Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over (...) algebraically closed fields is the model-completion of the theory of vector spaces. (shrink)

This paper introduces a compositional semantics of locativeprepositional phrases which is based on a vector space ontology.Model-theoretic properties of prepositions like monotonicity andconservativity are defined in this system in a straightforward way.These notions are shown to describe central inferences with spatialexpressions and to account for the grammaticality of prepositionmodification. Model-theoretic constraints on the set of possibleprepositions in natural language are specified, similar to the semanticuniversals of Generalized Quantifier Theory.

We study the theory of K-vector spaces with a predicate for the union X of an infinite family of independent subspaces. We show that if K is infinite then the theory is complete and admits quantifier elimination in the language of K-vector spaces with predicates for the n-fold sums of X with itself. If K is finite this is no longer true, but we still have that a natural completion is near-model-complete.

The Distributional Compositional Categorical model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated (...) methods that could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, something which the other methods lack, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambekʼs pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, the apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings, and also reflects the structure of the parse trees of the Lambek calculus. (shrink)

We provide a simple and transparent construction of Hrushovski's strongly minimal fusions in the case where the fused strongly minimal sets are vector spaces. We strengthen Hrushovski's result by showing that the strongly minimal fusions are model complete.

Over the history of research on sign languages, much scholarship has highlighted the pervasive presence of signs whose forms relate to their meaning in a non-arbitrary way. The presence of these forms suggests that sign language vocabularies are shaped, at least in part, by a pressure toward maintaining a link between form and meaning in wordforms. We use a vector space approach to test the ways this pressure might shape sign language vocabularies, examining how non-arbitrary forms are distributed (...) within the lexicons of two unrelated sign languages. Vector space models situate the representations of words in a multi-dimensional space where the distance between words indexes their relatedness in meaning. Using phonological information from the vocabularies of American Sign Language and British Sign Language, we tested whether increased similarity between the semantic representations of signs corresponds to increased phonological similarity. The results of the computational analysis showed a significant positive relationship between phonological form and semantic meaning for both sign languages, which was strongest when the sign language lexicons were organized into clusters of semantically related signs. The analysis also revealed variation in the strength of patterns across the form-meaning relationships seen between phonological parameters within each sign language, as well as between the two languages. This shows that while the connection between form and meaning is not entirely language specific, there are cross-linguistic differences in how these mappings are realized for signs in each language, suggesting that arbitrariness as well as cognitive or cultural influences may play a role in how these patterns are realized. The results of this analysis not only contribute to our understanding of the distribution of non-arbitrariness in sign language lexicons, but also demonstrate a new way that computational modeling can be harnessed in lexicon-wide investigations of sign languages. (shrink)

Most, if not all, philosophers agree that computers cannot learn what words refers to from raw text alone. While many attacked Searle’s Chinese Room thought experiment, no one seemed to question this most basic assumption. For how can computers learn something that is not in the data? Emily Bender and Alexander Koller ( 2020 ) recently presented a related thought experiment—the so-called Octopus thought experiment, which replaces the rule-based interlocutor of Searle’s thought experiment with a neural language model. The Octopus (...) thought experiment was awarded a best paper prize and was widely debated in the AI community. Again, however, even its fiercest opponents accepted the premise that what a word refers to cannot be induced in the absence of direct supervision. I will argue that what a word refers to _is_ probably learnable from raw text alone. Here’s why: higher-order concept co-occurrence statistics are stable across languages and across modalities, because language use (universally) reflects the world we live in (which is relatively stable). Such statistics are sufficient to establish what words refer to. My conjecture is supported by a literature survey, a thought experiment, and an actual experiment. (shrink)

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

The rise of big digital data is changing the framework within which linguists, sociologists, anthropologists, and other researchers are working. Semiotics is not spared by this paradigm shift. A data-driven computational semiotics is the study with an intensive use of computational methods of patterns in human-created contents related to semiotic phenomena. One of the most promising frameworks in this research program is the Semantic Vector Space (SVS) models and their methods. The objective of this article is to (...) contribute to the exploration of the SVS for a computational semiotics by showing what types of semiotic analysis can be accomplished within this framework. The study is applied to a unique body of digitized artworks. We conducted three short experiments in which we explore three types of semiotic analysis: paradigmatic analysis, componential analysis, and topic modelling analysis. The results reported show that the SVS constitutes a powerful framework within which various types of semiotic analysis can be carried out. (shrink)

The aim of this paper is to describe an analogue of the theory of nontrivial torsion-free divisible abelian groups for metabelian groups. We obtain illustrations for “old-fashioned” model theoretic algebra and “new” examples in the theory of stable groups. We begin this paper with general considerations about model theory. In the second section we present our results and we give the structure of the rest of the paper. Most parts of this paper use only basic concepts from model theory and (...) group theory. However, in Section 5, we need some somewhat elaborate notions from stability theory. One can find the beginnings of this theory in [14], and we refer the reader to [16] or [21] for stability theory and to [22] for stable groups.§1. Some model theoretic considerations. Denote by the theory of torsion-free abelian groups in the language of groups ℒgp. A finitely generated group G satisfies iff G is isomorphic to a finite direct power of ℤ. It follows that axiomatizes the universal theory of free abelian groups and that the theory of nontrivial torsion-free abelian groups is complete for the universal sentences. Denote by the theory of nontrivial divisible torsion-free abelian groups. (shrink)

The aim of this paper is to describe an analogue of the theory of nontrivial torsion-free divisible abelian groups for metabelian groups. We obtain illustrations for “old-fashioned” model theoretic algebra and “new” examples in the theory of stable groups. We begin this paper with general considerations about model theory. In the second section we present our results and we give the structure of the rest of the paper. Most parts of this paper use only basic concepts from model theory and (...) group theory. However, in Section 5, we need some somewhat elaborate notions from stability theory. One can find the beginnings of this theory in [14], and we refer the reader to [16] or [21] for stability theory and to [22] for stable groups.§1. Some model theoretic considerations. Denote by the theory of torsion-free abelian groups in the language of groups ℒgp. A finitely generated group G satisfies iff G is isomorphic to a finite direct power of ℤ. It follows that axiomatizes the universal theory of free abelian groups and that the theory of nontrivial torsion-free abelian groups is complete for the universal sentences. Denote by the theory of nontrivial divisible torsion-free abelian groups. (shrink)

§1. Introduction.The motivation of this work comes from two different directions: infinite abelian groups, and ordered algebraic structures. A challenging problem in both cases is that of classification. In the first case, it is known for example (cf. [KA]) that the classification of abelian torsion groups amounts to that of reducedp-groups by numerical invariants called theUlm invariants(given by Ulm in [U]). Ulm's theorem was later generalized by P. Hill to the class of totally projective groups. As to the second case, (...) let us consider for instance the class of divisible ordered abelian groups. These may be viewed as ordered ℚ-vector spaces. Their theory being unstable, we cannot hope to classify them by numerical invariants. On the other hand, being o-minimal, the theory enjoys several good model theoretic properties (cf. [P-S]), so the search for some reasonable invariants is well motivated. The common denominator of the two cases, as well as of many others, is valuation theory. Indeed given an ordered vector space, one can consider it as a valued vector space, endowed with the natural valuation. Also, the socleG[p] of a reduced abelianp-groupG, endowed with the height functionhG, is a valued vector space over(the prime field of characteristicp) with values in the ordinals (cf. [F]). (shrink)

Recent metaphor research has revealed that metaphor comprehension involves both categorization and comparison processes. This finding has triggered the following central question: Which property determines the choice between these two processes for metaphor comprehension? Three competing views have been proposed to answer this question: the conventionality view (Bowdle & Gentner, 2005), aptness view (Glucksberg & Haught, 2006b), and interpretive diversity view (Utsumi, 2007); these views, respectively, argue that vehicle conventionality, metaphor aptness, and interpretive diversity determine the choice between the categorization (...) and comparison processes. This article attempts to answer the question regarding which views are plausible by using cognitive modeling and computer simulation based on a semantic space model. In the simulation experiment, categorization and comparison processes are modeled in a semantic space constructed by latent semantic analysis. These two models receive word vectors for the constituent words of a metaphor and compute a vector for the metaphorical meaning. The resulting vectors can be evaluated according to the degree to which they mimic the human interpretation of the same metaphor; the maximum likelihood estimation determines which of the two models better explains the human interpretation. The result of the model selection is then predicted by three metaphor properties (i.e., vehicle conventionality, aptness, and interpretive diversity) to test the three views. The simulation experiment for Japanese metaphors demonstrates that both interpretive diversity and vehicle conventionality affect the choice between the two processes. On the other hand, it is found that metaphor aptness does not affect this choice. This result can be treated as computational evidence supporting the interpretive diversity and conventionality views. (shrink)

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only (...) if the ‘usual’ first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. (shrink)

This article describes the use of continuous vector space models for reasoning with a formal knowledge base. The practical significance of these models is that they support fast, approximate but robust inference and hypothesis generation, which is complementary to the slow, exact, but sometimes brittle behaviour of more traditional deduction engines such as theorem provers.The article explains the way logical connectives can be used in semantic vector models, and summarizes the development of Predication-based Semantic (...) Indexing, which involves the use of Vector Symbolic Architectures to represent the concepts and relationships from a knowledge base of subject-predicate-object triples. Experiments show that the use of continuous models for formal reasoning is not only possible, but already demonstrably effective for some recognized informatics tasks, and showing promise in other traditional problem areas. Examples described in this article include: predicting new uses for existing drugs in biomedical informatics; removing unwanted meanings from search results in information retrieval and concept navigation; type inference from attributes; comparing words based on their orthography; and representing tabular data, including modelling numerical values.The algorithms and techniques described in this article are all publicly released and freely available in the Semantic Vectors open-source software package.1. (shrink)

Although great progress in neuroanatomy and physiology has occurred lately, we still cannot go directly to those levels to discover the neural mechanisms of higher cognition and consciousness. But we can use neurocomputational methods based on these details to push this project forward. Here we describe vector subtraction as an operation that computes sequential paths through high-dimensional vector spaces. Vector-space interpretations of network activity patterns are a fruitful resource in recent computational neuroscience. Vector subtraction also (...) appears to be implemented neurally in primate frontal eye field activity, which computes dimensions of saccadic eye movements. We use this apparent neural implementation as a model and construct from it a general neurocomputational account of an important type of sequential cognitive and conscious process. We defend the biological plausibility of all components of the general model and show that it yields testable anatomical and physiological predictions. We close by suggesting some interesting consequences for consciousness if our model characterizes correctly the neural mechanisms producing a common type of episode in our conscious streams. (shrink)

Vector-based models of word meaning have become increasingly popular in cognitive science. The appeal of these models lies in their ability to represent meaning simply by using distributional information under the assumption that words occurring within similar contexts are semantically similar. Despite their widespread use, vector-based models are typically directed at representing words in isolation, and methods for constructing representations for phrases or sentences have received little attention in the literature. This is in marked contrast (...) to experimental evidence (e.g., in sentential priming) suggesting that semantic similarity is more complex than simply a relation between isolated words. This article proposes a framework for representing the meaning of word combinations in vector space. Central to our approach is vector composition, which we operationalize in terms of additive and multiplicative functions. Under this framework, we introduce a wide range of composition models that we evaluate empirically on a phrase similarity task. (shrink)

Lexical ambiguity—the phenomenon of a single word having multiple, distinguishable senses—is pervasive in language. Both the degree of ambiguity of a word (roughly, its number of senses) and the relatedness of those senses have been found to have widespread effects on language acquisition and processing. Recently, distributional approaches to semantics, in which a word's meaning is determined by its contexts, have led to successful research quantifying the degree of ambiguity, but these measures have not distinguished between the ambiguity of words (...) with multiple related senses versus multiple unrelated meanings. In this work, we present the first assessment of whether distributional meaning representations can capture the ambiguity structure of a word, including both the number and relatedness of senses. On a very large sample of English words, we find that some, but not all, distributional semantic representations that we test exhibit detectable differences between sets of monosemes (unambiguous words; N = 964), polysemes (with multiple related senses; N = 4,096), and homonyms (with multiple unrelated senses; N = 355). Our findings begin to answer open questions from earlier work regarding whether distributional semantic representations of words, which successfully capture various semantic relationships, also reflect fine‐grained aspects of meaning structure that influence human behavior. Our findings emphasize the importance of measuring whether proposed lexical representations capture such distinctions: In addition to standard benchmarks that test the similarity structure of distributional semantic models, we need to also consider whether they have cognitively plausible ambiguity structure. (shrink)

We develop a vector space semantics for verb phrase ellipsis with anaphora using type-driven compositional distributional semantics based on the Lambek calculus with limited contraction of Jäger. Distributional semantics has a lot to say about the statistical collocation based meanings of content words, but provides little guidance on how to treat function words. Formal semantics on the other hand, has powerful mechanisms for dealing with relative pronouns, coordinators, and the like. Type-driven compositional distributional semantics brings these two (...) class='Hi'>models together. We review previous compositional distributional models of relative pronouns, coordination and a restricted account of ellipsis in the DisCoCat framework of Coecke et al. :1079–1100, 2013). We show how DisCoCat cannot deal with general forms of ellipsis, which rely on copying of information, and develop a novel way of connecting typelogical grammar to distributional semantics by assigning vector interpretable lambda terms to derivations of LCC in the style of Muskens and Sadrzadeh Logical aspects of computational linguistics, Springer, Berlin, 2016). What follows is an account of ellipsis in which word meanings can be copied: the meaning of a sentence is now a program with non-linear access to individual word embeddings. We present the theoretical setting, work out examples, and demonstrate our results with a state of the art distributional model on an extended verb disambiguation dataset. (shrink)

With the advent of the cloud computing era, big data technology has also developed rapidly. Due to the huge volume, variety, fast processing speed and low value density of big data, traditional data storage, extraction, transformation and analysis technologies are not suitable, so new solutions for big data application technologies are needed. However, with the development of economic theory and the practice of market economy, some links in the industrial chain of natural monopoly industries already have a certain degree of (...) competitiveness. In this context, the article conducts a research on the anti-monopoly supervision mode of platform economy based on big data and sentiment analysis. This paper introduces the main idea of MapReduce, the current software implementation specifies a Map function that maps a set of key-value pairs into a new set of key-value pairs. It specifies a concurrent Reduce function that guarantees that each of all mapped key-value pairs share the same set of keys. establishes a vector space model, and basically realizes the extraction of text emotional elements. It introduces the theoretical controversy of antitrust regulation of predatory pricing behavior of third-party payment platforms, and conducted model experiments. The experimental results show that the throughput of 40 test users in 1 h of test is determined by two factors, QPS and the number of concurrent, where QPS = 40/ transactions/second. The time for each test user to log in to the system is 10 min, and the average response time is 10*60 s, then the number of concurrency = QPS*average response time = 40/*10*60 = 6.66. This paper has successfully completed the research on the anti-monopoly supervision model of platform economy based on big data and sentiment analysis. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous (...) attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These regularities (...) have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

We define a Lie differential field as a field of characteristic 0 with an action, as derivations on , of some given Lie algebra . We assume that is a finite-dimensional vector space over some sub-field given in advance. As an example take the field of rational functions on a smooth algebraic variety, with .For every simple extension of Lie differential fields we find a finite system of differential equations that characterizes it. We then define, using first-order conditions, (...) a collection of allowed systems of differential equations s.t. the above characteristic systems are allowed. We prove that for every allowed system there exists a generic solution in some extension, and this solution is unique .We construct the model completion of the theory of Lie differential fields by adding axioms stating that every allowed system has almost generic solutions. The construction is a generalization of Blum's axioms for DCF0. We also show that this model completion is ω-stable. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These regularities (...) have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in (...) ; “No infinite‐dimensional Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)

We present statistical analyses of the large‐scale structure of 3 types of semantic networks: word associations, WordNet, and Roget's Thesaurus. We show that they have a small‐world structure, characterized by sparse connectivity, short average path lengths between words, and strong local clustering. In addition, the distributions of the number of connections follow power laws that indicate a scale‐free pattern of connectivity, with most nodes having relatively few connections joined together through a small number of hubs with many connections. These regularities (...) have also been found in certain other complex natural networks, such as the World Wide Web, but they are not consistent with many conventional models of semantic organization, based on inheritance hierarchies, arbitrarily structured networks, or high‐dimensional vector spaces. We propose that these structures reflect the mechanisms by which semantic networks grow. We describe a simple model for semantic growth, in which each new word or concept is connected to an existing network by differentiating the connectivity pattern of an existing node. This model generates appropriate small‐world statistics and power‐law connectivity distributions, and it also suggests one possible mechanistic basis for the effects of learning history variables (age of acquisition, usage frequency) on behavioral performance in semantic processing tasks. (shrink)

Exploratory analysis is an area of increasing interest in the computational linguistics arena. Pragmatically speaking, exploratory analysis may be paraphrased as natural language processing by means of analyzing large corpora of text. Concerning the analysis, appropriate means are statistics, on the one hand, and artificial neural networks, on the other hand. As a challenging application area for exploratory analysis of text corpora we may certainly identify text databases, be it information retrieval or information filtering systems. With this paper we present (...) recent findings of exploratory analysis based on both statistical and neural models applied to legal text corpora. Concerning the artificial neural networks, we rely on a model adhering to the unsupervised learning paradigm. This choice appears naturally when taking into account the specific properties of large text corpora where one is faced with the fact that input-output-mappings as required by supervised learning models cannot be provided beforehand to a satisfying extent. This is due to the fact of the highly changing contents of text archives. In a nutshell, artificial neural networks count for their highly robust behavior regarding the parameters for model optimization. In particular, we found statistical classification techniques much more susceptible to minor parameter variations than unsupervised artificial neural networks. In this paper we describe two different lines of research in exploratory analysis. First, we use the classification methods for concept analysis. The general goal is to uncover different meanings of one and the same natural language concept. A task that, obviously, is of specific importance during the creation of thesauri. As a convenient environment to present the results we selected the legal term of neutrality, which is a perfect representative of a concept having a number of highly divergent meanings. Second, we describe the classification methods in the setting of document classification. The ultimate goal in such an application is to uncover semantic similarities of various text documents in order to increase the efficiency of an information retrieval system. In this sense, document classification has its fixed position in information retrieval research from the very beginning. Nowadays renewed massive interest in document classification may be witnessed due to the appearance of large-scale digital libraries. (shrink)

Semantic memory encompasses one's knowledge about the world. Distributional semantic models, which construct vector spaces with embedded words, are a proposed framework for understanding the representational structure of human semantic knowledge. Unlike some classic semantic models, distributional semantic models lack a mechanism for specifying the properties of concepts, which raises questions regarding their utility for a general theory of semantic knowledge. Here, we develop a computational model of a binary semantic classification task, in which participants judged (...) target words for the referent's size or animacy. We created a family of models, evaluating multiple distributional semantic models, and mechanisms for performing the classification. The most successful model constructed two composite representations for each extreme of the decision axis (e.g., one averaging together representations of characteristically big things and another of characteristically small things). Next, the target item was compared to each composite representation, allowing the model to classify more than 1,500 words with human‐range performance and to predict response times. We propose that when making a decision on a binary semantic classification task, humans use task prompts to retrieve instances representative of the extremes on that semantic dimension and compare the probe to those instances. This proposal is consistent with the principles of the instance theory of semantic memory. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous (...) attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Suppose that λ=λ <λ ≥ℵ0, and we are considering a theory T. We give a criterion on T which is sufficient for the consistent existence of λ++ universal models of T of size λ+ for models of T of size ≤λ+, and is meaningful when 2λ +>λ++. In fact, we work more generally with abstract elementary classes. The criterion for the consistent existence of universals applies to various well known theories, such as triangle-free graphs and simple theories. Having (...) in mind possible applications in analysis, we further observe that for such λ, for any fixed μ>λ+ regular with μ=μλ+, it is consistent that 2λ=μ and there is no normed vector space over ℚ of size <μ which is universal for normed vector spaces over ℚ of dimension λ+ under the notion of embedding h which specifies (a,b) such that ||h(x)/||x∈(a,b) for all x. (shrink)

Djordjević [Dj 1] proved that under natural technical assumptions, if a complete L n -theory is stable and has amalgamation over sets, then it has arbitrarily large finite models. We extend his study and prove the existence of arbitrarily large finite models for classes of models of L n -theories (maybe omitting types) under weaker amalgamation properties. In particular our analysis covers the case of vector spaces.

Linguists have debated whether complex prepositions deserve a constituent status, but none have proposed a dynamic model that can both predict what construal a given pattern imposes and account for the emergence of non-spatial readings. This paper reframes the debate on constituency as a justification of the constructional status of complex prepositional patterns from a historical perspective. It focuses on the Prep NP IL of NP lm construction, which denotes a relation of internal location between a located entity and a (...) reference entity. Four subschemas of the Internal Location construction are examined: middle cxn, center cxn, heart cxn, and midst cxn. All occurrences are extracted from the COHA, along with their co-occurring landmark NPs. Using vocabulary growth curves, all patterns are shown to be productive over the whole period covered by the corpus, although at different levels. Using word2vec, a semantic vector space with the landmark collocates of each pattern is made. Curves indexed on association scores are plotted to see how densely semantic areas have been populated across four consecutive periods: 1810s–1860s, 1870s–1910s, 1920s–1970s, and 1980s–2000s. Two divisions of labor have emerged. midst cxn and heart cxn are in complementary distribution and operate mostly at the level of abstract locations whereas middle cxn and center cxn are in parallel distribution and operate at the level of concrete locations. (shrink)

We demonstrate that the key components of cognitive architectures (declarative and procedural memory) and their key capabilities (learning, memory retrieval, probability judgment, and utility estimation) can be implemented as algebraic operations on vectors and tensors in a high‐dimensional space using a distributional semantics model. High‐dimensional vector spaces underlie the success of modern machine learning techniques based on deep learning. However, while neural networks have an impressive ability to process data to find patterns, they do not typically model high‐level (...) cognition, and it is often unclear how they work. Symbolic cognitive architectures can capture the complexities of high‐level cognition and provide human‐readable, explainable models, but scale poorly to naturalistic, non‐symbolic, or big data. Vector‐symbolic architectures, where symbols are represented as vectors, bridge the gap between the two approaches. We posit that cognitive architectures, if implemented in a vector‐space model, represent a useful, explanatory model of the internal representations of otherwise opaque neural architectures. Our proposed model, Holographic Declarative Memory (HDM), is a vector‐space model based on distributional semantics. HDM accounts for primacy and recency effects in free recall, the fan effect in recognition, probability judgments, and human performance on an iterated decision task. HDM provides a flexible, scalable alternative to symbolic cognitive architectures at a level of description that bridges symbolic, quantum, and neural models of cognition. (shrink)

1 Boolean retrieval 1 2 The term vocabulary and postings lists 19 3 Dictionaries and tolerant retrieval 49 4 Index construction 67 5 Index compression 85 6 Scoring, term weighting and the vector space model 109 7 Computing scores in a complete search system 135 8 Evaluation in information retrieval 151 9 Relevance feedback and query expansion 177 10 XML retrieval 195 11 Probabilistic information retrieval 219 12 Language models for information retrieval 237 13 Text classification and (...) Naive Bayes 253 14 Vector space classification 289 15 Support vector machines and machine learning on documents 319 16 Flat clustering 349 17 Hierarchical clustering 377 18 Matrix decompositions and latent semantic indexing 403 19 Web search basics 421 20 Web crawling and indexes 443 21 Link analysis 461.. (shrink)

The present paper intends to draw the conception of language implied in the technique of word embeddings that supported the recent development of deep neural network models in computational linguistics. After a preliminary presentation of the basic functioning of elementary artificial neural networks, we introduce the motivations and capabilities of word embeddings through one of its pioneering models, word2vec. To assess the remarkable results of the latter, we inspect the nature of its underlying mechanisms, which have been characterized (...) as the implicit factorization of a word-context matrix. We then discuss the ordinary association of the “distributional hypothesis” with a “use theory of meaning,” often justifying the theoretical basis of word embeddings, and contrast them to the theory of meaning stemming from those mechanisms through the lens of matrix models (such as vector space models and distributional semantic models). Finally, we trace back the principles of their possible consistency through Harris’s original distributionalism up to the structuralist conception of language of Saussure and Hjelmslev. Other than giving access to the technical literature and state of the art in the field of natural language processing to non-specialist readers, the paper seeks to reveal the conceptual and philosophical stakes involved in the recent application of new neural network techniques to the computational treatment of language. (shrink)

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index is derived from (...) the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to (...) S remains r.e., while that corresponding to R is not r.e.; immune; hyperimmune. The results are applied to vector spaces, Boolean algebras and abelian groups. In the case of vector spaces, this leads to a new kind supermaximal subspace of V∞. (shrink)

We present a longitudinal computational study on the connection between emotional and amodal word representations from a developmental perspective. In this study, children's and adult word representations were generated using the latent semantic analysis (LSA) vector space model and Word Maturity methodology. Some children's word representations were used to set a mapping function between amodal and emotional word representations with a neural network model using ratings from 9‐year‐old children. The neural network was trained and validated in the child (...) semantic space. Then, the resulting neural network was tested with adult word representations using ratings from an adult data set. Samples of 1210 and 5315 words were used in the child and the adult semantic spaces, respectively. Results suggested that the emotional valence of words can be predicted from amodal vector representations even at the child stage, and accurate emotional propagation was found in the adult word vector representations. In this way, different propagative processes were observed in the adult semantic space. These findings highlight a potential mechanism for early verbal emotional anchoring. Moreover, different multiple linear regression and mixed‐effect models revealed moderation effects for the performance of the longitudinal computational model. First, words with early maturation and subsequent semantic definition promoted emotional propagation. Second, an interaction effect between age of acquisition and abstractness was found to explain model performance. The theoretical and methodological implications are discussed. (shrink)

A structure is a triple A = (A, {Ri: i ∈ I}, {ej: j ∈ J}), where A, the domain or universe of A, is a nonempty set, {Ri: i ∈ I} is an indexed family of relations on A and {ej: j ∈ J}) is an indexed set of elements —the designated elements of A. For each i ∈ I there is then a natural number λ(i) —the degree of Ri —such that Ri is a λ(i)-place relation on A, (...) i.e., Ri ⊆ Aλ(i). This λ may be regarded as a function from I to the set ω of natural numbers; the pair (λ, J) is called the type of A. Structures of the same type are said to be similar. Note that since an n-place operation f: An → A can be regarded as an (n+1)-place relation on A, algebraic structures containing operations such as groups, rings, vector spaces, etc. may be construed as structures in the above sense. (shrink)

In [6], Metakides and Nerode introduced the study of the lattice of recursively enumerable substructures of a recursively presented model as a means to understand the recursive content of certain algebraic constructions. For example, the lattice of recursively enumerable subspaces,, of a recursively presented vector spaceV∞has been studied by Kalantari, Metakides and Nerode, Retzlaff, Remmel and Shore. Similar studies have been done by Remmel [12], [13] for Boolean algebras and by Metakides and Nerode [9] for algebraically closed fields. In (...) all of these models, the algebraic closure of a set is nontrivial., is given in §1, however in vector spaces, cl is just the subspace generated byS, in Boolean algebras, cl is just the subalgebra generated byS, and in algebraically closed fields, cl is just the algebraically closed subfield generated byS.)In this paper, we give a general model theoretic setting in which we are able to give constructions which generalize many of the constructions of classical recursion theory. One of the main features of the modelswhich we study is that the algebraic closure of setis just itself, i.e., cl = S. Examples of such models include the natural numbers under equality 〈N, = 〉, the rational numbers under the usual ordering 〈Q, ≤〉, and a large class ofn-dimensional partial orderings. (shrink)

In this paper, we propose an inter-personal information sharing model among individuals based on personalized recommendations. In the proposed model, we define an information resource as shared between people when both of them consider it important --- not merely when they both possess it. In other words, the model defines the importance of information resources based on personalized recommendations from identifiable acquaintances. The proposed method is based on a collaborative filtering system that focuses on evaluations from identifiable acquaintances. It utilizes (...) both user evaluations for documents and their contents. In other words, each user profile is represented as a matrix of credibility to the other users' evaluations on each domain of interests. We extended the content-based collaborative filtering method to distinguish other users to whom the documents should be recommended. We also applied a concept-based vector space model to represent the domain of interests instead of the previous method which represented them by a term-based vector space model. We introduce a personalized concept-base compiled from each user's information repository to improve the information retrieval in the user's environment. Furthermore, the concept-spaces change from user to user since they reflect the personalities of the users. Because of different concept-spaces, the similarity between a document and a user's interest varies for each user. As a result, a user receives recommendations from other users who have different view points, achieving inter-personal information sharing based on personalized recommendations. This paper also describes an experimental simulation of our information sharing model. In our laboratory, five participants accumulated a personal repository of e-mails and web pages from which they built their own concept-base. Then we estimated the user profiles according to personalized concept-bases and sets of documents which others evaluated. We simulated inter-personal recommendation based on the user profiles and evaluated the performance of the recommendation method by comparing the recommended documents to the result of the content-based collaborative filtering. (shrink)

A method of generating synonyms for a stimulus word using a computer is proposed. Vector Space Model, where words in text data are arranged in a multi-dimensional space and degree of similarity between two words of them is calculated from how close the words are in the space, may be available to the method. However, it is not easy to optimize parameters in the method because there is no appropriate standard synonym database where proper synonyms for (...) a stimulus word are thoroughly collected. Therefore, we first built such a standard database employing two steps of human subjects expriments, and optimized the parameters of the method of generating synonyms. As the result, it was found that the Vector Space Model-based method using an electronic dictionary as source is better to generate synonyms than the one using a text corpus and an ordinal method using a thesaurus. (shrink)

In this information-oriented society that we live in, a method of retrieving necessary information is needed. Obtaining necessary information, by information retrieval using the Boolean method, which uses keywords given by the user, narrows corresponding documents down to the thousands or ten thousands, which results in the user not knowing which document to look at first. Therefore, by transferring the user's retrieval query and documents into quantitative values and ranking the requested information in order of relation to the user's demand, (...) it is needed to give the user information that fits the user's demand. As a calculation method to transfer the retrieval query and the documents into quantitative values, the vector space model exists, but this paper shows that the method of ranking information, using the concept-base and the degree of association, is effective. (shrink)

A historical review and philosophical look at the introduction of “negative probability” as well as “complex probability” is suggested. The generalization of “probability” is forced by mathematical models in physical or technical disciplines. Initially, they are involved only as an auxiliary tool to complement mathematical models to the completeness to corresponding operations. Rewards, they acquire ontological status, especially in quantum mechanics and its formulation as a natural information theory as “quantum information” after the experimental confirmation the phenomena of (...) “entanglement”. Philosophical interpretations appear. A generalization of them is suggested: ontologically, they correspond to a relevant generalization to the relation of a part and its whole where the whole is a subset of the part rather than vice versa. The structure of “vector space” is involved necessarily in order to differ the part “by itself” from it in relation to the whole as a projection within it. That difference is reflected in the new dimension of vector space both mathematically and conceptually. Then, “negative or complex probability” are interpreted as a quantity corresponding the generalized case where the part can be “bigger” than the whole, and it is represented only partly in general within the whole. (shrink)

In this study, we analyzed the relationship between the amodal (semantic) development of words and two popular emotional norms (emotional valence and arousal) in English and Spanish languages. To do so, we combined the strengths of semantics from vector space models (vector length, semantic diversity, and word maturity measures), and feature-based models of emotions. First, we generated a common vector space representing the meaning of words at different developmental stages (five and four developmental (...) stages for English and Spanish, respectively) using the Word Maturity methodology to align different vector spaces. Second, we analyzed the amodal development of words through mixed-effects models with crossed random effects for words and variables using a continuous time metric. Third, the emotional norms were included as covariates in the statistical models. We evaluated more than 23,000 words, whose emotional norms were available for more than 10,000 words, in each language separately. Results showed a curve of amodal development with an increasing linear effect and a small quadratic deceleration. A relevant influence on the amodal development of words was found only for emotional valence (not for arousal), suggesting that positive words have an earlier amodal development and a less pronounced semantic change across early lifespan. (shrink)

If the words of natural human language possess a universal positivity bias, as assumed by Boucher and Osgood’s (1969) famous Pollyanna hypothesis and computationally confirmed for large text corpora in several languages (Dodds et al., 2015), then children and youth literature (CYL) should also show a Pollyanna effect. Here we tested this prediction applying a vector space model- based sentiment analysis tool called SentiArt (Jacobs, 2019) to two CYL corpora, one in English (372 books) and one in German (...) (500 books). Pitching our analysis at the sentence level, and assessing semantic as well as lexico-grammatical information, bBoth corpora show the Pollyanna effect and thus add further evidence to the universality hypothesis. The results of our multivariate sentiment analyses provide interesting testable predictions for future scientific studies of literature. (shrink)

Automatically clustering web pages into semantic groups promises improved search and browsing on the web. In this paper, we demonstrate how user-generated tags from largescale social bookmarking websites such as del.icio.us can be used as a complementary data source to page text and anchor text for improving automatic clustering of web pages. This paper explores the use of tags in 1) K-means clustering in an extended vector space model that includes tags as well as page text and 2) (...) a novel generative clustering algorithm based on latent Dirichlet allocation that jointly models text and tags. We evaluate the models by comparing their output to an established web directory. We find that the naive inclusion of tagging data improves cluster quality versus page text alone, but a more principled inclusion can substantially improve the quality of all models with a statistically signifi- cant absolute F-score increase of 4%. The generative model outperforms K-means with another 8% F-score increase. (shrink)