Related papers: Theory Exploration Powered By Deductive Synthesis
We introduce and elaborate a novel formalism for the manipulation and analysis of proofs as objects in a global manner. In this first approach the formalism is restricted to first-order problems characterized by condensed detachment. It is…
Scientists have long aimed to discover meaningful formulae which accurately describe experimental data. A common approach is to manually create mathematical models of natural phenomena using domain knowledge, and then fit these models to…
Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
Hypothesis generation is a fundamental step in scientific discovery, yet it is increasingly challenged by information overload and disciplinary fragmentation. Recent advances in Large Language Models (LLMs) have sparked growing interest in…
Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…
In settings from fact-checking to question answering, we frequently want to know whether a collection of evidence (premises) entails a hypothesis. Existing methods primarily focus on the end-to-end discriminative version of this task, but…
In the information era, how learners find, evaluate, and effectively use information has become a challenging issue, especially with the added complexity of large language models (LLMs) that have further confused learners in their…
Large language models (LLMs) have rapidly evolved from text generators into powerful problem solvers. Yet, many open tasks demand critical thinking, multi-source, and verifiable outputs, which are beyond single-shot prompting or standard…
Exploratory search aims to guide users through a corpus rather than pinpointing exact information. We propose an exploratory search system based on hierarchical clusters and document summaries using sentence embeddings. With sentence…
Modern recommendation systems ought to benefit by probing for and learning from delayed feedback. Research has tended to focus on learning from a user's response to a single recommendation. Such work, which leverages methods of supervised…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
Using multisets, we develop novel techniques for mechanizing the proofs of the synthesis conjectures for list-sorting algorithms, and we demonstrate them in the Theorema system. We use the classical principle of extracting the algorithm as…
Search-based test generators are effective at producing unit tests with high coverage. However, such automatically generated tests have no meaningful test and variable names, making them hard to understand and interpret by developers. On…
We take two key steps in automating the open-ended discovery of new mathematical theories, a grand challenge in artificial intelligence. First, we introduce $\emph{FERMAT}$, a reinforcement learning (RL) environment that models concept…
In this paper, we demonstrate how to do automated theorem proving in the presence of a large knowledge base of potential premises without learning from human proofs. We suggest an exploration mechanism that mixes in additional premises…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
Proving equivalence between functional programs is a fundamental problem in program verification, which often amounts to reasoning about algebraic data types (ADTs) and compositions of structural recursions. Modern theorem provers address…