Related papers: Enriching a Linear/Non-linear Lambda Calculus: A P…

Particle-style token machines are a way to interpret proofs and programs, when the latter are written following the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those…

LMNtal is a programming and modeling language based on hierarchical graph rewriting that uses logical variables to represent connectivity and membranes to represent hierarchy. On the theoretical side, it allows logical interpretation based…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…

Large Language Models (LLMs) achieve impressive performance in a wide range of tasks, even if they are often trained with the only objective of chatting fluently with users. Among other skills, LLMs show emergent abilities in mathematical…

We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…

The field of Math-NLP has witnessed significant growth in recent years, motivated by the desire to expand LLM performance to the learning of non-linguistic notions (numerals, and subsequently, arithmetic reasoning). However, non-linguistic…

Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown…

We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…

We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…

We explore a neural network architecture that stacks a recurrent layer and a feedforward layer that is also connected to the input, and compare it to standard Elman and LSTM architectures in terms of accuracy and interpretability. When…

We investigate the effective memory depth of RNN models by using them for $n$-gram language model (LM) smoothing. Experiments on a small corpus (UPenn Treebank, one million words of training data and 10k vocabulary) have found the LSTM cell…

Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences…

Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly…

Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…

Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…

Despite the broad applicability of large language models (LLMs), their reliance on probabilistic inference makes them vulnerable to errors such as hallucination in generated facts and inconsistent output structure in natural language…

Neural language models (LMs) are typically trained using only lexical features, such as surface forms of words. In this paper, we argue this deprives the LM of crucial syntactic signals that can be detected at high confidence using existing…

Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from…