part of this work also includes the classification of non-compact $3$ -manifolds up to homeomorphism (the case of compact $3$ -manifolds has already been solved: indeed, there are only countably many $3$ -manifolds up to homeomorphism; see [7]), and that of Cantor sets of $\mathbb {R}^3$ up to conjugation (answering to Question 5.5 of [3]). Here we resort to algebraic tools. Stone duality gives a neat way to go back-and-forth between totally disconnected Polish spaces and countable Boolean algebras (see [1]). The main ingredient is the Stone space of all ultrafilters on a Boolean algebra. In this work we introduce a weaker concept which we call “blurry filter”. Using blurry filters instead of ultrafilters enables one to extend the class of spaces under consideration beyond totally disconnected. As an application of this method, we show that both homeomorphism on non-compact $3$ -manifolds and conjugation of Cantor sets in $\mathbb {R}^3$ are completely classifiable by countable structures. These results are part of an upcoming paper in collaboration with Vadim Weinstein.The last part of this thesis concerns the natural generalization of descriptive set theory that occurs when countable is replaced by uncountable, called Generalized Descriptive Set Theory (briefly: GDST). In particular, we focus on the case of GDST for a singular cardinal $\kappa $ of countable cofinality. The goal here is to study the generalizations of the Perfect Set Property and the Baire Property to subsets of spaces of higher cardinalities, like the power set $\mathcal {P}(\kappa )$. We consider the question under which large cardinal hypotheses classes of definable subsets of these spaces possess such regularity properties, focusing on rank-into-rank axioms, like I2, and classes of sets definable by $\Sigma _1$ -formulas with parameters from various collections of sets. The obtained results are included in [2], a joint work with my co-supervisor Vincenzo Dimonte and Philipp Lücke (University of Hamburg).Abstract prepared by Martina IannellaE-mail: [email protected]: https://air.uniud.it/handle/11390/1262824. (shrink)

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ -formula, (...) φ order theory T in a countable language ${\mathcal{L}}$ with a distinguished linear order:Some model of T has an elementary end extension with a first new element.T ⊢ REF ${(\mathcal{L})}$ .T has an ω 1-like model that continuously embeds ω 1.For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.For some regular uncountable cardinal κ, T has a κ-like model ${\mathfrak{M}}$ that has an elementary extension in which the supremum of M exists.Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to: T has a κ + -like model that continuously embeds a stationary subset of κ. (shrink)

Regular polysemes are sets of ambiguous words that all share the same relationship between their meanings, such as CHICKEN and LOBSTER both referring to an animal or its meat. To probe how a context embedding model, here exemplified by BERT, represents regular polysemy, we analyzed whether its embeddings support answering sense analogy questions similar to “is the mapping be- tween CHICKEN (as an animal) and CHICKEN (as a meat) the same as that which maps between LOBSTER (as an (...) animal) to LOBSTER (as a meat)?” We found that (1) the model was sensitive to the shared structure within a regularity type; (2) the shared structure varies across regularity types, potentially reflective of a “regularity continuum;” (3) some high-order latent structure may be shared across regularity types, suggestive of a similar la- tent structure across types; and (4) there is equivocal ev- idence that the aforementioned effects are explained by meaning overlap. (shrink)

As part of a research project on confrontational maneuvering in the spokespersons’ argumentative replies at the regular press conferences of China’s Ministry of Foreign Affairs between 2015 and 2018, this article analyzes, within the framework of Pragma-Dialectics, how the spokespersons declare a standpoint at issue unallowed or indisputable in order to avoid having to resolve a difference of opinion as it is, according to the questioning journalist, presented by their immediate opponents. Starting from the various rationales the spokespersons (...) presuppose to be understood and regarded acceptable by the questioning journalist and the international general public, three subtypes of declaring a standpoint unallowed or indisputable are differentiated: the “Necessity Rationale” subtype, the “Desirability Rationale” subtype, and the “Feasibility Rationale” subtype. The confrontational maneuvering by declaring a standpoint unallowed or indisputable carried out by the spokespersons is directed both at the immediate opponent and at the international general public. However, it is the international general public that the spokespersons primarily intend to convince. For this purpose, they make in all three subtypes of the unallowed or indisputable declaration an effort to adapt their response to their primary audience’s demand by making strategic choices from the available topical potential and the available presentational devices. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases (...) of the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)