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.     

Type Logics and Pregroups

We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Parsing Pregroup Grammars and Lambek Calculus Using Partial Composition

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.     

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.     

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.     

Some Observations on Group Therapy with the Blind

This study integrates the theoretical assumptions underlying member preparation for group into a series of pregroup interview guidelines, which are then field tested for reliability and validity using a Solomon Four-Group design. Findings indicate a significant relationship exists between those individuals having the pregroup interview and a realistic perception of group membership and understanding of group purpose. The third dimension, which tested congruence between member goals and group purpose due to having the pregroup interview, was not significant. Implications of the study and suggestions for further research are discussed.     

A Common Abstraction of MV-Algebras and Abelian l-groups

We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.     

On the Logic of β-pregroups

In this paper we concentrate mainly on the notion of β-pregroups, which are pregroups (first introduced by Lambek [18] in 1999) enriched with modality operators. β-pregroups were first proposed by Fadda [11] in 2001. The motivation to introduce them was to limit (locally) the associativity in the calculus considered. In this paper we present this new calculus in the form of a rewriting system, prove the very important feature of this system - that in a given derivation the non-expanding rules must always proceed non-contracting ones in order the derivation to be minimal (normalization theorem). We also propose a sequent system for this calculus and prove the cut elimination theorem for it. As an illustration we show how to use β-pregroups for linguistical applications. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Limitations on Embedding in Coordinate Structures

Coordinate structures have traditionally been analyzed as having no internal structure other than the sequencing of their members. In particular, the possibility that the members of coordinate structures may themselves be coordinate structures has not been widely recognized. Those who have recognized the possibility of such embedding of coordinate structures have assumed that there are no limits on the depth of such embedding, just as there are no limits on the depth of embedding in subordinate structures. However, coordinate-structure embedding in English occurs only in order to prevent coordinate structures from containing distinct connectives (e.g., and and or), distinct junctures (breaks) between members, and sequences of members in which the first is introduced by a connective while the second is not. In order to prevent these conditions from arising, the depth of coordinate-structure embedding does not have to exceed 2. This limitation on coordinate-structure embedding must be dealt with by the grammars of natural languages; it is not simply a performance limitation. Standard generative mechanisms (finite-state, phrase-structure, and transformational grammars, including recently proposed analyses of coordinate structures based on the minimalist program) do not provide an adequate account of this limitation. On the other hand, a theory of constraint satisfaction such as optimality theory, in which ranked constraints select the optimally structured outputs for given inputs made up of members, connectives, and junctures, does do so. A detailed optimality theoretic analysis of coordinate structures in English is proposed which accounts for the limitation on coordinate-structure embedding, as well as several other properties of those structures, and of their interactions with subordinate constructions.     

Applying Pregroups to Italian Statements and Questions

We know from the literature in theoretical linguistics that interrogative constructions in Italian have particular syntactic properties, due to the liberal word order and the rich inflectional system. In this paper we show that the calculus of pregroups represents a flexible and efficient computational device for the analysis and derivation of Italian sentences and questions. In this context the distinction between direct vs. indirect statements and questions is explored. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

The Pentus Theorem for Lambek Calculus with Simple Nonlogical Axioms

The Lambek calculus introduced in Lambek [6] is a strengthening of the type reduction calculus of Ajdukiewicz [1]. We study Associative Lambek Calculus L in Gentzen style axiomatization enriched with a finite set Γ of nonlogical axioms, denoted by L(Γ).It is known that finite axiomatic extensions of Associative Lambek Calculus generate all recursively enumerable languages (see Buszkowski [2]). Then we confine nonlogical axioms to sequents of the form p → q, where p and q are atomic types. For calculus L(Γ) we prove interpolation lemma (modifying the Roorda proof for L [10]) and the binary reduction lemma (using the Pentus method [9] with modification from [3]). In consequence we obtain the weak equivalence of the Context-Free Grammars and grammars based on L(Γ).     

On the Compositional Extension Problem

A semantics may be compositional and yet partial, in the sense that not all well-formed expressions are assigned meanings by it. Examples come from both natural and formal languages. When can such a semantics be extended to a total one, preserving compositionality? This sort of extension problem was formulated by Hodges, and solved there in a particular case, in which the total extension respects a precise version of the fregean dictum that the meaning of an expression is the contribution it makes to the meanings of complex phrases of which it is a part. Hodges' result presupposes the so-called Husserl property, which says roughly that synonymous expressions must have the same category. Here I solve a different version of the compositional extension problem, corresponding to another type of linguistic situation in which we only have a partial semantics, and without assuming the Husserl property. I also briefly compare Hodges' framework for grammars in terms of partial algebras with more familiar ones, going back to Montague, which use many-sorted algebras instead.

     

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.     

Processing typology and why psychologists need to know about it

This paper illustrates an interdisciplinary research program based on cross-linguistic comparison that is of relevance for psychologists working on language processing, so-called “processing typology” [Hawkins, J. A. (1994). A performance theory of order and constituency. Cambridge: Cambridge University Press; (2004). Efficiency and complexity in grammars. Oxford: Oxford University Press]. Its most original feature is the hypothesis that patterns and preferences found in performance in languages with several structures of a given type (e.g. preferences among alternative word orders) are the same patterns and preferences one finds across languages in the fixed conventions of grammars that permit less variation (i.e. in fixed word orders). Data supporting this “performance-grammar correspondence hypothesis” are summarized. One of its consequences is that principles of performance can be used to make predictions for patterns of grammatical variation, while preferences in grammars become relevant for the testing of psycholinguistic ideas. Two proposed principles of ordering in performance, in terms of “end weight” and “memory cost”, are criticized on the basis of cross-linguistic data. Both predict an asymmetry in ordering, whereby some category A precedes B. But end weight is not a valid cross-linguistic asymmetry, and memory cost cannot explain certain asymmetries for which it has been invoked when different language types are considered. The paper argues for greater mutual awareness between processing theorists and language typologists, for more consideration of non-European grammars and language types in psycholinguistics, and for a greater appeal to processing in the explanation of typological variation.     

Psychological Interpbetation by Leon H. Levy

Hispanics in the United States mainland underutilize mental health services and drop out of treatment sooner than dominant culture groups. One reason for this problem is that the sociocultural value orientation and expectations of the Hispanic patient are discordant with the values and expectations of the professional offering help. This paper focuses on the special problems resulting from the sociocultural differences between therapist and patient, and discusses why group therapy is uniquely suited to address these problems. It argues that group therapy offered by a leader with knowledge of the culture has an advantage over other forms of treatment in engaging Hispanic patients and in helping them to increase the effective use of mental health services. Issues of group formation, pregroup contracting, and the stages in the life of a Hispanic therapy group are also discussed.     

Completeness and conservative extension results for some boolean relevant logics

This paper presents completeness and conservative extension results for the boolean extensions of the relevant logic T of Ticket Entailment, and for the contractionless relevant logics TW and RW. Some surprising results are shown for adding the sentential constant t to these boolean relevant logics; specifically, the boolean extensions with t are conservative of the boolean extensions without t, but not of the original logics with t. The special treatment required for the semantic normality of T is also shown along the way.     

Sufficient completeness verification for conditional and constrained TRS

We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership, …). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is integrated into a framework for inductive theorem proving based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form.The procedure is presented by an inference system which is shown sound and complete. A precondition of one inference of this system refers to a (undecidable) property called strong ground reducibility which is discharged to the above inductive theorem proving system. We have successfully applied our method to several examples, yielding readable proofs and, in case of negative answer, a counter-example suggesting how to complete the specification. Moreover, we show that it is a decision procedure when the TRS is unconditional but constrained, for an expressive class of constrained constructor axioms.     

A Presuppositional Approach to Conceptual Schemes

Abstract

The current discussions of conceptual schemes and related topics are misguided; for they have been focused too much on the truth-conditional notions of meaning/concepts and translation/interpretation in Tarski’s style. It is exactly due to such a Quinean interpretation of the notion of conceptual schemes that the very notion of conceptual schemes falls prey to Davidson’s attack. I argue that what should concern us in the discussions of conceptual schemes and related issues, following the initiatives of I. Hacking, T. Kuhn, and N. Rescher, is not the truth-values of assertions, but rather the truth-value-status of the sentences used to make the assertions. This is because the genuine conceptual innovation between alternative theories/languages does not lie in differences in determining the truth-values of their sentences, but turns on whether these sentences have truth-values when considered within the context of a competing one. The core of conceptual relativism does not consist in the claim that different conceptual schemes may yield incommensurable truth claims, but rather that different conceptual schemes may yield incompatible truth-value-status and therefore lead to distinct perceptions of reality. Conceptual schemes are no longer seen as sentential languages consisting of a set of sentences accepted as true, but rather seen as metaphysical presuppositions of presuppositional languages.     

“Big” Sounds Bigger in More Widely Spoken Languages

Larger communities face more communication barriers. We propose that languages spoken by larger communities adapt and overcome these greater barriers by increasing their reliance on sound symbolism, as sound symbolism can facilitate communication. To test whether widely spoken languages are more sound symbolic, participants listened to recordings of the words big and small in widely spoken and less common languages and guessed their meanings. Accuracy was higher for words from widely spoken languages providing evidence that widely spoken languages harbor more sound symbolism. Preliminary results also suggest that widely spoken languages rely on different sound symbolic patterns than less common languages. Community size can thus shape linguistic forms and influence the tools that languages use to facilitate communication.