Closure Hyperdoctrines, with Paths
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The Interpretation of Tense — I Didn't Turn Off the Stove Toshiyuki Ogihara
The interpretation of tense — I didn’t turn off the stove Toshiyuki Ogihara — University of Washington [email protected] Kiyomi Kusumoto — Kwansei Gakuin University [email protected] Abstract This chapter examines Partee’s (1973) celeBrated claim that tenses are not existential quantifiers but pronouns. In the first half of the chapter, we show that this proposal successfully accounts for the Behavior of tense morphemes regarding deixis, anaphora, and presupposition. It is also compatiBle with cases where tense morphemes Behave like Bound variables. In the second half of the chapter, we turn to the syntax-semantics interface and propose some concrete implementations Based on three different assumptions aBout the semantics of tense: (i) quantificational; (ii) pronominal; (iii) relational. Finally, we touch on some tense-related issues involving temporal adverBials and cross-linguistic differences. Keywords tense, pronoun, quantification, Bound variaBle, referential, presupposition, temporal adverbial (7 key words) 1. Introduction This article discusses the question of whether the past tense morpheme is analogous to pronouns and if so how tense is encoded in the system of the interfaces between syntax and semantics. The languages we will deal with in this article have tense morphemes that are attached to verbs. We use 1 this type of language as our guide and model. Whether tense is part of natural language universals, at least in the area of semantic interpretation, is debatable.1 Montague’s PTQ (1973) introduces a formal semantic system that incorporates some tense and aspect forms in natural language and their model-theoretic interpretation. It introduces tense operators based on Prior’s (1957, 1967) work on tense logic. -
Overt Existential Closure in Bura (Central Chadic)
Overt Existential Closure in Bura (Central Chadic) Malte Zimmermann University of Potsdam 1. Introduction The article presents a semantic-based account of the syntactic distribution of the morpheme adi in Bura. This morpheme is traditionally glossed as an existential predicate there is (Hoffmann 1955) and occurs only in a limited set of – at first sight – heterogeneous syntactic environments, namely (i.) in (most) negative clauses; (ii.) in thetic constructions used for introducing new discourse referents (there is x ...); and (iii.) in existential clefts (there is some x that ...). The article will identify the semantic contribution of adi and give a unified account of its distribution. It is argued that adi is an overt marker of existential closure that can bind individual or event variables with existential force. The insertion of adi is argued to be a last resort operation. It applies if and only if alternative means of existentially closing a variable fail. The analysis of adi as an overt indicator of existential closure has repercussions for semantic theory as whole. For once, given that adi is overt, it gives us a better insight into the workings and the grammatical locus of existential closure, which can be accessed only indirectly in European languages (Diesing 1992). Second, given that adi must existentially close off event variables in negative clauses, it can be used as a diagnostic for the ability of verbal predicates to introduce an event argument into the semantic representation (Kratzer 1995). The structure of the article is as follows: Section 2 provides some background information on Bura. Section 3 lays out the main facts surrounding the distribution of adi. -
Quantification and Predication in Mandarin Chinese: a Case Study of Dou
University of Pennsylvania ScholarlyCommons IRCS Technical Reports Series Institute for Research in Cognitive Science December 1996 Quantification and Predication in Mandarin Chinese: A Case Study of Dou Shi-Zhe Huang University of Pennsylvania Follow this and additional works at: https://repository.upenn.edu/ircs_reports Huang, Shi-Zhe, "Quantification and Predication in Mandarin Chinese: A Case Study of Dou" (1996). IRCS Technical Reports Series. 114. https://repository.upenn.edu/ircs_reports/114 University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-96-36. This paper is posted at ScholarlyCommons. https://repository.upenn.edu/ircs_reports/114 For more information, please contact [email protected]. Quantification and Predication in Mandarin Chinese: A Case Study of Dou Abstract In the more recent generalized quantifier theory, 'every' is defined as a elationr between two sets such that the first set is a subset of the second set (Cooper (1987), anv Benthem (1986)). We argue in this dissertation that the formal definition of e' very' ought to reflect our intuition that this quantifier is always associated with a pairing. For instance, 'Every student left' means that for every student there is an event (Davidson (1966), Kroch (1974), Mourelatos (1978), Bach (1986)) such that the student left in that event. We propose that the formal translation of EVERY be augmented by relating its two arguments via a skolem function. A skolem function links two variables by making the choice of a value for one variable depend on the choice of a value for the other. This definition of EVERY, after which 'every' and its Chinese counterpart 'mei' can be modeled, can help us explain the co-occurrence pattern between 'mei' and the adverb 'dou'. -
Anaphoric Reference to Propositions
ANAPHORIC REFERENCE TO PROPOSITIONS A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Todd Nathaniel Snider December 2017 c 2017 Todd Nathaniel Snider ALL RIGHTS RESERVED ANAPHORIC REFERENCE TO PROPOSITIONS Todd Nathaniel Snider, Ph.D. Cornell University 2017 Just as pronouns like she and he make anaphoric reference to individuals, English words like that and so can be used to refer anaphorically to a proposition introduced in a discourse: That’s true; She told me so. Much has been written about individual anaphora, but less attention has been paid to propositional anaphora. This dissertation is a com- prehensive examination of propositional anaphora, which I argue behaves like anaphora in other domains, is conditioned by semantic factors, and is not conditioned by purely syntactic factors nor by the at-issue status of a proposition. I begin by introducing the concepts of anaphora and propositions, and then I discuss the various words of English which can have this function: this, that, it, which, so, as, and the null complement anaphor. I then compare anaphora to propositions with anaphora in other domains, including individual, temporal, and modal anaphora. I show that the same features which are characteristic of these other domains are exhibited by proposi- tional anaphora as well. I then present data on a wide variety of syntactic constructions—including sub- clausal, monoclausal, multiclausal, and multisentential constructions—noting which li- cense anaphoric reference to propositions. On the basis of this expanded empirical do- main, I argue that anaphoric reference to a proposition is licensed not by any syntactic category or movement but rather by the operators which take propositions as arguments. -
GALOIS THEORY for ARBITRARY FIELD EXTENSIONS Contents 1
GALOIS THEORY FOR ARBITRARY FIELD EXTENSIONS PETE L. CLARK Contents 1. Introduction 1 1.1. Kaplansky's Galois Connection and Correspondence 1 1.2. Three flavors of Galois extensions 2 1.3. Galois theory for algebraic extensions 3 1.4. Transcendental Extensions 3 2. Galois Connections 4 2.1. The basic formalism 4 2.2. Lattice Properties 5 2.3. Examples 6 2.4. Galois Connections Decorticated (Relations) 8 2.5. Indexed Galois Connections 9 3. Galois Theory of Group Actions 11 3.1. Basic Setup 11 3.2. Normality and Stability 11 3.3. The J -topology and the K-topology 12 4. Return to the Galois Correspondence for Field Extensions 15 4.1. The Artinian Perspective 15 4.2. The Index Calculus 17 4.3. Normality and Stability:::and Normality 18 4.4. Finite Galois Extensions 18 4.5. Algebraic Galois Extensions 19 4.6. The J -topology 22 4.7. The K-topology 22 4.8. When K is algebraically closed 22 5. Three Flavors Revisited 24 5.1. Galois Extensions 24 5.2. Dedekind Extensions 26 5.3. Perfectly Galois Extensions 27 6. Notes 28 References 29 Abstract. 1. Introduction 1.1. Kaplansky's Galois Connection and Correspondence. For an arbitrary field extension K=F , define L = L(K=F ) to be the lattice of 1 2 PETE L. CLARK subextensions L of K=F and H = H(K=F ) to be the lattice of all subgroups H of G = Aut(K=F ). Then we have Φ: L!H;L 7! Aut(K=L) and Ψ: H!F;H 7! KH : For L 2 L, we write c(L) := Ψ(Φ(L)) = KAut(K=L): One immediately verifies: L ⊂ L0 =) c(L) ⊂ c(L0);L ⊂ c(L); c(c(L)) = c(L); these properties assert that L 7! c(L) is a closure operator on the lattice L in the sense of order theory. -
Some Order Dualities in Logic, Games and Choices Bernard Monjardet
Some order dualities in logic, games and choices Bernard Monjardet To cite this version: Bernard Monjardet. Some order dualities in logic, games and choices. International Game Theory Review, World Scientific Publishing, 2007, 9 (1), pp.1-12. 10.1142/S0219198907001242. halshs- 00202326 HAL Id: halshs-00202326 https://halshs.archives-ouvertes.fr/halshs-00202326 Submitted on 9 Jan 2008 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1 SOME ORDER DUALITIES IN LOGIC, GAMES AND CHOICES B. MONJARDET CERMSEM, Université Paris I, Maison des Sciences Économiques, 106-112 bd de l’Hôpital 75647 Paris Cedex 13, France and CAMS, EHESS. [email protected] 20 February 2004 Abstract We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally we present two "concrete" dualities occuring in social choice and in choice functions theories. Keywords: antiexchange closure operator, closure system, Galois connection, implicational system, Galois lattice, path-independent choice function, preference aggregation rule, simple game. -
The Poset of Closure Systems on an Infinite Poset: Detachability and Semimodularity Christian Ronse
The poset of closure systems on an infinite poset: Detachability and semimodularity Christian Ronse To cite this version: Christian Ronse. The poset of closure systems on an infinite poset: Detachability and semimodularity. Portugaliae Mathematica, European Mathematical Society Publishing House, 2010, 67 (4), pp.437-452. 10.4171/PM/1872. hal-02882874 HAL Id: hal-02882874 https://hal.archives-ouvertes.fr/hal-02882874 Submitted on 31 Aug 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Portugal. Math. (N.S.) Portugaliae Mathematica Vol. xx, Fasc. , 200x, xxx–xxx c European Mathematical Society The poset of closure systems on an infinite poset: detachability and semimodularity Christian Ronse Abstract. Closure operators on a poset can be characterized by the corresponding clo- sure systems. It is known that in a directed complete partial order (DCPO), in particular in any finite poset, the collection of all closure systems is closed under arbitrary inter- section and has a “detachability” or “anti-matroid” property, which implies that the collection of all closure systems is a lower semimodular complete lattice (and dually, the closure operators form an upper semimodular complete lattice). After reviewing the history of the problem, we generalize these results to the case of an infinite poset where closure systems do not necessarily constitute a complete lattice; thus the notions of lower semimodularity and detachability are extended accordingly. -
Arxiv:1301.2793V2 [Math.LO] 18 Jul 2014 Uaeacnetof Concept a Mulate Fpwrbet Uetepwre Xo) N/Rmk S Ff of Use Make And/Or Axiom), Presupp Principles
ON TARSKI’S FIXED POINT THEOREM GIOVANNI CURI To Orsola Abstract. A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive version of Tarski’s fixed point theorem is obtained. Introduction The fixed point theorem referred to in this paper is the one asserting that every monotone mapping on a complete lattice L has a least fixed point. The proof, due to A. Tarski, of this result, is a simple and most significant example of a proof that can be carried out on the base of intuitionistic logic (e.g. in the intuitionistic set theory IZF, or in topos logic), and that yet is widely regarded as essentially non-constructive. The reason for this fact is that Tarski’s construction of the fixed point is highly impredicative: if f : L → L is a monotone map, its least fixed point is given by V P , with P ≡ {x ∈ L | f(x) ≤ x}. Impredicativity here is found in the fact that the fixed point, call it p, appears in its own construction (p belongs to P ), and, indirectly, in the fact that the complete lattice L (and, as a consequence, the collection P over which the infimum is taken) is assumed to form a set, an assumption that seems only reasonable in an intuitionistic setting in the presence of strong impredicative principles (cf. Section 2 below). In concrete applications (e.g. in computer science and numerical analysis) the monotone operator f is often also continuous, in particular it preserves suprema of non-empty chains; in this situation, the least fixed point can be constructed taking the supremum of the ascending chain ⊥,f(⊥),f(f(⊥)), ..., given by the set of finite iterations of f on the least element ⊥. -
CLOSURE OPERATORS I Dikran DIKRANJAN Eraldo GIULI
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Topology and its Applications 27 (1987) 129-143 129 North-Holland CLOSURE OPERATORS I Dikran DIKRANJAN Institute of Mathematics, Bulgarian Academy of Sciences, Sojia, Bulgaria Eraldo GIULI* Department of Pure and Applied Mathematics, University of L’Aquila, 67100-L’Aquila, Italy Received 8 June 1986 Revised 24 September 1986 Closure operators in an (E, M)-category X are introduced as concrete endofunctors of the comma category whose objects are the elements of M. Various kinds of closure operators are studied. There is a Galois equivalence between the conglomerate of idempotent and weakly hereditary closure operators of X and the conglomerate of subclasses of M which are part of a factorization system. There is a one-to-one correspondence between the class of regular closure operators and the class of strongly epireflective subcategories of X. Every closure operator admits an idempotent hull and a weakly hereditary core. Various examples of additive closure operators in Top are given. For abelian categories standard closure operators are considered. It is shown that there is a one-to-one correspondence between the class of standard closure operators and the class of preradicals. Idempotenf weakly hereditary, standard closure operators correspond to idempotent radicals ( = torsion theories). AMS (MOS) Subj. Class.: 18A32, 18B30, 18E40, 54A05, 54B30, 18A40, A-regular morphism weakly hereditary core sequential closure (pre)-radical Introduction Closure operators have always been one of the main concepts in topology. For example, Herrlich [21] characterized coreflections in the category Top of topological spaces by means of Kuratowski closure operators finer than the ordinary closure. -
CLOSURE OPERATORS on ALGEBRAS 3 Extended Power Algebra (P>0A, Ω, ∪) Is a Semilattice Ordered ✵-Algebra
CLOSURE OPERATORS ON ALGEBRAS A. PILITOWSKA1 AND A. ZAMOJSKA-DZIENIO2,∗ Abstract. We study connections between closure operators on an algebra (A, Ω) and congruences on the extended power algebra defined on the same algebra. We use these connections to give an alternative description of the lattice of all subvarieties of semilattice ordered algebras. 1. Introduction In this paper we study closure operators on algebras. M. Novotn´y [12] and J. Fuchs [4] introduced the notion of admissible closure operators for monoids and applied them to study some Galois connections in language theory. In [10] M. Kuˇril and L. Pol´ak used such operators to describe the varieties of semilattice ordered semigroups. In this paper we use a similar approach but apply it to arbitrary alge- bras. In particular, we use concepts from the theory of (extended) power algebras (see e.g. C. Brink [2]). This allows us to generalize and simplify methods presented in [10]. In a natural way one can ”lift” any operation defined on a set A to an operation on the set of all non-empty subsets of A and obtain from any algebra (A, Ω) its power algebra of subsets. Power algebras of non-empty subsets with the additional operation of set-theoretical union are known as extended power algebras. Extended power algebras play a crucial rˆole in the theory of semilattice ordered algebras. The main aim of this paper is to investigate how congruences on the extended power algebra on (A, Ω) and closure operators defined on (A, Ω) are related. The correspondence obtained allows us to give an alternative (partially simpler) descrip- tion of the subvariety lattice of semilattice ordered algebras, comparing to [16]. -
Completion and Closure Cahiers De Topologie Et Géométrie Différentielle Catégoriques, Tome 41, No 2 (2000), P
CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES DAVID HOLGATE Completion and closure Cahiers de topologie et géométrie différentielle catégoriques, tome 41, no 2 (2000), p. 101-119 <http://www.numdam.org/item?id=CTGDC_2000__41_2_101_0> © Andrée C. Ehresmann et les auteurs, 2000, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ CAHIERS DE TOPOLOGIE ET Volume XLI-2 (2000) GEOMETRIE DIFFERENTIELLE CATEGORIQUES COMPLETION AND CLOSURE by David HOLGATE RESUME. La fermeture (ou, de fagon synonyme la densite) a tou- jours jou6 un role important dans la th6orie des compl6tions. S’ap- puyant sur des id6es de Birkhoff, une fermeture est extraite de ma- niere canonique d’un processus de completion r6flexive dans une categorie. Cette fermeture caract6rise la compl6tude et la compl6- tion elle-meme. La fermeture n’a pas seulement de bonnes propri6t6s internes, mais c’est la plus grande parmi les fermetures qui d6crivent la completion. Le theoreme principal montre que, equivalent aux descriptions fermeture/densite naturelle d’une completion, est le simple fait mar- quant que les r6flecteurs de completion sont exactement ceux qui pr6servent les plongements. De tels r6flecteurs peuvent 6tre deduits de la fermeture elle-m6me. Le role de la pr6servation de la ferme- ture et du plongement jette alors une nouvelle lumi6re sur les exem- ples de completion. -
1 Introduction
Partial variables and specificity Gerhard Jager¨ University of Bielefeld Abstract In this paper I propose a novel analysis of the semantics of specific indefinites. Following standard DRT, I assume that indefinites introduce a free variable into the logical repre- sentation, but I assume the the descriptive content of an indefinite DP is interpreted as a precondition for the corresponding variable to denote. Formally this is implemented as an extension of classical predicate logic with partial variables—variables that come with a restriction. This leads to a reconception of restricted quantification: the restriction is tied to the variable, not to the quantifier. After an overview over the major existing theories of the scope of indefinites, the cen- tral part of the paper is devoted to develop a model-theoretic semantics for this extension of predicate logic. Finally the paper argues that the notion of partial variables lends itself to the analysis of other linguistic phenomena as well. Especially presuppositions can be analyzed as restrictions on variables in a natural way. 1 Introduction This article deals with the peculiar scope taking properties of indefinite DPs, which differ mas- sively from other scope bearing elements. The theory that I am going to propose can be seen as a variant of the DRT approach in the version of Heim (1982), according to which the se- mantic contribution of an indefinite is basically a free variable, while its scope is determined by a non-lexical operation of existential closure. The crucial innovation lies in the treatment of the descriptive material of indefinites. While DRT analyzes it as part of the truth conditions, I will argue that it is to be considered as a precondition for the accompanying variable to denote.