相关论文: IST is more than an algorithm to prove ZFC theorem…

Transformers have recently been shown to be capable of reliably performing logical reasoning over facts and rules expressed in natural language, but abductive reasoning - inference to the best explanation of an unexpected observation - has…

This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…

Natural language is an intuitive way for humans to communicate tasks to a robot. While natural language (NL) is ambiguous, real world tasks and their safety requirements need to be communicated unambiguously. Signal Temporal Logic (STL) is…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

Recent advances show that large language models (LLMs) generalize strong performance across different natural language benchmarks. However, the large size of LLMs makes training and inference expensive and impractical to run in…

While there have been several contributions exploring state of the art techniques for text normalization, the problem of inverse text normalization (ITN) remains relatively unexplored. The best known approaches leverage finite state…

Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe $U$ can be considered a deterministic dynamical system evolving precisely on a (suitably constructed)…

Measurement of social bias in language models is typically by token probability (TP) metrics, which are broadly applicable but have been criticized for their distance from real-world language model use cases and harms. In this work, we test…

We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…

Einstein's distinction between principle theories and constructive theories is methodological rather than metaphysical. Principle theories such as thermodynamics and relativity articulate empirically distilled constraints that delimit…

While paragraph embedding models are remarkably effective for downstream classification tasks, what they learn and encode into a single vector remains opaque. In this paper, we investigate a state-of-the-art paragraph embedding method…

Neural machine translation (NMT) systems have been shown to give undesirable translation when a small change is made in the source sentence. In this paper, we study the behaviour of NMT systems when multiple changes are made to the source…

Despite the impressive quality improvements yielded by neural machine translation (NMT) systems, controlling their translation output to adhere to user-provided terminology constraints remains an open problem. We describe our approach to…

The standard axioms of set theory, the Zermelo-Fraenkel axioms (ZFC), do not suffice to answer all questions in mathematics. While this follows abstractly from Kurt G\"odel's famous incompleteness theorems, we nowadays know numerous…

Several explanation methods such as Integrated Gradients (IG) can be characterised as path-based methods, as they rely on a straight line between the data and an uninformative baseline. However, when applied to language models, these…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the…

Russell is a logical framework for the specification and implementation of deductive systems. It is a high-level language with respect to Metamath language, so inherently it uses a Metamath foundations, i.e. it doesn't rely on any…

Much mathematical writing exists that is, explicitly or implicitly, based on set theory, often Zermelo-Fraenkel set theory (ZF) or one of its variants. In ZF, the domain of discourse contains only sets, and hence every mathematical object…

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…