Type-Logical Grammar

The goal of this paper is to propose a unification of two strands of research within the semantics of spatial prepositions. The first strand focuses on the so-called modification problem, which can be stated as follows. Some, but not all spatial prepositions can occur in sentences including measure phrases, such as ten meters (Mario went ten meters in front of the car). The second strand focuses on so-called prepositional aspect: the fact that some but not all spatial prepositions can occur with temporal adverbial phrases such as in one hour. A unified account is proposed, based on a minimal version of Type-Logical syntax combined with situation semantics. This unified account is shown to explain and predict why, for instance, telic prepositions cannot occur with measure phrases (viz. *ten meters to the park). A compositional analysis of the contribution to lexical aspect of measure phrases, and their compositional interplay with spatial prepositions and temporal adverbials, is offered in detail. The main conclusion is that measure phrases do contribute to the lexical aspect reading of a sentence, but do so in fairly subtle (and compositionally-based) ways.

The goal of this paper is to offer a unified analysis of the morphological structure of spatial adpositions and spatial case markers in three languages: English, Spanish, and Finnish. This analysis combines Distributed Morphology assumptions with a Type-Logical formal treatment. Two key results emerge from this unified morpho-syntactic analysis. First, spatial adpositions (behind, encima, laelta) can be accounted as the result of merging different “types” of spatial morphemes, including spatial case markers and particles. Second, cross-linguistic syntactic phenomena involving these categories (e.g. argument demotion) can also be accounted for straightforwardly, via our analysis. We suggest that these results also support a “morphology all the way up” view of Distributed Morphology.

We give a type logical categorial grammar for the syntax and semantics of Montague’s seminal fragment, which includes ambiguities of quantification and intensionality and their interactions, and we present the analyses assigned by a parser/theorem prover CatLog to the examples of the first half of Chapter 7 of the classic text Introduction to Montague Semantics

The goal of this paper is to propose a novel compositional analysis of literal and metaphoric readings in spatial prepositions and prepositional phrases. It is shown that these types of readings emerge as the result of prepositions interacting with other parts of speech, such as verbs, DPs and temporal adverbs (e.g., in one hour). Two types of understudied data are discussed. The first set of data involves the interaction of literal and metaphoric readings with lexical aspect, including their distribution with temporal adverbs (e.g., in one hour/for one hour). The second set of data involves the coexistence of literal and metaphoric readings for prepositions in coordinated structures (e.g., under the table and through the briefing). The account suggests that both readings emerge as types of possible relations that spatial prepositions can denote, as part of a complex semantic domain that includes distinct semantic dimensions.

This paper aims to show that a new pattern of non-canonical coordination (NCC), going under the rubric Right-Node Wrapping (RNW), follows naturally from independently motivated accounts of coordination and discontinuous constituency. The analysis is seated in a combinatory variant of Categorial Grammar (CG) which licenses discontinuous constituency in a highly constrained way that nonetheless describes a broad range of phenomena. It also demonstrates that the coordination data captured by Dowty's (1988) continuous combinatory CG can be accounted for straightforwardly in the present system with minor extensions. The central claim then is that these independent accounts together predict nearly the full range of observed RNW data, including some previously unknown variants of the phenomenon. In RNW coordinations , the pivot expression shared by the conjuncts is followed by some additional expression interpreted as part of the rightmost conjunct alone (Wilder, 1999; Whit-man, 2009). Due to empirical similarities between RNW and NCC, any adequate account of NCC should naturally predict RNW. However, previous like-category coordination analyses of NCC in CG can only generate peripheral pivots, thereby failing on RNW. The proposal succeeds in this respect by assigning the right conjunct discontin-uous constituency. The present formulation of discontinuity is compared favorably to existing discontinuity-based analyses of RNW in multimodal Type Logical Grammar (TLG) (Whitman, 2009; Kubota, 2014, Ms.) and Linearization Based HPSG (Chaves, 2014). Finally, it is argued that the variety of discontinuity found in RNW cannot be subsumed under more general notions of discontinuity in TLG (e.g. Kubota and Levine, forthcoming; Morrill and Valentín, 2012).

The goal of this paper is to offer a unified analysis of the morphological structure of spatial adpositions and spatial case markers in three languages: English, Spanish, and Finnish. This analysis combines Distributed Morphology assumptions with a Type-Logical formal treatment. Two key results emerge from this unified morpho-syntactic analysis. First, spatial adpositions (behind, encima, laelta) can be accounted as the result of merging different “types” of spatial morphemes, including spatial case markers and particles. Second, cross-linguistic syntactic phenomena involving these categories (e.g. argument demotion) can also be accounted for straightforwardly, via our analysis. We suggest that these results also support a “morphology all the way up” view of Distributed Morphology.

This paper proposes an analysis of preposition stranding in English and Swedish, based on a variant of Type-Logical Syntax. Since the paper tackles novel and poorly understood discourse-bound phenomena, it introduces a simple extension of type-logical syntax to these phenomena.

The goal of this paper is to investigate the polysemy of Spanish spatial prepositions (a, en, hacia, among others), and offer a syntactic and semantic treatment of this phenomenon. The core idea behind this account is that these prepositions can denote sets of possible locations that are involved in spatial relations. Consequently, the compositional interaction of polysemous prepositions with other parts of speech can determine which specific sense emerges in a sentence. The analysis is couched in a Type-Logical Grammar approach. It addresses data that have not previously been analysed in the literature, involving so-called Boolean constructions (e.g. en la estación y la calle). Also, the paper shows that a single treatment can capture all the relevant data. Therefore, the analysis shows that polysemy is a grammar phenomenon that is better accounted for in architectures with a distinct syntactic/derivational component (e.g. Distributed Morphology), than in architectures lacking this...

This paper offers a unified approach to Italian spatial prepositions, such as di fronte a 'in front of', verso 'towards', in 'in', dietro a 'behind', and nel mezzo di 'in the middle of'. Three assumptions play a key role. First, Italian spatial prepositions can differ sensibly in their morphological structure, but share the same syntactic properties. Second, their sentential distribution is in part context-sensitive, thus based on the categories with which they combine. Third, their semantic contribution is "layered", in the sense that it includes the meaning dimensions of both aspectual boundedness and specificity. The main result is a generalised theory on the structure and semantic interpretation of these prepositions.

The goal of this paper is to investigate the polysemy of Spanish spatial prepositions (a, en, hacia, among others), and offer a syntactic and semantic treatment of this phenomenon. The core idea behind this account is that these prepositions can denote sets of possible locations that are involved in spatial relations. Consequently, the compositional interaction of polysemous prepositions with other parts of speech can determine which specific sense emerges in a sentence. The analysis is couched in a Type-Logical Grammar approach. It addresses data that have not previously been analysed in the literature, involving so-called Boolean constructions (e.g. en la estación y la calle). Also, the paper shows that a single treatment can capture all the relevant data. Therefore, the analysis shows that polysemy is a grammar phenomenon that is better accounted for in architectures with a distinct syntactic/derivational component (e.g. Distributed Morphology), than in architectures lacking this component (e.g. Cognitive Linguistics approaches). Consequences for a theory of grammar are discussed. RESUMEN. El objetivo de este artículo es investigar la polisemia de las preposiciones espaciales españolas (a, en, hacia, entre otras), y proporcionar un tratamiento sintáctico y semántico de este fenómeno. La idea fundamental de nuestra propuesta es que estas preposiciones pueden denotar conjuntos de locaciones posibles que están involucradas en las relaciones espaciales. En consecuencia, la interacción composicional de las preposiciones polisémicas con otras categorías determinan qué significado específico surge en una oración. El análisis se incardina en una aproximación de Type-Logical Grammar. Discute datos que no han sido analizados previamente en la bibliografía, incluyendo las construcciones booleanas (e.g. en la estación y la calle). Este trabajo también muestra que un tratamiento unificado puede dar cuenta de todos los datos relevantes. Así, el análisis muestra que la polisemia es un fenómeno gramatical que se debe discutir en arquitecturas gramaticales con un componente sintáctico / derivacional independiente (por ejemplo, Morfología Distribuida) y no en arquitecturas que carecen de este componente (por ejemplo, las aproximaciones de lingüística cognitiva). Se discuten las consecuencias de esto para una teoría de la gramática.

The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity.
This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD.
More concretely, we present a faithful embedding translation (·)♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.

The goal of this paper is to offer a novel account on the Syntax and
Semantics of Spanish Spatial Prepositions. This account is novel in at least three aspects. First, the account offers a unified syntactic analysis that covers understudied types of Spanish Spatial Prepositions (e.g. en el centro de, junto y a la izquierda de).
Second, the account shows that such treatment can be extended to morphological phenomena, and can capture both their internal structure (e.g. de-bajo), and licensing patterns pertaining to argument demotion. The account also captures an alternation
between “a-“ (e.g. alante) and “de-“ Prepositions (e.g. debajo), with respect to demotion, and is consistent with standard treatments of where-questions (dónde, in Spanish). Third, the account offers a “direct compositionality” semantic treatment, in which the interpretation of Spanish Spatial Prepositions is directly “read off” from their structure. This account is shown to capture all the semantic data discussed in the paper (argument demotion, interaction of Prepositions with Verbs, coordinated Prepositions),
and to successfully extend previous accounts of this category.

The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability

This paper offers a unified approach to Italian Spatial prepositions, such as di fronte a ‘in front of’, verso ‘towards’, in ‘in’, dietro a ‘behind’, and nel mezzo di ‘in the middle of’. Three assumptions play a key role. First, Italian Spatial Prepositions can differ sensibly in their morphological structure, but share the same syntactic properties. Second, their sentential distribution is in part context-sensitive, thus based on the categories with which they combine. Third, their semantic contribution is “layered”, in the sense that it includes the meaning dimensions of both aspectual boundedness and specificity. The main results are a generalised theory on the structure of these prepositions and their distribution, as well as an analysis of their compositional contribution to lexical aspect.

The goal of this talk is to present a unified theory of the distribution of the Spanish copulae and auxiliary verbs "ser", "estar", "aver" and "tener". The talk presents an ongoing project already presented in Bologna (Copula workshop), although the current talk is a version for the Toronto graduate school seminar in syntax and semantics.

"Dedicated to Jim Lambek, a profoundly inspirational mathematician, whose contributions cover an extraordinarily large range of topics, from mathematics to linguistics to physics Contains papers by leading researchers in the fields of algebra, category theory, linguistics, theoretical physics, logic and proof theory Preface contains some personal recollections, describing different ways the editors of this book have come to know Jim Lambek For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring upcoming generations of scholars."

This paper presents a unified approach on two poorly understood problems of auxiliary selection in the Aquilan dialect. The first problem pertains to the distribution of an auxiliary verb that denotes the notion of “possession”, tene’. The second problem pertains to the distribution of a more standard auxiliary verb, ave´, which denotes the notion of “existence” in compound tenses, in suppletive distribution with esse. A proposed solution is that the distribution of both auxiliary verbs can be accounted via a simple analysis of Aquilan’s person-driven agreement: how a verb interacts with its arguments. This analysis is based on a formal (type-logical) representation of Distributed Morphology combined with Type-Logical calculi, and shown to correctly account and predict the distribution of these auxiliary verbs.