Related papers: The Relative Monadic Metalanguage
Metaphors are everywhere. They appear extensively across all domains of natural language, from the most sophisticated poetry to seemingly dry academic prose. A significant body of research in the cognitive science of language argues for the…
A new class of languages of infinite words is introduced, called the max-regular languages, extending the class of $\omega$-regular languages. The class has two equivalent descriptions: in terms of automata (a type of deterministic counter…
Abstract Meaning Representation (AMR) is a recently designed semantic representation language intended to capture the meaning of a sentence, which may be represented as a single-rooted directed acyclic graph with labeled nodes and edges.…
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality $!_r$ captures how many times a…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms…
Large Language Models (LLMs) excel at capturing latent semantics and contextual relationships across diverse modalities. However, in modeling user behavior from sequential interaction data, performance often suffers when such semantic…
Cross-modal reasoning (CMR), the intricate process of synthesizing and drawing inferences across divergent sensory modalities, is increasingly recognized as a crucial capability in the progression toward more sophisticated and…
Classical mathematical models used in the semantics of programming languages and computation rely on idealized abstractions such as infinite-precision real numbers, unbounded sets, and unrestricted computation. In contrast, concrete…
Lambda Prolog is known to be well-suited for expressing and implementing logics and inference systems. We show that lemmas and definitions in such logics can be implemented with a great economy of expression. We encode a higher-order logic…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
The evolving capabilities of large language models are accompanied by growing sizes and deployment costs, necessitating effective inference optimisation techniques. We propose a novel pruning method utilising centrality measures from graph…
The downward closure of a language $L$ of words is the set of all (not necessarily contiguous) subwords of members of $L$. It is well known that the downward closure of any language is regular. Although the downward closure seems to be a…
Our goal is to learn a semantic parser that maps natural language utterances into executable programs when only indirect supervision is available: examples are labeled with the correct execution result, but not the program itself.…
We investigate the hypothesis that word representations ought to incorporate both distributional and relational semantics. To this end, we employ the Alternating Direction Method of Multipliers (ADMM), which flexibly optimizes a…
We investigate the hypothesis that word representations ought to incorporate both distributional and relational semantics. To this end, we employ the Alternating Direction Method of Multipliers (ADMM), which flexibly optimizes a…
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)}…
The development of artificial intelligence systems capable of understanding and reasoning about complex real-world scenarios is a significant challenge. In this work we present a novel approach to enhance and exploit LLM reactive capability…
A fundamental theme in automata theory is regular languages of words and trees, and their many equivalent definitions. Salvati has proposed a generalization to regular languages of simply typed $\lambda$-terms, defined using denotational…