Related papers: Quantifiers, Anaphora, and Intensionality
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We provide a unified account of sentence-level and text-level anaphora within the framework of a dependency-based grammar model. Criteria for anaphora resolution within sentence boundaries rephrase major concepts from GB's binding theory,…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the…
We propose a system for the interpretation of anaphoric relationships between unbound pronouns and quantifiers. The main technical contribution of our proposal consists in combining generalized quantifiers with dependent types. Empirically,…
Transformer-based language models are effective but complex, and understanding their inner workings and reasoning mechanisms is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name…
Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting…
Understanding texts requires memory: the reader has to keep in mind enough words to create meaning. This calls for a relation between the memory of the reader and the structure of the text. To investigate this interaction, we first identify…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
The controllability of Large Language Models (LLMs) when used as conversational agents is a key challenge, particularly to ensure predictable and user-personalized responses. This work proposes an ontology-based approach to formally define…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Large Language Models (LLMs) often struggle with deductive judgment in syllogistic reasoning, systematically conflating semantic plausibility with formal validity a phenomenon known as content effect. This bias persists even when models…
Categorical compositional distributional semantics provide a method to derive the meaning of a sentence from the meaning of its individual words: the grammatical reduction of a sentence automatically induces a linear map for composing the…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
In this paper we propose a categorical theory of intensionality. We first revisit the notion of intensionality, and discuss we its relevance to logic and computer science. It turns out that 1-category theory is not the most appropriate…
Distributional semantic models provide vector representations for words by gathering co-occurrence frequencies from corpora of text. Compositional distributional models extend these from words to phrases and sentences. In categorical…
Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…