TheBench is a tool to study monadic structures in natural language. It is for writing monadic grammars to explore analyses, compare diverse languages through their categories, and to train models of grammar from form-meaning pairs where syntax is latent variable. Monadic structures are binary combinations of elements that employ semantics of composition only. TheBench is essentially old-school categorial grammar to syntacticize the idea, with the implication that although syntax is autonomous (recall \emph{colorless green ideas sleep furiously}), the treasure is in the baggage it carries at every step, viz. semantics, more narrowly, predicate-argument structures indicating choice of categorial reference and its consequent placeholders for decision in such structures. There is some new thought in old school. Unlike traditional categorial grammars, application is turned into composition in monadic analysis. Moreover, every correspondence requires specifying two command relations, one on syntactic command and the other on semantic command. A monadic grammar of TheBench contains only synthetic elements (called `objects' in category theory of mathematics) that are shaped by this analytic invariant, viz. composition. Both ingredients (command relations) of any analytic step must therefore be functions (`arrows' in category theory). TheBench is one implementation of the idea for iterative development of such functions along with grammar of synthetic elements.

A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that is, context-free grammars enhanced with conjunction. It is also shown that categorial grammars with conjunction can be naturally embedded into the Lambek calculus with conjunction and disjunction operations. This further implies that a certain NP-complete set can be defined in the Lambek calculus with conjunction. We also show how to handle some subtle issues connected with the empty string. Finally, we prove that a language generated by a conjunctive grammar can be described by a Lambek grammar with disjunction (but without conjunction).

DisCoCat [1, 2] (Categorical Compositional Distributional) models are structure-preserving maps which send grammatical types to vector spaces and grammatical structures to linear maps. Concretely, the meaning of words is given by tensors with shapes induced by their grammatical types; the meaning of sentences is given by contracting the tensor networks induced by their grammatical structure. String diagrams provide an intuitive graphical language to visualise and reason formally about the evaluation of DisCoCat models; which can be formalised in terms of functors F: G Vect from the category generated by a formal grammar G to the monoidal category Vect of vector spaces and linear maps with the tensor product [3, 2.5]. Although this functorial definition applies equally to any kind of formal grammar, most of the DisCoCat literature focuses on pregroup grammars and more generally on categorial grammars such as the Lambek calculus [4, 5] and combinatory categorial grammars (CCG) [6]. In that case, G is a closed monoidal category and the DisCoCat models F: G Vect map grammatical structures to the closed structure of Vect in a canonical way. In practice, this means that once the meaning of each word is computed from a dataset, the meaning of any new grammatical sentence can be computed automatically from its grammatical structure.

In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal grammar or a mechanism which explains significant aspects of the human faculty of language, which in turn can be considered a natural disposition for the evolution and deployment of the diverse human languages. We describe such a mechanism, which differs from existing logical and grammatical approaches by its geometric nature. Our main contribution is to explore the assumption that sentence recognition takes place by forming chains of tokens representing words, followed by matching these chains with pre-existing chains representing grammatical word orders. The aligned chains of tokens give rise to two- and three-dimensional complexes. The resulting model gives an alternative presentation for subtle rules, traditionally formalized using categorial grammar.

In addition to their limpid interface with semantics, categorial grammars enjoy another important property: learnability. This was first noticed by Buskowsky and Penn and further studied by Kanazawa, for Bar-Hillel categorial grammars. What about Lambek categorial grammars? In a previous paper we showed that product free Lambek grammars where learnable from structured sentences, the structures being incomplete natural deductions. These grammars were shown to be unlearnable from strings by Foret and Le Nir. In the present paper we show that Lambek grammars, possibly with product, are learnable from proof frames that are incomplete proof nets. After a short reminder on grammatical inference \`a la Gold, we provide an algorithm that learns Lambek grammars with product from proof frames and we prove its convergence. We do so for 1-valued also known as rigid Lambek grammars with product, since standard techniques can extend our result to $k$-valued grammars. Because of the correspondence between cut-free proof nets and normal natural deductions, our initial result on product free Lambek grammars can be recovered. We are sad to dedicate the present paper to Philippe Darondeau, with whom we started to study such questions in Rennes at the beginning of the millennium, and who passed away prematurely. We are glad to dedicate the present paper to Jim Lambek for his 90 birthday: he is the living proof that research is an eternal learning process.

But each They are linked by an arrow which is labeled by discourse method for representing a context is quite different. Our relations R. We represent SDRS in the form of boxes like study is based on two representational methods of temporal DRS. To induce a temporal and hierarchical structure, relations: the Segmented Discourse Representation Theory SDRT distinguish discourse relations'coordinating' from (SDRT) and the model of Cognitive and Applicative'subordinating', therefore coordination and subordination Grammar (CAG). This paper presents a comparison of affect the temporal order of text: the former indicate a continuation these two approaches about aspect and tense by an analysis of some discourses pattern, like relations of'Narration' of relations between events. We are not going to show all or'Result' in discourse segmentation, and the later steps of SDRT's representations, but we take a simple discourse indicate with types of information like relations of'Elaboration' (Asher and Lascarides 2003) and we analyze the or'Explanation'. These relations are appeared same discourse with the framework of the CAG.

This paper intends to demonstrate how Applicative and Combinatory Categorial Grammar (ACCG) can be drawn on to design powerful software applications for the teaching of languages. To this end, we present some modules from our “pictographic translator”, a software that performs syntactical analysis of sentences in natural language directly written by the user, and then dynamically displays series of pictograms that illustrate the words and structure of the user’s sentences. After a short presentation of our application and an introduction to ACCG, we will examine how this formalism enables the building of several high-level functions in our system, such as disambiguation, structure exhibition and grammatical correction/validation. We finally open a short discussion concerning the potential (and limits) of this architecture with regards to multilingualism.