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Generic sentences express generalisations about the world without explicit quantification. Although generics are central to everyday communication, building a precise semantic framework has proven difficult, in part because speakers use…
In Probabilistic Logic Nilsson uses the device of a probability distribution over a set of possible worlds to assign probabilities to the sentences of a logical language. In his paper Nilsson concentrated on inference and associated…
Distributional word representation methods exploit word co-occurrences to build compact vector encodings of words. While these representations enjoy widespread use in modern natural language processing, it is unclear whether they accurately…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling…
Credal sets are sets of probability distributions that are considered as candidates for an imprecisely known ground-truth distribution. In machine learning, they have recently attracted attention as an appealing formalism for uncertainty…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
Language models (LMs) estimate a probability distribution over strings in a natural language; these distributions are crucial for computing perplexity and surprisal in linguistics research. While we are usually concerned with measuring…
Simple representations of documents based on the occurrences of terms are ubiquitous in areas like Information Retrieval, and also frequent in Natural Language Processing. In this work we propose a logical-probabilistic approach to the…
Classical semantics assumes that one can model reference, predication and quantification with respect to a fixed domain of precise referent objects. Non-logical terms and quantification are then interpreted directly in terms of elements and…
Ontological models are attempts to quantitatively describe the results of a probabilistic theory, such as Quantum Mechanics, in a framework exhibiting an explicit realism-based underpinning. Unlike either the well known quasi-probability…
Functional Distributional Semantics provides a linguistically interpretable framework for distributional semantics, by representing the meaning of a word as a function (a binary classifier), instead of a vector. However, the large number of…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…