Related papers: Rewriting and Inductive Reasoning
We present techniques to prove termination of cycle rewriting, that is, string rewriting on cycles, which are strings in which the start and end are connected. Our main technique is to transform cycle rewriting into string rewriting and…
Large Reasoning Models (LRMs) achieve strong performance through explicit chain-of-thought reasoning but suffer from \textit{overthinking}: generating excessive reasoning tokens even for trivial queries. {Beyond inflating cost, overthinking…
The wave of pre-training language models has been continuously improving the quality of the machine-generated conversations, however, some of the generated responses still suffer from excessive repetition, sometimes repeating words from…
We introduce a class of rooted graphs which allows one to encode various kinds of classical or quantum circuits. We then follow a set-theoretic approach to define rewrite systems over the considered graphs and propose a new complete…
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
Large reasoning models (LRMs) often consume excessive tokens, inflating computational cost and latency. More broadly, in goal reaching sequential decision problems we often want to reach the goal quickly, and LRM reasoning can be viewed…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
With help of a compact Prolog-based theorem prover for Intuitionistic Propositional Logic, we synthesize minimal assumptions under which a given formula formula becomes a theorem. After applying our synthesis algorithm to cover basic…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Many large language models (LLMs) use reasoning to generate responses but do not reveal their full reasoning traces (a.k.a. chains of thought), instead outputting only final answers and brief reasoning summaries. To demonstrate that hiding…
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…
We develop a class of algebraic interpretations for many-sorted and higher-order term rewriting systems that takes type information into account. Specifically, base-type terms are mapped to \emph{tuples} of natural numbers and higher-order…
The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the…
Magic sets are a Datalog to Datalog rewriting technique to optimize query answering. The rewritten program focuses on a portion of the stable model(s) of the input program which is sufficient to answer the given query. However, the…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…
The application of Large Language Models to Question Answering has shown great promise, but important challenges such as hallucinations and erroneous reasoning arise when using these models, particularly in knowledge-intensive,…
This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…