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State-of-the-art sequential reasoning in Large Language Models (LLMs) has expanded the capabilities of Copilots beyond conversational tasks to complex function calling, managing thousands of API calls. However, the tendency of compositional…

Tool-integrated reasoning (TIR) augments large language models (LLMs) with the ability to invoke external tools during long-form reasoning, such as search engines and code interpreters, to solve tasks beyond the capabilities of internal…

Large Language Models (LLMs) can solve previously intractable tasks given only natural-language instructions and a few examples, but they remain difficult to steer precisely and lack a key capability for building reliable software at scale:…

The Transformer architecture excels in a variety of language modeling tasks, outperforming traditional neural architectures such as RNN and LSTM. This is partially due to its elimination of recurrent connections, which allows for parallel…

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC;…

Chain-of-Thought (CoT) and Looped Transformers have been shown to empirically improve performance on reasoning tasks and to theoretically enhance expressivity by recursively increasing the number of computational steps. However, their…

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…

This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…

Transformer based language models (LMs) demonstrate increasing performance with scale across a wide variety of tasks. Scale alone however cannot enable models to solve tasks that require access to ephemeral, changing, or private data that…

In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the…

We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…

For effective human-robot interaction, robots need to understand, plan, and execute complex, long-horizon tasks described by natural language. Recent advances in large language models (LLMs) have shown promise for translating natural…

This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…

Tool learning has emerged as a crucial capability for large language models (LLMs) to solve complex real-world tasks through interaction with external tools. Existing approaches face significant challenges, including reliance on…

This paper introduces a flexible framework for the estimation of the conditional tail index of heavy tailed distributions. In this framework, the tail index is computed from an auxiliary linear regression model that facilitates estimation…

We present an argument for {\em construction grammars} based on the minimum description length (MDL) principle (a formal version of the Ockham Razor). The argument consists in using linguistic and computational evidence in setting up a…

Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…