Related papers: A Higher-Order Vampire (Short Paper)
Planning as theorem proving in situation calculus was abandoned 50 years ago as an impossible project. But we have developed a Theorem Proving Lifted Heuristic (TPLH) planner that searches for a plan in a tree of situations using the A*…
Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
Higher-order functions and imperative states are language features supported by many mainstream languages. Their combination is expressive and useful, but complicates specification and reasoning, due to the use of yet-to-be-instantiated…
We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon…
With the more and more growing demand for semantic Web services over large databases, an efficient evaluation of Datalog queries is arousing a renewed interest among researchers and industry experts. In this scenario, to reduce memory…
A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…
In recent years, neuro-symbolic methods have become a popular and powerful approach that augments artificial intelligence systems with the capability to perform abstract, logical, and quantitative deductions with enhanced precision and…
The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…
Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…
Decision theories offer principled methods for making choices under various types of uncertainty. Algorithms that implement these theories have been successfully applied to a wide range of real-world problems, including materials and drug…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
This paper introduces ThoughtProbe, a novel inference time framework that leverages the hidden reasoning features of Large Language Models (LLMs) to improve their reasoning performance. Unlike previous works that manipulate the hidden…
Scientific computing has experienced a surge empowered by advancements in technologies such as neural networks. However, certain important tasks are less amenable to these technologies, benefiting from innovations to traditional inference…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Previous work on policy learning for Malaria control has often formulated the problem as an optimization problem assuming the objective function and the search space have a specific structure. The problem has been formulated as multi-armed…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…