Related papers: Faithful Logic Embeddings in HOL -- Deep and Shall…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
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.…
Large Language Models (LLMs) have rapidly transformed the landscape of artificial intelligence, enabling natural language interfaces and dynamic orchestration of software components. However, their reliance on probabilistic inference limits…
Deep learning has recently gained high interest in ophthalmology, due to its ability to detect clinically significant features for diagnosis and prognosis. Despite these significant advances, little is known about the ability of various…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
We introduce our implementation in HOL Light of the metatheory for G\"odel-L\"ob provability logic (GL), covering soundness and completeness w.r.t. possible world semantics and featuring a prototype of a theorem prover for GL itself. The…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby…
The integration of structured hierarchical embeddings into transformer-based architectures introduces a refined approach to lexical representation, ensuring that multi-scale semantic relationships are preserved without compromising…
Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable…
We study how to extend chain-of-thought (CoT) beyond language to better handle multimodal reasoning. While CoT helps LLMs and VLMs articulate intermediate steps, its text-only form often fails on vision-intensive problems where key…
Large Language Models (LLMs) can generate factually inaccurate content even if they have corresponding knowledge, which critically undermines their reliability. Existing approaches attempt to mitigate this by incorporating uncertainty in QA…
In this paper, we propose three novel models to enhance word embedding by implicitly using morphological information. Experiments on word similarity and syntactic analogy show that the implicit models are superior to traditional explicit…
The advent of large language models (LLMs) capable of producing general-purpose representations lets us revisit the practicality of deep active learning (AL): By leveraging frozen LLM embeddings, we can mitigate the computational costs of…
This position paper defends post-hoc explainability methods as legitimate tools for scientific knowledge production in machine learning. Addressing criticism of these methods' reliability and epistemic status, we develop a philosophical…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…