Related papers: A Novice-Friendly Induction Tactic for Lean

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…

We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…

Building models of the world from observation, i.e., induction, is one of the major challenges in machine learning. In order to be useful, models need to maintain accuracy when used in novel situations, i.e., generalize. In addition, they…

The recent "pre-train, prompt, predict training" paradigm has gained popularity as a way to learn generalizable models with limited labeled data. The approach involves using a pre-trained model and a prompting function that applies a…

Modern large language models (LLMs) employ diverse logical inference mechanisms for reasoning, making the strategic optimization of these approaches critical for advancing their capabilities. This paper systematically investigate the…

The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…

Intelligent tutoring systems have demonstrated effectiveness in teaching formal propositional logic proofs, but their reliance on template-based explanations limits their ability to provide personalized student feedback. While large…

Inductive logic programming (ILP) is a form of logic-based machine learning. The goal is to induce a hypothesis (a logic program) that generalises given training examples. As ILP turns 30, we review the last decade of research. We focus on…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

Despite recent advances in modern machine learning algorithms, the opaqueness of their underlying mechanisms continues to be an obstacle in adoption. To instill confidence and trust in artificial intelligence systems, Explainable Artificial…

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing…

An advantage of scientific workflow systems is their ability to collect runtime provenance information as an execution trace. Traces include the computation steps invoked as part of the workflow run along with the corresponding data…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

Strong inductive biases give humans the ability to quickly learn to perform a variety of tasks. Although meta-learning is a method to endow neural networks with useful inductive biases, agents trained by meta-learning may sometimes acquire…

Induction is typically formalized as a rule or axiom extension of the LK-calculus. While this extension of the sequent calculus is simple and elegant, proof transformation and analysis can be quite difficult. Theories with an induction…

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…

Within this paper, we show that the evaluation protocol currently used for inductive link prediction is heavily flawed as it relies on ranking the true entity in a small set of randomly sampled negative entities. Due to the limited size of…

Several instance-based explainability methods for finding influential training examples for test-time decisions have been proposed recently, including Influence Functions, TraceIn, Representer Point Selection, Grad-Dot, and Grad-Cos.…

We implement three Coq plugins regarding inductive types in MetaCoq. The first plugin is a simple syntax transformation generating alternative constructors for inductive types by abstracting over concrete indices in the types of the…