Related papers: Rewriting Induction for Existentially Quantified E…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
We study variants of Buss's theories of bounded arithmetic axiomatized by induction schemes disallowing the use of parameters, and closely related induction inference rules. We put particular emphasis on $\hat\Pi^b_i$ induction schemes,…
We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the…
AI researchers and practitioners increasingly apply large language models (LLMs) to what we call reasoning-intensive regression (RiR), i.e., deducing subtle numerical scores from text. Unlike standard language regression tasks such as…
We study the notion of boundedness in the context of positive existential rules, that is, whether there exists an upper bound to the depth of the chase procedure, that is independent from the initial instance. By focussing our attention on…
Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on…
Mathematical reasoning is a central challenge for large language models (LLMs), requiring not only correct answers but also faithful reasoning processes. Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising…
Prompt engineering is critical for the development of LLM-based applications. However, it is usually done manually in a "trial and error" fashion that can be time consuming, ineffective, and sub-optimal. Even for the prompts which seemingly…
Curriculum learning helps language models tackle complex reasoning by gradually increasing task difficulty. However, it often fails to generate consistent step-by-step reasoning, especially in multilingual and low-resource settings where…
For the Hermitian inexact Rayleigh quotient iteration (RQI), we present a new general theory, independent of iterative solvers for shifted inner linear systems. The theory shows that the method converges at least quadratically under a new…
Intelligence-biological, artificial, or collective-requires structural coherence across recursive reasoning processes to scale effectively. As complex systems grow, coherence becomes fragile unless a higher-order structure ensures semantic…
This paper deals with a problem from discrete-time robust control which requires the solution of constraints over the reals that contain both universal and existential quantifiers. For solving this problem we formulate it as a program in a…
With the advent of real-world quantum computing, the idea that parametrized quantum computations can be used as hypothesis families in a quantum-classical machine learning system is gaining increasing traction. Such hybrid systems have…
Knowledge refactoring compresses a logic program by introducing new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Existing neural networks are memory-consuming and computationally intensive, making deploying them challenging in resource-constrained environments. However, there are various methods to improve their efficiency. Two such methods are…
Reverse Mathematics (RM for short) is a program in the foundations of mathematics with the aim of finding the minimal axioms required for proving theorems about countable and separable objects. RM usually takes place in second-order…
Inductive logic programming is a form of machine learning based on mathematical logic that generates logic programs from given examples and background knowledge. In this project, we extend the Popper ILP system to make use of multi-task…