Related papers: Automating Induction by Reflection
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Despite their impressive capabilities, large pre-trained language models (LMs) struggle with consistent reasoning; recently, prompting LMs to generate explanations that self-guide the inference has emerged as a promising direction to amend…
This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
Machine learning models such as Transformers or LSTMs struggle with tasks that are compositional in nature such as those involving reasoning/inference. Although many datasets exist to evaluate compositional generalization, when it comes to…
Large language models (LLMs) can perform complex reasoning by generating intermediate reasoning steps. Providing these steps for prompting demonstrations is called chain-of-thought (CoT) prompting. CoT prompting has two major paradigms. One…
A system may be modelled as an operational model (which has explicit notions of state and transitions between states) or an axiomatic model (which is specified entirely as a set of invariants). Most formal methods techniques (e.g., IC3,…
Epistemic and doxastic logics are modal logics for knowledge and belief, and serve as foundational models for rational agents in game theory, philosophy, and computer science. We examine the consequences of modeling agents capable of a…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
Human ability at solving complex tasks is helped by priors on object and event semantics of their environment. This paper investigates the use of similar prior knowledge for transfer learning in Reinforcement Learning agents. In particular,…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
Large Language Models (LLMs) exhibit impressive performance across various domains but still struggle with arithmetic reasoning tasks. Recent work shows the effectiveness of prompt design methods in enhancing reasoning capabilities.…
Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to…
Formal reasoning about inductively defined relations and structures is widely recognized not only for its mathematical interest but also for its importance in computer science, and has applications in verifying properties of programs and…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
Rewriting Induction (RI) is a method to prove inductive theorems, originating from equational reasoning. By using Logically Constrained Simply-typed Term Rewriting Systems (LCSTRSs) as an intermediate language, rewriting induction becomes a…
A cyclic proof system is a proof system whose proof figure is a tree with cycles. The cut-elimination in a proof system is fundamental. It is conjectured that the cut-elimination in the cyclic proof system for first-order logic with…
Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on…