Related papers: Anaphora and Ellipsis in Lambek Calculus with a Re…
Symbolic sentence meaning representations, such as AMR (Abstract Meaning Representation) provide expressive and structured semantic graphs that act as intermediates that simplify downstream NLP tasks. However, the instruction-following…
Recent advances on the Vector Space Model have significantly improved some NLP applications such as neural machine translation and natural language generation. Although word co-occurrences in context have been widely used in…
The main contribution of this paper is that every convex function with non-empty relative algebraic interior of its domain is Lipschitz and subdifferentiable in some algebraic sense without any additional topological constraints. The…
Deep compositional models of meaning acting on distributional representations of words in order to produce vectors of larger text constituents are evolving to a popular area of NLP research. We detail a compositional distributional…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
Resolving abstract anaphora is an important, but difficult task for text understanding. Yet, with recent advances in representation learning this task becomes a more tangible aim. A central property of abstract anaphora is that it…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…
The Categorical Compositional Distributional (DisCoCat) framework models meaning in natural language using the mathematical framework of quantum theory, expressed as formal diagrams. DisCoCat diagrams can be associated with tensor networks…
Anaphora resolution is a challenging task which has been the interest of NLP researchers for a long time. Traditional resolution techniques like eliminative constraints and weighted preferences were successful in many languages. However,…
We extend the theory of unified correspondence to a very broad class of logics with algebraic semantics given by varieties of normal lattice expansions (LEs), also known as `lattices with operators'. Specifically, we introduce a very…
In this paper, we provide an account of how to generate sentences with coordination constructions from clause-sized semantic representations. An algorithm is developed to generate sentences with ellipsis, gapping, right-node-raising, and…
In compositional model-theoretic semantics, researchers assemble truth-conditions or other kinds of denotations using the lambda calculus. It was previously observed that the lambda terms and/or the denotations studied tend to follow the…
Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…
Lexical entailment, such as hyponymy, is a fundamental issue in the semantics of natural language. This paper proposes distributional semantic models which efficiently learn word embeddings for entailment, using a recently-proposed…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
Intuitionistic modal logics (IMLs) extend intuitionistic propositional logic with modalities such as the box and diamond connectives. Advances in the study of IMLs have inspired several applications in programming languages via the…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…