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Recent state-of-the-art natural language understanding models, such as BERT and XLNet, score a pair of sentences (A and B) using multiple cross-attention operations - a process in which each word in sentence A attends to all words in…
"[M]athematicians care no more for logic than logicians for mathematics." Augustus de Morgan, 1868. Proofs are traditionally syntactic, inductively generated objects. This paper presents an abstract mathematical formulation of propositional…
We introduce here the notion of syntactic lattice algebra which is an analogy of the syntactic monoid and of the syntactic semiring. We present a unified approach to get those three structures.
There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…
In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…
Although language models demonstrate remarkable proficiency on mathematical benchmarks, it remains unclear whether this reflects true mathematical reasoning or statistical pattern matching over learning formal syntax. Most existing…
This thesis deals with the specification and construction of syntax and operational semantics of a programming language. We work with a general notion of signature for specifying objects of a given category as initial objects in a suitable…
Transformer architectures show significant promise for natural language processing. Given that a single pretrained model can be fine-tuned to perform well on many different tasks, these networks appear to extract generally useful linguistic…
The intricate hierarchical structure of syntax is fundamental to the intricate and systematic nature of human language. This study investigates the premise that language models, specifically their attention distributions, can encapsulate…
We propose a new uniform framework for text classification and ranking that can automate the process of identifying check-worthy sentences in political debates and speech transcripts. Our framework combines the semantic analysis of the…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
We consider two styles of proof calculi for a family of tense logics, presented in a formalism based on nested sequents. A nested sequent can be seen as a tree of traditional single-sided sequents. Our first style of calculi is what we call…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
I review evidence for the claim that syntactic ambiguities are resolved on the basis of the meaning of the competing analyses, not their structure. I identify a collection of ambiguities that do not yet have a meaning-based account and…
Structured claim decomposition is often proposed as a solution for verifying complex, multi-faceted claims, yet empirical results have been inconsistent. We argue that these inconsistencies stem from two overlooked bottlenecks: evidence…
Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel…
This thesis details a project to define a fully compositional theory of synchronous sequential circuits built from primitive components, motivated by applying techniques successfully used in programming languages to hardware. The first part…
Friedman and Stanley developed the notion of Borel reducibility and illustrated its use in comparing classification problems for some familiar classes of countable structures. For many embeddings, the fact that the embedding is $1-1$ on…
A key part of any dependent type-checker is the method for checking whether two types are equal. A common claim is that syntax-directed equality is more performant, although type-directed equality is more expressive. However, this claim is…