Yes / The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota’s formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

No description available.

Esta dissertação apresenta uma análise semântica, no paradigma da Semântica Formal, da (i) restrição de domínio no DP e da (ii) expressão kar, que veicula a ideia de totalidade, no dialeto paranaense da língua Kaingang, do tronco Macro-Jê, família Jê, falada nas regiões sul e sudeste do Brasil. Num primeiro momento, o artigo definido parece ter, no Kaingang Paranaense, uma distribuição não trivial: aplica-se primeiro a um determinante quantificacional e restringe, via essa combinação, o domínio do quantificador, tal como no Basco, Grego e Státimcets (Giannakidou 2003, Etxeberria 2005 e Etxeberria & Giannakidou 2009), línguas muito parecidas com o Kaingang no domínio nominal. Alguns dados, contudo, apontaram a análise em outra direção. Entendemos que certos padrões de comportamento semântico e sintático apresentado por kar nas sentenças, tal como sua neutralidade quanto à propriedade de distributividade e a possibilidade da conjunção de duas sequências de [NP+kar] sob um mesmo artigo definido (ao contrário do Basco, no qual a mesma estrutura é agramatical, sugerindo que os quantificadores universais em Basco criam um QP), são algumas das evidências que, no conjunto, dão suporte para a hipótese, defendida nesta dissertação, de que kar, no Kaingang Paranaense, parece ser um modificador - à la Lasersohn (1999) -, não tendo, por isso, uma força quantificacional própria. A função semântica de kar seria de controlar o quanto de desvio da verdade é pragmaticamente permissível. Como consequência desta análise, no Kaingang Paranaense o artigo definido não operaria sobre um determinante quantificacional, mas sim sobre um NP. O que aponta no sentido de que os artigos definidos ag/fag (os/as) no Kaingang Paranaense, em contextos em que eles co-ocorrem com kar, não perderiam a sua função max, i.e., de formadores de indivíduo a partir de um conjunto, para funcionar meramente como um operador preservador de tipo e restritor de domínio adjungido ao determinante quantificacional, como proposto por Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) para o Basco e o Grego. Ag/fag continuariam sendo artigos definidos clássicos ocupando o núcleo de uma projeção DP e kar um modificador. Também discutimos brevemente algumas das vantagens e problemas de se tentar estender esta análise para o Basco, Grego e Státimcets. E, por último, investigamos o comportamento de kar na sentença, as possíveis leituras quando da sua interação com indefinidos, numerais, tipos de predicados e o operador distributivo introduzido via reduplicação verbal. Com base nos dados, nossa proposta é de que - em função de a leitura distributiva, na maioria dos exemplos, ser permitida pelos informantes somente quando houve reduplicação verbal - kar é neutro quanto à propriedade da distributividade e que o operador distributivo introduzido por reduplicação verbal tem escopo sobre todo o VP. / This dissertation presents, in the paradigm of formal semantics, a semantic analysis of both (i) the phenomenon of domain restriction in the DP and (ii) the expression kar, which conveys the idea of totality, in a dialect of the Kaingang language, a Brazilian language from the Macro-Jê Stock, Jê family, spoken in southern and southeastern Brazil. Although, at first, the definite article in Kaingang seems to have a non-trivial distribution: it applies first to a quantificational expression, and via such combination restricts the domain of quantifier, such as in Basque, Greek and Státimcets (Giannakidou 2003, Etxeberria 2005 and Etxeberria & Giannakidou 2009), some data pointed the analysis in another direction. Patterns of semantic and syntactic bevavior presented by kar in some sentences, such as its neutralite regarding the property of distributivity and the possibility of conjoining two [NP + kar] sequences under the same definite article (unlike Basque, which does not allow such structure, suggesting that in Basque the universal quantifier creats a QP), seem to be as a whole evidences for the hypothesis, advocated in this thesis, that the expression kar may be a modifier - à la Lasersohn (1999) - and as such would not have a quantificational force of its own. The semantic function of kar would be to control how much deviation from the truth conditions of the sentences is pragmatically allowed. As a result of this analysis, the definite articles ag/fag in Kaingang do not operate on a quantificational expression, as in Basque and Greek, but on the NP. Such fact suggests that the definite articles in Kaingang, in contexts they co-occur with kar, do not lose their max function in order to work merely as a type preserver and a domain restrictor combined with a quantificational expression, as proposed by Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) for Basque and Greek. Ag/fag would still be a classical definite article occupying the head of a DP projection and kar a modifier, instead of a universal quantifier. We also discuss briefly some of the advantages and problems of trying to extend this analysis to the Basque, Greek and Státimcets languages. And lastly, we investigated the behavior of kar in the sentence, its interaction with indefinites, numerals, types of predicates and the distributive operator introduced via verbal reduplication. Based on such data, once distributive readings were permitted by the informants only via verbal reduplication, our proposal is that kar is neutral regarding the property of distributivity and that the distributive operator introduced via verbal reduplication has scope over the VP.

Esta dissertação apresenta uma análise semântica, no paradigma da Semântica Formal, da (i) restrição de domínio no DP e da (ii) expressão kar, que veicula a ideia de totalidade, no dialeto paranaense da língua Kaingang, do tronco Macro-Jê, família Jê, falada nas regiões sul e sudeste do Brasil. Num primeiro momento, o artigo definido parece ter, no Kaingang Paranaense, uma distribuição não trivial: aplica-se primeiro a um determinante quantificacional e restringe, via essa combinação, o domínio do quantificador, tal como no Basco, Grego e Státimcets (Giannakidou 2003, Etxeberria 2005 e Etxeberria & Giannakidou 2009), línguas muito parecidas com o Kaingang no domínio nominal. Alguns dados, contudo, apontaram a análise em outra direção. Entendemos que certos padrões de comportamento semântico e sintático apresentado por kar nas sentenças, tal como sua neutralidade quanto à propriedade de distributividade e a possibilidade da conjunção de duas sequências de [NP+kar] sob um mesmo artigo definido (ao contrário do Basco, no qual a mesma estrutura é agramatical, sugerindo que os quantificadores universais em Basco criam um QP), são algumas das evidências que, no conjunto, dão suporte para a hipótese, defendida nesta dissertação, de que kar, no Kaingang Paranaense, parece ser um modificador - à la Lasersohn (1999) -, não tendo, por isso, uma força quantificacional própria. A função semântica de kar seria de controlar o quanto de desvio da verdade é pragmaticamente permissível. Como consequência desta análise, no Kaingang Paranaense o artigo definido não operaria sobre um determinante quantificacional, mas sim sobre um NP. O que aponta no sentido de que os artigos definidos ag/fag (os/as) no Kaingang Paranaense, em contextos em que eles co-ocorrem com kar, não perderiam a sua função max, i.e., de formadores de indivíduo a partir de um conjunto, para funcionar meramente como um operador preservador de tipo e restritor de domínio adjungido ao determinante quantificacional, como proposto por Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) para o Basco e o Grego. Ag/fag continuariam sendo artigos definidos clássicos ocupando o núcleo de uma projeção DP e kar um modificador. Também discutimos brevemente algumas das vantagens e problemas de se tentar estender esta análise para o Basco, Grego e Státimcets. E, por último, investigamos o comportamento de kar na sentença, as possíveis leituras quando da sua interação com indefinidos, numerais, tipos de predicados e o operador distributivo introduzido via reduplicação verbal. Com base nos dados, nossa proposta é de que - em função de a leitura distributiva, na maioria dos exemplos, ser permitida pelos informantes somente quando houve reduplicação verbal - kar é neutro quanto à propriedade da distributividade e que o operador distributivo introduzido por reduplicação verbal tem escopo sobre todo o VP. / This dissertation presents, in the paradigm of formal semantics, a semantic analysis of both (i) the phenomenon of domain restriction in the DP and (ii) the expression kar, which conveys the idea of totality, in a dialect of the Kaingang language, a Brazilian language from the Macro-Jê Stock, Jê family, spoken in southern and southeastern Brazil. Although, at first, the definite article in Kaingang seems to have a non-trivial distribution: it applies first to a quantificational expression, and via such combination restricts the domain of quantifier, such as in Basque, Greek and Státimcets (Giannakidou 2003, Etxeberria 2005 and Etxeberria & Giannakidou 2009), some data pointed the analysis in another direction. Patterns of semantic and syntactic bevavior presented by kar in some sentences, such as its neutralite regarding the property of distributivity and the possibility of conjoining two [NP + kar] sequences under the same definite article (unlike Basque, which does not allow such structure, suggesting that in Basque the universal quantifier creats a QP), seem to be as a whole evidences for the hypothesis, advocated in this thesis, that the expression kar may be a modifier - à la Lasersohn (1999) - and as such would not have a quantificational force of its own. The semantic function of kar would be to control how much deviation from the truth conditions of the sentences is pragmatically allowed. As a result of this analysis, the definite articles ag/fag in Kaingang do not operate on a quantificational expression, as in Basque and Greek, but on the NP. Such fact suggests that the definite articles in Kaingang, in contexts they co-occur with kar, do not lose their max function in order to work merely as a type preserver and a domain restrictor combined with a quantificational expression, as proposed by Giannakidou 2003, Etxeberria (2005) e Etxeberria & Giannakidou (2009) for Basque and Greek. Ag/fag would still be a classical definite article occupying the head of a DP projection and kar a modifier, instead of a universal quantifier. We also discuss briefly some of the advantages and problems of trying to extend this analysis to the Basque, Greek and Státimcets languages. And lastly, we investigated the behavior of kar in the sentence, its interaction with indefinites, numerals, types of predicates and the distributive operator introduced via verbal reduplication. Based on such data, once distributive readings were permitted by the informants only via verbal reduplication, our proposal is that kar is neutral regarding the property of distributivity and that the distributive operator introduced via verbal reduplication has scope over the VP.

The basic properties of distributivity and deletion of pure and o-substitution are investigated. The obtained results are applied to show preservation of recognizability in a number of surprising cases. It is proved that linear and recognizable tree series are closed under o-substitution provided that the underlying semiring is commutative, continuous, and additively idempotent. It is known that, in general, pure substitution does not preserve recognizability (not even for linear target tree series), but it is shown that recognizable linear probability distributions (represented as tree series) are closed under pure substitution.

Les ambiguïtés de phrases sont au cœur de la recherche sur la compréhension du langage depuis un certain temps. Pour les sémanticiens, ces ambigüités ont été utilisées pour suggérer l’existence de différents mécanismes abstraits qui pourraient s’appliquer à une même structure syntaxique au stade de l’interprétation. Pour les psycholinguistes, les ambiguïtés sémantiques ont offert un outil d’étude de la dynamique du traitement de phrases : puisque les ambiguïtés tendent à être résolues incrémentalement (c’est-à-dire avant la fin de la phrase), le schéma de traitement des phrases ambiguës peut permettre d’identifier les facteurs linguistiques et non linguistiques qui jouent un rôle dans la compréhension online. Cette dissertation traite des théories de la compréhension du langage en explorant deux questions complémentaires : (1) comment différents sens peuvent-ils être associés à une seule tournure de phrase, et (2) comment sommes-nous capables d’accéder à ces interprétations alternatives et de les traiter pendant l’analyse syntaxique. Pour répondre à ces questions, la présente étude se focalise principalement sur ce qu’on appelle les ambiguïtés de pluriel, qui surgissent par l’interaction entre certains prédicats et leurs arguments pluriels. Par exemple, la phrase Amir et Milica ont construit un château de sable a une interprétation non distributive, collective (c’est-à-dire qu’Amir et Milica ont construit ensemble un château de sable) mais aussi une interprétation distributive (c’est-à-dire qu’Amir et Milica ont chacun construit un château de sable). La plupart des approches linguistiques partent du principe que les lectures distributives dérivent d’interprétations non distributives, plus élémentaires, par l’application d’un opérateur de « distributivité » phonologiquement nul (Link, 1987 ; Champollion, 2014). La première partie de cette dissertation présente deux études qui visent à identifier les mécanismes abstraits qui sous-tendent le contraste distributif/non distributif à travers un paradigme d’amorçage. Cette méthode d’amorçage est ensuite étendue à d’autres phénomènes sémantiques (c’est-à-dire des ambiguïtés de portée) dans la deuxième partie de la dissertation, dans laquelle des interactions entre pluralité et phénomène de portée sont aussi testées expérimentalement. Pour évaluer la dynamique de la résolution des ambiguïtés, la troisième partie de cette dissertation présente une étude de suivi des mouvements de souris, conçue pour établir les caractéristiques de trajectoires de souris qui se corrèlent avec la prise de décision et la désambiguïsation. La méthodologie développée dans cette étude est ensuite utilisée pour analyser des données préliminaires relatives au traitement de phrases à ambiguïtés de pluriel. / Sentence ambiguities have been at the center of the research on language comprehension for some time. For semanticists, these ambiguities have been taken to suggest the existence of different abstract mechanisms that may apply to the same syntactic structure at the interpretation stage. For psycholinguists, semantic ambiguities have provided a tool to analyze the dynamics of sentence parsing: since ambiguities tend to be solved incrementally (i.e. before the end of the sentence), the processing pattern of ambiguous sentences might allow identifying the linguistic and non-linguistic factors that play a role during online comprehension. This dissertation informs theories of language comprehension by exploring two complementary questions: (1) how are different meanings associated to a single sentence form, and (2) how are we able to access and compute these alternative interpretations during parsing. To address these questions, the present work mainly focuses on the so-called plural ambiguities, which arise by the interaction between certain predicates and their plural arguments. For instance, the sentence Amir and Milica built a sandcastle has a non-distributive, collective, interpretation (i.e. Amir and Milica together built a sandcastle) as well as a distributive one (i.e. Amir and Milica each built a sandcastle). Most linguistic approaches assume that distributive readings are derived from more basic non-distributive interpretations by the application of a covert “distributivity” operator (Link, 1987; Champollion, 2014) . The first part of this dissertation presents two studies that aim to identify the abstract mechanisms underlying the distributive/non-distributive contrast through a priming paradigm. This priming method is then extended to other semantic phenomena (i.e. scope ambiguities) in the second part of the dissertation, where some interactions between plurality and scope phenomena are also tested experimentally. To assess the dynamics of ambiguity resolution, the third part of this work presents a mouse-tracking study designed to establish the features of mouse-trajectories that correlate with decision making and disambiguation. The methodology developed in this study is then used to analyze preliminary data on the processing of plural ambiguous sentences.

The basic properties of distributivity and deletion of pure and o-substitution are investigated. The obtained results are applied to show preservation of recognizability in a number of surprising cases. It is proved that linear and recognizable tree series are closed under o-substitution provided that the underlying semiring is commutative, continuous, and additively idempotent. It is known that, in general, pure substitution does not preserve recognizability (not even for linear target tree series), but it is shown that recognizable linear probability distributions (represented as tree series) are closed under pure substitution.

Cette thèse est consacrée à l’étude des syntagmes nominaux sémantiquement pluriels en chinois mandarin et aux interprétations collective et distributive qui leur sont associées. Elle offre une analyse des formes de pluralité suivantes : le syntagme coordonne par gen, les nominaux modifiés par le suffixe -men, ainsi que les sujets ou les objets des groupes verbaux modifies par quan (‘tout’-flottant). A propos du syntagme coordonne par gen, nous montrons que la conjonction gen dans le syntagme ‘A gen B’ lexicalise une contrainte de pluralité nominale par le biais de restrictions sur les conjoints. Notre argument est bâti sur trois points principaux, à savoir que la catégorie des conjoints est nécessairement [+N], que le syntagme coordonne par gen n’introduit que des individus pluriels dans le discours et que ce syntagme porte la valeur sémantique pluriel [+Pl]. Nous passons aussi en revue différents types de prédicats afin de retracer la distribution des interprétations collective et distributive des syntagmes coordonnés par gen. Ensuite, nous nous penchons sur le suffixe -men et sur l’expression formée par ce suffixe et un nom commun ou un nom propre. Notre examen couvre principalement deux questions, celle de la nature de -men et celle de la (in)définitude de l’expression suffixée par -men en mandarin. Nous soutenons que -men n’est pas un marqueur collectif mais plutôt un marqueur pluriel. Cependant, ce marqueur n’est pas obligatoire, à la différence des marqueur du pluriel tels que -s dans les langues occidentales, le mandarin étant une langue à classificateur. Quant à l’(in)définitude de l’expression suffixée par -men, nous admettons que c’est un pluriel défini, mais ceci du fait que -men ne s’attache qu’aux pronoms personnels et aux noms d’humains, noms qui occupent le hautde la hiérarchie d’animacité. Donc l’expression suffixée par -men hériterait de la définitude en partie de la nature de son domaine fortement individué. Enfin, nous nous intéressons a l’interprétation distributive des syntagmes nominaux dans la phrase ou figure l’adverbe quan (‘tout’-flottant). Nous affirmons que quan impose la lecture distributive de manière autonome et nous en proposons une analyse en tant que modificateur de prédicat d’évènement. Quan cible un nominal relie par un θ-rôle et encapsule dans ce rôle l’instruction de distribution. La distributivité renforcée par quan implique une relation distributive entre deux entités : le nominal qui est sémantiquement pluriel et l’évènement pluriel / The thesis invested the research on the semantically plural nominal phrases in Mandarin Chinese and on their collectif and distributif interpretations. It offered an analysis of the following form of pluralities : the coordinated phrase with gen, the nominals modified by the suffix -men, and the subjects or the objects of the VP modified by quan (the floating quantifier). Concerning the coordinated phrase with gen, we will show that the conjunction gen of the phrase ‘A gen B’ lexicalize the constraint of the plurality via the restrictions on the conjoint elements. Our argument is mainly based on three points : 1) the category of the conjuncts is necessarily [+N] ; 2) coordinated phrases with gen introduce only the plural individuals in the discourse and 3) this nominal phrase characterizes the semantic plural value [+Pl]. We will also examine the different types of predicates in order to retrace thedistribution of collective and distributive interpretations of the coordinated phrases with gen. Then, we look into the suffix –men and the expressions formed by this suffix and a common noun or a proper noun. The investigation will mainly concern two questions : the question of the nature of –men and the question of the (in)definitude of the expressions suffixed by –men in Mandarin Chinese. We will argue that –men is not a collectif marker, but preferably a plural marker. However, different from plural markers in the western languages for exemple –s, the marker –men in Mandarin Chinese which is typically a classifer language, is not obligatory. Regarding the (in)definitude of the expressions suffixed by -men, we will admit that they are definite plurals, because of the fact that –men attaches only to only to personal pronouns and humain nouns, the nouns which occupy a high hierarchy of animacity. In consequence, the expressions suffixed by –men partly inherit the definitude of the nature of its considerably individuated domain. Finally, we are interested in the distributive interpretation of the nominal phrases in the sentences wherethe adverbial quan (the floating quantifier) appeares. We will claim that quan imposes the distributive reading in an autonomous manner and we will put forward an analysis of adverbial quan as a modifier of event predicate. Quan targets nominals linked by θ-roles and encapsulate in this role the instruction of distribution. The distributivity reinforced by quan involves a distributive relation between two entities : the nominal which is semantically plural and the plural event.

<p>Disertacija je posvećena re&scaron;avanju jednačina distributivnosti gde&nbsp;nepoznate funkcije pripadaju nekim poznatim klasama operacija agregacije&nbsp;i primeni dobijenih re&scaron;enja u teoriji korisnosti. Dobijeni rezultati se generalno mogu podeliti u tri grupe. Prvu grupu čine rezultati iz Glave 2 dobijeni re&scaron;avanjem jednačina distributivnosti između GM-operacija agregacije i&nbsp;oslabljenih uninormi, GM-operacija agregacije i oslabljenih nulanormi, kao i&nbsp;GM-operacija agregacije i operacija agregacije bez neutralnog i absorbujućeg&nbsp;elementa. Druga grupa rezultata, takođe iz Glave 2, je dobijena re&scaron;avanjem&nbsp;jednačina uslovne (oslabljene) distributivnosi neprekidne nulanorme u odnosu&nbsp;na neprekidnu t-konormu, i neprekidne nulanonorme u odnosu na uninorme iz&nbsp;<br />klasa U_min &cup;U_max. Treća grupa rezultata (Glava 3) je proistekla iz primene dobijenih rezultata o uslovoj distributivnosti nulanorme u odnosu na t-konormu&nbsp;u teoriji korisnosti.</p> / <p>This dissertation is devoted to solving distributivity equations involving some well-known classes of aggregation operators, and application&nbsp;the obtained results to utility theory. In general, the obtained results can&nbsp;be divided into three groups. The first group are results from Chapter 2 obtained by solving distributivity equations between GM-aggregation operators&nbsp;and relaxed nullnorm, GM-aggregation operators and relaxed uninorms, as&nbsp;well as GM-aggregation operators and aggregation operators without neutral&nbsp;and absorbing element. The second group are results, also from Chapter 2,&nbsp;obtained by solving conditional (relaxed) distributivity of continuous nullnorm with respect to &nbsp;continuous t-conorm, as well as continuous nullnorm&nbsp;with respect to uninorms from the classes U_min &cup; U_max. The third group are&nbsp;results (Chapter 3) arising from the application results on conditional distributivity of nullnorm with respect to t-conorm in utility theory.</p>

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