Related papers: Skolemization for Weighted First-Order Model Count…
To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…
Weighted First Order Model Counting (WFOMC) is fundamental to probabilistic inference in statistical relational learning models. As WFOMC is known to be intractable in general ($\#$P-complete), logical fragments that admit polynomial time…
The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…
We investigate lifted inference on ordered domains with predecessor relations, where the elements of the domain respect a total (cyclic) order, and every element has a distinct (clockwise) predecessor. Previous work has explored this…
A prototype system is described whose core functionality is, based on propositional logic, the elimination of second-order operators, such as Boolean quantifiers and operators for projection, forgetting and circumscription. This approach…
A key problem in the application of first-order probabilistic methods is the enormous size of graphical models they imply. The size results from the possible worlds that can be generated by a domain of objects and relations. One of the…
Analysis of large data collections using popular machine learning and statistical algorithms has been a topic of increasing research interest. A typical analysis workload consists of applying an algorithm to build a model on a data…
Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various down-stream tasks.…
First-order logic, and quantifiers in particular, are widely used in deductive verification. Quantifiers are essential for describing systems with unbounded domains, but prove difficult for automated solvers. Significant effort has been…
Liveness properties are traditionally proven using a ranking function that maps system states to some well-founded set. Carrying out such proofs in first-order logic enables automation by SMT solvers. However, reasoning about many natural…
Transformers, the backbone of modern large language models (LLMs), face inherent architectural limitations that impede their reasoning capabilities. Unlike recurrent networks, Transformers lack recurrent connections, confining them to…
We describe a method for inverting Gentzen's cut-elimination in classical first-order logic. Our algorithm is based on first computign a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize…
Large language models~(LLMs) have recently demonstrated promising performance in many tasks. However, the high storage and computational cost of LLMs has become a challenge for deploying LLMs. Weight quantization has been widely used for…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
1-bit LLM quantization offers significant advantages in reducing storage and computational costs. However, existing methods typically train 1-bit LLMs from scratch, failing to fully leverage pre-trained models. This results in high training…
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…
In the field of large language model (LLM)-based proof generation, despite extensive training on large datasets such as ArXiv, LLMs still exhibit only modest performance on proving tasks of moderate difficulty. We believe that this is…
We consider the problem of computing optimal generalised policies for relational Markov decision processes. We describe an approach combining some of the benefits of purely inductive techniques with those of symbolic dynamic programming…
We provide a novel computer-assisted technique for systematically analyzing first-order methods for optimization. In contrast with previous works, the approach is particularly suited for handling sublinear convergence rates and stochastic…