Learning the Semantics of Manipulation Action

In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation actions as well as executing them with a robotic mechanism (e.g. a humanoid robot). It is based on a Combinatory Categorial Grammar. The goal of the introduced framework is to: (1) represent manipulation actions with both syntax and semantic parts, where the semantic part employs $\lambda$-calculus; (2) enable a probabilistic semantic parsing schema to learn the $\lambda$-calculus representation of manipulation action from an annotated action corpus of videos; (3) use (1) and (2) to develop a system that visually observes manipulation actions and understands their meaning while it can reason beyond observations using propositional logic and axiom schemata. The experiments conducted on a public available large manipulation action dataset validate the theoretical framework and our implementation

Paracompositionality, MWEs and Argument Substitution

Multi-word expressions, verb-particle constructions, idiomatically combining phrases, and phrasal idioms have something in common: not all of their elements contribute to the argument structure of the predicate implicated by the expression. Radically lexicalized theories of grammar that avoid string-, term-, logical form-, and tree-writing, and categorial grammars that avoid wrap operation, make predictions about the categories involved in verb-particles and phrasal idioms. They may require singleton types, which can only substitute for one value, not just for one kind of value. These types are asymmetric: they can be arguments only. They also narrowly constrain the kind of semantic value that can correspond to such syntactic categories. Idiomatically combining phrases do not subcategorize for singleton types, and they exploit another locally computable and compositional property of a correspondence, that every syntactic expression can project its head word. Such MWEs can be seen as empirically realized categorial possibilities, rather than lacuna in a theory of lexicalizable syntactic categories.Comment: accepted version (pre-final) for 23rd Formal Grammar Conference, August 2018, Sofi

Efficient Normal-Form Parsing for Combinatory Categorial Grammar

Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combinatory Categorial Grammar, by means of an efficient, correct, and easy to implement normal-form parsing technique. The parser is proved to find exactly one parse in each semantic equivalence class of allowable parses; that is, spurious ambiguity (as carefully defined) is shown to be both safely and completely eliminated.Comment: 8 pages, LaTeX packaged with three .sty files, also uses cgloss4e.st

Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics

We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a categorial grammar along the lines of Lambek. For the semantics we use so-called lexical and logical combinators inspired by work in natural logic. Nabla provides a concise interpretation and a sequent calculus as the basis for implementations.Comment: 20 page

Principles and Implementation of Deductive Parsing

We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definite-clause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of tree-adjoining grammars, categorial grammars, and lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod

A Frobenius Algebraic Analysis for Parasitic Gaps

The interpretation of parasitic gaps is an ostensible case of non-linearity in natural language composition. Existing categorial analyses, both in the typelogical and in the combinatory traditions, rely on explicit forms of syntactic copying. We identify two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon. Parasitic gaps in adjuncts are analysed as forms of generalized coordination with a polymorphic type schema for the head of the adjunct phrase. For parasitic gaps affecting arguments of the same predicate, the polymorphism is associated with the lexical item that introduces the primary gap. Our analysis is formulated in terms of Lambek calculus extended with structural control modalities. A compositional translation relates syntactic types and derivations to the interpreting compact closed category of finite dimensional vector spaces and linear maps with Frobenius algebras over it. When interpreted over the necessary semantic spaces, the Frobenius algebras provide the tools to model the proposed instances of lexical polymorphism.Comment: SemSpace 2019, to appear in Journal of Applied Logic

Categorial Grammar

The paper is a review article comparing a number of approaches to natural language syntax and semantics that have been developed using categorial frameworks. It distinguishes two related but distinct varieties of categorial theory, one related to Natural Deduction systems and the axiomatic calculi of Lambek, and another which involves more specialized combinatory operations