Related papers: Bounded Rewriting Induction for LCSTRSs
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
The central challenge of reinforcement learning for reasoning lies not only in the sparsity of outcome-level supervision, but more fundamentally in how to transform feedback provided only at the end of a sequence into fine-grained learning…
Proof terms are syntactic expressions that represent computations in term rewriting. They were introduced by Meseguer and exploited by van Oostrom and de Vrijer to study equivalence of reductions in (left-linear) first-order term rewriting…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Essentially, in a reversible programming language, for each forward computation from state $S$ to state $S'$, there exists a constructive method to go backwards from state $S'$ to state $S$. Besides its theoretical interest, reversible…
Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is already coNP-complete, i.e. that every Boolean tautology can…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Large language models (LLMs) achieve high performance on mathematical reasoning, but these results can be inflated by training data leakage or superficial pattern matching rather than genuine reasoning. To this end, an adversarial…
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…
Large Reasoning Models (LRMs) often suffer from overthinking, generating unnecessarily long reasoning chains even for simple tasks. This leads to substantial computational overhead with limited performance gain, primarily due to redundant…
We propose regular expression inference (REI) as a challenge for code/language modelling, and the wider machine learning community. REI is a supervised machine learning (ML) and program optimisation task, and poses the problem of finding…
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were…
Humans can observe a single, imperfect demonstration and immediately generalize to very different problem settings. Robots, in contrast, often require hundreds of examples and still struggle to generalize beyond the training conditions. We…
In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
An established method for Word Sense Induction (WSI) uses a language model to predict probable substitutes for target words, and induces senses by clustering these resulting substitute vectors. We replace the ngram-based language model (LM)…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…
Programs offer compactness and structure that makes them an attractive representation for visual data. We explore how code rewriting can be used to improve systems for inferring programs from visual data. We first propose Sparse…
Term rewriting plays a crucial role in software verification and compiler optimization. With dozens of highly parameterizable techniques developed to prove various system properties, automatic term rewriting tools work in an extensive…