Linear Processing with Pregroups

Pregroup grammars have a cubic recognition algorithm. Here, we define a correct and complete recognition and parsing algorithm and give sufficient conditions for the algorithm to run in linear time. These conditions are satisfied by a large class of pregroup grammars, including grammars that handle coordinate structures and distant constituents.     

On The Computational Consequences of Independence in Propositional Logic

Sandu and Pietarinen [Partiality and Games: Propositional Logic. Logic J. IGPL 9 (2001) 101] study independence friendly propositional logics. That is, traditional propositional logic extended by means of syntax that allow connectives to be independent of each other, although the one may be subordinate to the other. Sandu and Pietarinen observe that the IF propositional logics have exotic properties, like functional completeness for three-valued functions. In this paper we focus on one of their IF propositional logics and study its properties, by means of notions from computational complexity. This approach enables us to compare propositional logic before and after the IF make-over. We observe that all but one of the best-known decision problems experience a complexity jump, provided that the complexity classes at hand are not equal. Our results concern every discipline that incorporates some notion of independence such as computer science, natural language semantics, and game theory. A corollary of one of our theorems illustrates this claim with respect to the latter discipline.     

Parsing to Learn

Learning a language by parameter setting is almost certainly less onerous than composing a grammar from scratch. But recent computational modeling of how parameters are set has shown that it is not at all the simple mechanical process sometimes imagined. Sentences must be parsed to discover the properties that select between parameter values. But the sentences that drive learning cannot be parsed with the learner's current grammar. And there is not much point in parsing them with just one new grammar. They must apparently be parsed with all possible grammars, in order to find out which one is most successful at licensing the language. The research task is to reconcile this with the fact that the human sentence parsing mechanism, even in adults, has only very limited parallel parsing capacity. I have proposed that all possible grammars can be folded into one, if parameter values are fragments of sentential tree structures that the parser can make use of where necessary to assign a structure to an input sentence. However, the problem of capacity limitations remains. The combined grammar will afford multiple analyses for some sentences, too many to be computed on-line. I propose that the parser computes only one analysis per sentence but can detect ambiguity, and that the learner makes use of unambiguous input only. This provides secure information but relatively little of it, particularly at early stages of learning where few grammars have been excluded and ambiguity is rife. I consider three solutions: improving the parser's ability to extract unambiguous information from partially ambiguous sentences, assuming default parameter values to temporarily eliminate ambiguity, reconfiguring the parameters so that some are subordinate to others and do not present themselves to the learner until the others have been set. A more radical alternative is to give up the quest for error-free learning and permit parameters to be set without regard for whether the parser may have overlooked an alternative analysis of the sentence. If it can be assumed that the human parser keeps a running tally of the parameter values it has accessed, then the learner would do nothing other than parse sentences for comprehension, as adults do. The most useful parameter values would become more and more easily accessed; the noncontributors would drop out of the running. There would be no learning mechanism at all, over and above the parser. But how accurate this system would be remains to be established.     

Persistence and Atomic Generation for Varieties of Boolean Algebras with Operators

A variety V of Boolean algebras with operators is singleton-persistent if it contains a complex algebra whenever it contains the subalgebra generated by the singletons. V is atom-canonical if it contains the complex algebra of the atom structure of any of the atomic members of V.This paper explores relationships between these "persistence" properties and questions of whether V is generated by its complex algebras or its atomic members, or is closed under canonical embedding algebras or completions. It also develops a general theory of when operations involving complex algebras lead to the construction of elementary classes of relational structures.     

Probability: A new logico-semantical approach

This approach does not define a probability measure by syntactical structures. It reveals a link between modal logic and mathematical probability theory. This is shown (1) by adding an operator (and two further connectives and constants) to a system of lower predicate calculus and (2) regarding the models of that extended system. These models are models of the modal systemS ₅ (without the Barcan formula), where a usual probability measure is defined on their set of possible worlds. Mathematical probability models can be seen as models ofS ₅.     

The impact of connectives on the memory for expository texts

Three experiments investigated the influence of connectives on memory for expository text. Subjects in Experiments 1 and 2 read and later recalled passages with either no connectives, temporal connectives (before/ and then), causal connectives (which caused/which enabled), or intentional connectives (in order that/so that). There was connective interference rather than connective facilitation in the studies reported here: the recall for passages without connectives was higher than the recall for passages with connectives. The results partially supported a semantic complexity hypothesis, which predicted that recall should increase with the semantic complexity of the connective (i.e. temporal < causal < intentional). In a third experiment, the semantic appropriateness of the connective was manipulated. Recall for passages without connectives was better than recall for passages with either appropriate or inappropriate connectives. In a fourth experiment, the subjects filled in missing connectives in natural expository texts. Subjects were able to select the connective category which was originally used by the author. The influence of connectives on text was discussed from the perspective of resource limitations, elaborations, and the semantic compatibility of the connectives to the text.     

Varieties of crossing dependencies: structure dependence and mild context sensitivity

Four different kinds of grammars that can define crossing dependencies in human language are compared here: (i) context sensitive rewrite grammars with rules that depend on context, (ii) matching grammars with constraints that filter the generative structure of the language, (iii) copying grammars which can copy structures of unbounded size, and (iv) generating grammars in which crossing dependencies are generated from a finite lexical basis. Context sensitive rewrite grammars are syntactically, semantically and computationally unattractive. Generating grammars have a collection of nice properties that ensure they define only “mildly context sensitive” languages, and Joshi has proposed that human languages have those properties too. But for certain distinctive kinds of crossing dependencies in human languages, copying or matching analyses predominate. Some results relevant to the viability of mildly context sensitive analyses and some open questions are reviewed.     

Group commitment as a moderator of attributional and behavioural responses to power use

This study used 50 Natural Science and English Literature students who held differential behavioural expectations of ingroup and outgroup members to investigate evaluative, attributional and behavioural responses to power use in an experimental research paradigm. It was hypothesized that subordinates interpret frequent power use by a superior differently depending on whether it is consistent or inconsistent with previous expectations. Frequent power use results in decreased satisfaction and negative evaluations of the superior. Attributional ratings indicated that when an outgroup member engaged in frequent power use, this negatively evaluated behaviour was attributed to the superior's group membership, and resulted in decreased cooperation on the part of the subordinate. To the extent that frequent power use of an ingroup member was attributed to external circumstances, subordinates maintained a sense of commitment to the ingroup superior, which resulted in displays of cooperative behaviour. © 1998 John Wiley & Sons, Ltd.     

Accommodating variability in voice and foreign accent: flexibility of early word representations

In six experiments with English‐learning infants, we examined the effects of variability in voice and foreign accent on word recognition. We found that 9‐month‐old infants successfully recognized words when two native English talkers with dissimilar voices produced test and familiarization items ( Experiment 1 ). When the domain of variability was shifted to include variability in voice as well as in accent, 13‐, but not 9‐month‐olds, recognized a word produced across talkers when only one had a Spanish accent ( Experiments 2 and 3 ). Nine‐month‐olds accommodated some variability in accent by recognizing words when the same Spanish‐accented talker produced familiarization and test items ( Experiment 4 ). However, 13‐, but not 9‐month‐olds, could do so when test and familiarization items were produced by two distinct Spanish‐accented talkers ( Experiments 5 and 6 ). These findings suggest that, although monolingual 9‐month‐olds have abstract phonological representations, these representations may not be flexible enough to accommodate the modifications found in foreign‐accented speech.     

Insertion of connectives by 9- to 11-year-old children in an argumentative text

The objective of the present study was to show that the use of adversative and conclusive connectives to mark off the prototypical schema of argumentative text begins to set in at approximately the age of 10 or 11. Based on Adam's (1992) proposals, we constituted an argumentative text with two blocks of arguments separated by an adversative instruction (the connective but or an equivalent) and followed by a conclusion introduced by a conclusive instruction (the connective thus or an equivalent). Four revising tasks (insertion or substitution with or without five connectives) have been used to asses children's knowledge of the argumentative schema and the use of connectives that punctuate them. The study of good and erroneous locations (concerning the placement of but and thus) showed that there was some regularity in the choices made by the children. The main result of this study shows that argumentative connectives are used differently by children aged 9 and children aged 10 or 11. The argumentative schema is used more consciously by 11-year-olds to guide revising tasks than by 10-year-olds.     

Children's understanding of sentences with contingent relations: Why are temporal and conditional connectives so difficult?

Children aged 5-, 7-, and 9 were tested on two different tasks to assess their understanding of sentences containing the connectives “when,” “as soon as,” “before,” “after,” “if,” “if-not,” “unless,” and “unless-not.” The results revealed significant improvement between the ages of 5 and 7. This improvement was attributed, in part, to an increased ability to retain information expressed in subordinate clauses. At all age levels, however, the connectives “unless” and “unless-not” were consistently misinterpreted; “unless” was treated as its polar opposite “if,” and “unless-not” was treated as its polar opposite “if-not.”     

Identical Twins,Deduction Theorems,and Pattern Functions: Exploring the Implicative BCSK Fragment of S5

We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we show that for the pure logic of one of these implicational connectives two – in general distinct – consequence relations (global and local) definable in the Kripke semantics for modal logic turn out to coincide, though this is not so for the pure logic of the other connective, and that there is an intimate relation between formulas constructed by means of the former connective and the local consequence relation. (Corollary 5.8. This, as we show in an Appendix, is connected to the fact that the ‘propositional operations’ associated with both of our implicational connectives are close to being what R. Quackenbush has called pattern functions.) Between these discussions Section 4 examines some of the replacement-of-equivalents properties of the two connectives, relative to these consequence relations, and Section 6 closes with some observations about the metaphor of identical twins as applied to such pairs of connectives.     

Sentential Connectives and Translation

In the first exposition of the doctrine of indeterminacy of translation, Quine asserted that the individuation and translation of truth-functional sentential connectives like ‘and’, ‘or’, ‘not’ are not indeterminate. He changed his mind later on, conjecturing that some sentential connectives might be interpreted in different non-equivalent ways. This issue has not been debated much by Quine, or in the subsequent literature, it is, as it were, an unsolved problem, not well understood. For the sake of the argument, I will adopt Quine’s background assumption that all the semantic features of a language can be reduced to the speakers’ dispositions toward assent and dissent, as far as only the truth-conditional core of the meaning of sentences is concerned. I will put forward an argument to the effect that the speech dispositions of most, if not all, English (French, Italian, etc.) speakers constrain a unique translation of their connectives. This argument crucially relies on an empirical conjecture concerning the behaviour of these operators.     

Conducting a Multi Family Member Interview Study

Family researchers have long recognized the utility of incorporating interview data from multiple family members. Yet, relatively few contemporary scholars utilize such an approach due to methodological underdevelopment. This article contributes to family scholarship by providing a roadmap for developing and executing in‐depth interview studies that include more than one family member. Specifically, it outlines the epistemological frames that most commonly underlie this approach, illustrates thematic research questions that it best addresses, and critically reviews the best methodological practices of conducting research with this approach. The three most common approaches are addressed in depth: separate interviews with each family member, dyadic or group interviews with multiple family members, and a combined approach that uses separate and dyadic or group interviews. This article speaks to family scholars who are at the beginning stages of their research project but are unsure of the best qualitative approach to answer a given research question.     

Extending Free Pregroups with Lower Bounds

In this paper, we propose an extension of free pregroups with lower bounds on sets of pregroup elements. Pregroup grammars based on such pregroups provide a kind of an algebraic counterpart to universal quantification over type-variables. In particular, we show how our pregroup extensions can be used for pregroup grammars expressing natural-language coordination and extraction.     

Line-based affine reasoning in Euclidean plane

We consider the binary relations of parallelism and convergence between lines in a 2-dimensional affine space. Associating with parallelism and convergence the binary predicates P and C and the modal connectives [P] and [C], we consider a first-order theory based on these predicates and a modal logic based on these modal connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.     

The Supposed Effect of Interactive Imagery in Paired Associate Learning

Previous experiments designed to investigate the effects of interactive imagery in paired associate learning have included the confounded variable of intralist similarity: Images of objects interacting have corresponded to pairs with different connectives, and images of independent objects have corresponded to pairs with the same connective (the conjunction 'and'). For the 'different' group of our first experiment, the members of the different pairs were linked by different connectives, most of which denoted an action. For the 'same' group, the members were linked by the same connective, usually one denoting an action. For the 'and' group, the members were linked by the connective 'and'. Cued recall by the 'different' group was superior to that of the other two groups. Recall by the 'same' and 'and' groups did not differ. Within the 'different' group, recall of 'and' pairs did not differ from the recall of 'action' pairs with which they had been mixed. In a second experiment, subjects were required to match the members of a pair. Analogous results were obtained. Overall, the findings imply that recall effects that have previously been interpreted as being a result of interactive imagery may be the result merely of variations in intralist similarity.     

The subordination effect: Evidence from self-paced reading and recall

Engelkamp and Rummer (2002) demonstrated that auditorily presented subordinate causal sentences are better retained than coordinate sentences. This subordination effect was explained by suggesting that subordinate sentences are merged more easily in memory than coordinate sentences. The present paper enlarges Engelkamp and Rummer's findings with respect to three aspects. First, it demonstrates that the subordination effect can only be found if a verbatim but not a content related recall score is used. Second, using self-paced reading, it demonstrates a processing advantage for subordinate sentences. This reading time advantage was only observed if the subordinate clause preceded the matrix clause. Third, it excludes an alternative explanation of the subordination effect which attributes memory differences to the fact that the critical causal conjunction word was presented earlier in subordinate than in coordinate sentences. In sum, our findings suggest a direct contribution of syntactic information to sentence regeneration.     

A direct proof of the equivalence of free categorial grammars and simple phrase structure grammars

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs.Allatum est die S Marlii 1976     

Morphological Development in the Speech of a Persian–English Bilingual Child

The present study aims at testing the two dominant hypotheses regarding the development of inflections and other functional categories namely the Structure-Building Model and the Continuity Hypothesis within the generative theory. According to the first view, functional categories are entirely absent in children’s early grammars, which contain only projections of lexical categories, most importantly ‘nouns’ and ‘verbs.’ This hypothesis holds that utterances produced by children are actually small clauses or verb phrases, and functional categories such as copula, determiners, and genitive are not acquired during the single-word or early multiword stages, but are implemented in the course of further acquisition, at around age 2 or later. The proponents of the second, i.e., the ‘Continuity Hypothesis,’ on the other hand, argue that functional categories are in fact present in children’s early syntax. These two hypotheses will be tested here against empirical data in English and Persian. Thus, longitudinal data will be provided on the acquisition of a few morphemes in the two languages acquired by the subject of the present study (i.e., English and Persian) including determiners, plural marker, genitive, and copula. The significance of the present study lies in the fact that it provides data on two typologically different languages in bilingual first language acquisition and thereby making a contribution to the field.