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The relevance between a query and a document in search can be represented as matching degree between the two objects. Latent space models have been proven to be effective for the task, which are often trained with click-through data. One…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
The evolution of 3D visual content calls for innovative methods for modelling shapes based on their intended usage, function and role in a complex scenario. Even if different attempts have been done in this direction, shape modelling still…
In this article, we introduce a reference model for interaction semantics among communicating discrete systems to guide the discourse on interoperability. The necessary set of unifying concepts is small and comprises essentially the notion…
I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word…
Definition modeling is an important task in advanced natural language applications such as understanding and conversation. Since its introduction, it focus on generating one definition for a target word or phrase in a given context, which…
Capturing word meaning in context and distinguishing between correspondences and variations across languages is key to building successful multilingual and cross-lingual text representation models. However, existing multilingual evaluation…
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we…
To correctly use in-context information, language models (LMs) must bind entities to their attributes. For example, given a context describing a "green square" and a "blue circle", LMs must bind the shapes to their respective colors. We…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
Prior work on language model pre-training has explored different architectures and learning objectives, but differences in data, hyperparameters and evaluation make a principled comparison difficult. In this work, we focus on…
Vision systems to see and reason about the compositional nature of visual scenes are fundamental to understanding our world. The complex relations between objects and their locations, ambiguities, and variations in the real-world…