Related papers: Polymorphism Meets DHOL
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
Large Language Models (LLMs) have recently developed new advanced functionalities. Their effectiveness relies on statistical learning and generalization capabilities. However, they face limitations in internalizing the data they process and…
The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to…
We propose Deep Optimistic Linear Support Learning (DOL) to solve high-dimensional multi-objective decision problems where the relative importances of the objectives are not known a priori. Using features from the high-dimensional inputs,…
Applications in the smart industry domain, such as interaction with collaborative robots using vocal commands or machine vision systems often requires the deployment of deep learning algorithms on heterogeneous low power computing…
Deep learning models have achieved remarkable success across various domains, yet their learned representations and decision-making processes remain largely opaque and hard to interpret. This work introduces HOLE (Homological Observation of…
Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
Humor is previously regarded as a gift exclusive to humans for the following reasons. Humor is a culturally nuanced aspect of human language, presenting challenges for its understanding and generation. Humor generation necessitates a…
Many potentially non-terminating functions cannot be directly defined in a logic of total functions, such as HOL. A well-known solution to this is to define non-terminating functions using a clock that forces termination at a certain depth…
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…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
Normative theories allow one to elicit key parts of a ML algorithm from first principles, which is crucial at a time of championed scrutiny for ML work. Direct Preference Optimization (DPO) cleverly bypasses reward modeling by making an…
While there exist several reasoners for Description Logics, very few of them can cope with uncertainty. BUNDLE is an inference framework that can exploit several OWL (non-probabilistic) reasoners to perform inference over Probabilistic…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
The success of deep learning (DL) is often achieved with large models and high complexity during both training and post-training inferences, hindering training in resource-limited settings. To alleviate these issues, this paper introduces a…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…