Related papers: A Symbolic Approach to Reasoning with Linguistic Q…
Pre-trained contextual representations have led to dramatic performance improvements on a range of downstream tasks. Such performance improvements have motivated researchers to quantify and understand the linguistic information encoded in…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
This paper introduces a novel type theory and logic for probabilistic reasoning. Its logic is quantitative, with fuzzy predicates. It includes normalisation and conditioning of states. This conditioning uses a key aspect that distinguishes…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
ProbLog is a popular probabilistic logic programming language/tool, widely used for applications requiring to deal with inherent uncertainties in structured domains. In this paper we study connections between ProbLog and a variant of…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
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…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
Prompting is now a dominant method for evaluating the linguistic knowledge of large language models (LLMs). While other methods directly read out models' probability distributions over strings, prompting requires models to access this…