Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...) the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally |$\vee $| complemented Heyting algebra (c|$\vee $|cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension |${\textrm {ILM}}$|-|${\vee }$| for c|$\vee (...) $|cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$| are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and |${\textrm {ILM}}$|-|${\vee }$| are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics |$K_{im}$| and |$K_{im-{\vee }}$| are discussed, where the language does not include implication. The |$K_{im}$|-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the |$K_{im}$|-algebras and |$K_{im-{\vee }}$|-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for |$K_{im}$| and |$K_{im-{\vee }}$| is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and |${\textrm {ILM}}$|-|${\vee }$|⁠. (shrink)

A complement clause is used instead of a noun phrase; for example one can say either I heard [the result] or I heard [that England beat France]. Languages differ in the grammatical properties of complement clauses, and the types of verbs which take them. Some languages lack a complement clause construction but instead employ other construction types to achieve similar ends; these are called complementation strategies. The book explores the variety of types of complementation found across the languages (...) of the world, their grammatical properties and meanings. Detailed studies of particular languages, including Akkadian, Israeli, Jarawara, and Pennsylvania German, are framed by R. M. W. Dixon's introduction, which sets out the range of issues, and his conclusion, which draws together the evidence and the arguments. This book will interest scholars of typology, language universals, syntax, information structure, and language contact in departments of linguistics and anthropology, as well as advanced and graduate students taking courses in these subjects. (shrink)

A key factor that affects whether and at what age children can demonstrate an understanding of false belief and complement‐clause constructions is the type of task used (whether it is implicit/indirect or explicit/direct). In the current study, we investigate, in an implicit/indirect way, whether children understand that a story character's belief can be true or false, and whether this understanding affects children's choice of linguistic structure to describe the character's belief or to explain the character's belief‐based action. We also measured (...) children's understanding of false belief in explicit false‐belief tasks. English‐ and German‐speaking young 4‐ and 5‐year‐olds as well as English‐ and German‐speaking adult controls heard complement‐clause constructions in a story context where the belief mentioned in the complement clause (e.g., “He thinks thatshe's not feeling well”) turned out to be false, true, or was left open. After hearing the test question (“Why does he not play with her?”), all age groups were most likely to repeat the whole complement‐clause construction when the belief turned out to be false. That is, they tended to explicitly refer to the character's perspective and say “He thinks…” When the belief turned out to be true, participants often reverted to a simple clause (“She's not feeling well”). Furthermore, children with better short‐term memory were more likely to repeat the whole complement‐clause construction. However, children's performance in explicit false‐belief tasks showed no relation to their performance in our novel, more implicit/indirect, task. Whether or not the complement clause was introduced by athatcomplementizer only had a small effect on the German adults’ responses, where leaving out the complementizer also changes the word order of the complement clause. Overall, our results suggest that task characteristics and individual differences in short‐term memory affect children's ability to demonstrate false‐belief understanding and to express this understanding linguistically. (shrink)

It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.

Say that a nonzero c. e. degree b is a quasi-complement of a c. e. degree a if a ∩ b = 0 and a ∪ b is high. It is well-known that each cappable degree has a high quasi-complement. However, by the existence of the almost deep degrees, there are nonzero cappable degrees having no low quasi-complements. In this paper, we prove that any nonzero cappable degree has a low2 quasi-complement.

Posner [6] has shown, by a nonuniform proof, that every ▵ 0 2 degree has a complement below 0'. We show that a 1-generic complement for each ▵ 0 2 set of degree between 0 and 0' can be found uniformly. Moreover, the methods just as easily can be used to produce a complement whose jump has the degree of any real recursively enumerable in and above $\varnothing'$ . In the second half of the paper, we show that the (...) class='Hi'>complementation of the degrees below 0' does not extend to all recursively enumerable degrees. Namely, there is a pair of recursively enumerable degrees a above b such that no degree strictly below a joins b above a. (This result is independently due to S. B. Cooper.) We end with some open problems. (shrink)

Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.

In this paper, I address the problem wherein the same English word permits one of its complement positions to be satisfied by phrases of different categories. A well-known example of such an English word is the copula to be, whose complements include adjective phrases, noun phrases, prepositional phrases and adverbial phrases. I provide a way to treat such words, in particular verbs, as single lexical items through a conservative extension of the usual treatment of word classification as a pair comprising (...) a part of speech category and a complement list. I then show how a further conservative extension of complement lists permits a satisfactory formalization of doubly complemented English verbs which are synonymous under a permutation of their complements. These verbs include, but are not limited to, so-called double object constructions. (shrink)

A finer-grained delineation of a given explanandum reveals a nexus of closely related causal and non- causal explanations, complementing one another in ways that yield further explanatory traction on the phenomenon in question. By taking a narrower construal of what counts as a causal explanation, a new class of distinctively mathematical explanations pops into focus; Lange’s characterization of distinctively mathematical explanations can be extended to cover these. This new class of distinctively mathematical explanations is illustrated with the Lotka-Volterra equations. There (...) are at least two distinct ways those equations might hold of a system, one of which yields straightforwardly causal explanations, but the other of which yields explanations that are distinctively mathematical in terms of nomological strength. In the first, one first picks out a system or class of systems, finds that the equations hold in a causal -explanatory way; in the second, one starts with the equations and explanations that must apply to any system of which the equations hold, and only then turns to the world to see of what, if any, systems it does in fact hold. Using this new way in which a model might hold of a system, I highlight four specific avenues by which causal and non- causal explanations can complement one another. (shrink)

We explore an analogue of major subset for Π0 1 classes, which leads to the definition and characterization of almost complemented Π0 1 classes.

We prove that for any computably enumerable degree c, if it is cappable in the computably enumerable degrees, then there is a d.c.e. degree d such that c d = 0′ and c ∩ d = 0. Consequently, a computably enumerable degree is cappable if and only if it can be complemented by a nonzero d.c.e. degree. This gives a new characterization of the cappable degrees.

Let us say that any (Turing) degree d > 0 satisfies the minimal complementation property (MCP) if for every degree 0 < a < d there exists a minimal degree b < d such that a ∨ b = d (and therefore a ∧ b = 0). We show that every degree d ≥ 0′ satisfies MCP. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and (...) the completeness of metric spaces. (shrink)

It is shown that for every (Turing) degree 0 < a < 0´ there is a minimal degree m < 0´ such that a ∨ m = 0´ (and therefore a ∧ m = 0).

This paper presents an analysis of wh-complements in Montague Grammar. We will be concerned primarily with semantics, though some remarks on syntax are made in Section 4. Questions and wh-comple ments in Montague Grammar have been studied in Hamblin (1976), Bennett (1979), Karttunen (1977) and Hauser (1978) among others. These proposals will not be discussed explicitly, but some differences with Karttunen's analysis will be pointed out along the way.

"The idea for this book arose in connection with the Workshop on Semantic functions of complementizers in European languages, which we organized in October 28-29, 2011, at the University of Copenhagen, Denmark. Around two thirds of the book chapters are elaborations on contributions to this workshop, the remaining one third arose independently of the workshop.".

Cet article critique le classement moderne des compléments que la grammaire traditionnelle associait au verbe. A la base de ce classement figurent un test de déplacement et une structure particulière associée à la phrase. On montre que le test ne caractérise pas une classe claire de compléments et on met en question la pertinence de la structure, notamment grâce à un contre-exemple évident. Enfin, on promeut une structure alternative plus simple, basée sur des dépendances et rendue possible par la prise (...) en compte du sens dans le processus de construction. (shrink)

Cet article met en débat deux méthodes d’analyse des compléments du verbe en grammaire scolaire : l’analyse traditionnelle en compléments d’objet et compléments circonstanciels et l’analyse en compléments « du verbe » et « de phrase » de ce qu’on appelle la « nouvelle grammaire ». Il porte un regard critique sur le point de vue de la nouvelle grammaire et défend celui de la grammaire traditionnelle en montrant notamment que, pour peu qu’on n’en déforme pas la définition initiale, celle-ci (...) met en œuvre une technique d’analyse conforme aux méthodes de la linguistique moderne. (shrink)

I show that words with indefinite implicit complements occasion a dilemma for their model theory. There has been only two previous attempts to address this problem, one by Fodor and Fodor (1980) and one by Dowty (1981). Each requires that any word tolerating an implicit complement be treated as ambiguous between two different lexical entries and that a meaning postulate or lexical rule be given to constrain suitably the meanings of the various entries for the word. I show that the (...) positing of such an ambiguity runs counter to the facts and propose an alternative solution which does not appeal to ambiguity, meaning postulates or lexical rules. Indeed, I show that the dilemma posed by indefinite implicit complements is posed by all implicit complements and that a general solution to the problem of implicit complements follows from an independently motivated, single treatment of five other problems, that of subcategorization, that of phrasal projections of words, that of defining a model theoretic structure for phrase structure grammars, that of complement polyvalence and that of complement polyadicity. (shrink)

We examine the multiplicity of complementation amongst subspaces of V ∞ . A subspace V is a complement of a subspace W if V ∩ W = {0} and (V ∪ W) * = V ∞ . A subspace is called fully co-r.e. if it is generated by a co-r.e. subset of a recursive basis of V ∞ . We observe that every r.e. subspace has a fully co-r.e. complement. Theorem. If S is any fully co-r.e. subspace then S (...) has a decidable complement. We give an analysis of other types of complements S may have. For example, if S is fully co-r.e. and nonrecursive, then S has a (nonrecursive) r.e. nowhere simple complement. We impose the condition of immunity upon our subspaces. Theorem. Suppose V is fully co-r.e. Then V is immune iff there exist M 1 , M 2 ∈ L(V ∞ ), with M 1 supermaximal and M 2 k-thin, such that $M_1 \oplus V = M_2 \oplus V = V_\infty$ . Corollary. Suppose V is any r.e. subspace with a fully co-r.e. immune complement W (e.g., V is maximal or V is h-immune). Then there exist an r.e. supermaximal subspace M and a decidable subspace D such that $V \oplus W = M \oplus W = D \oplus W = V_\infty$ . We indicate how one may obtain many further results of this type. Finally we examine a generalization of the concepts of immunity and soundness. A subspace V of V ∞ is nowhere sound if (i) for all Q ∈ L(V ∞ ) if $Q \supset V$ then Q = V ∞ , (ii) V is immune and (iii) every complement of V is immune. We analyse the existence (and ramifications of the existence) of nowhere sound spaces. (shrink)

Les livres deutérocanoniques constituent un «intertestament» entre les écrits de la Bible rabbinique et ceux du Nouveau Testament chrétien. Ils sont sur une frontière, un fossé ou un pont entre le christianisme naissant et le judaïsme renaissant après 135. Ils font aussi le lien entre la Gola araméenne et la Diaspora hellénistique. Les écrits intertestamentaires – et spécifiquement les deutérocanoniques qui sont comme un «intertestament» canonique – sont vraiment nécessaires à la compréhension de la Bible.

A l'occasion du soixantieme anniversaire d'Alain de Libera, une trentaine de collegues de France et de l'etranger ont souhaite, par une serie d'etudes d'histoire de la philosophie et de metaphysique, saluer son oeuvre scientifique et lui offrir un temoignage d'amitie. L'histoire de la metaphysique etant l'un des points cardinaux du travail philosophique d'Alain de Libera, a qui l'on doit notamment de magistraux ouvrages sur les universaux, il a semble judicieux d'etudier ces entites mineures mais neanmoins indispensables qui viennent completer la (...) substance pour constituer l'individu: les proprietes accidentelles. La question des accidents est ici etudiee sur la longue duree - d'Aristote a la metaphysique analytique contemporaine, avec une attention particuliere portee aux discussions medievales - et sous ses differents aspects: ontologique, semantique, epistemologique et psychologique. Sont ainsi abordes des problemes philosophiques aussi fondamentaux que ceux induits par les categories aristoteliciennes de qualite et de relation, les tropes, la causalite, l'individuation. (shrink)

This article presents a cross-cultural exploration of the interaction between religion and family in the lives of women. It focuses on elderly Middle Eastern Jewish women who, during the course of their life spans, moved from a conflicting to a complementary experience of family and religion. The author argues that opposition between religion and family seldom arises for women who control their own time or resources, or who control a domestic sphere they themselves see as sacred. Women who wish to (...) conduct their religious lives in the public sphere, especially in the context of an extrafamilial hierarchy or as religious professionals, are likely to come into conflict with their families over issues of competition for their time or allegiance. Official religious doctrines are not likely to determine how particular women experience family and religion; even women who maneuver within the same theological framework may experience the relationship between family and religion in very different ways. (shrink)