Related papers: A Higher-Order Vampire (Short Paper)
Various planning-based know-how logics have been studied in the recent literature. In this paper, we use such a logic to do know-how-based planning via model checking. In particular, we can handle the higher-order epistemic planning…
Fireworks algorithm is a new type of intelligent optimization algorithm. Because of its fast convergence speed, easy implementation, explosiveness, diversity, simplicity and randomness, it has attracted more and more attention in many…
Certain constructs allowed in Mizar articles cannot be represented in first-order logic but can be represented in higher-order logic. We describe a way to obtain higher-order theorem proving problems from Mizar articles that make use of…
We describe the translation of the Suggested Upper Merged Ontology (SUMO) to Typed First-order Form (TFF) with level 0 polymorphism. Building on our prior work to create a TPTP FOF translation of SUMO for use in the E and Vampire theorem…
Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
This article studies the problem of modifying the action ordering of a plan in order to optimise the plan according to various criteria. One of these criteria is to make a plan less constrained and the other is to minimize its parallel…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The ability to precisely derive mathematical objects is a core requirement for downstream STEM applications, including mathematics, physics, and chemistry, where reasoning must culminate in formally structured expressions. Yet, current LM…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
In this paper, we present a new necessary and sufficient condition for which the supremum exists with respect to the logic order. Moreover, we give out a new and much simpler representation of the supremum with respect to the order, our…
Bio-inspired optimization (including Evolutionary Computation and Swarm Intelligence) is a growing research topic with many competitive bio-inspired algorithms being proposed every year. In such an active area, preparing a successful…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
Explanation and high-order reasoning capabilities are crucial for real-world visual question answering with diverse levels of inference complexity (e.g., what is the dog that is near the girl playing with?) and important for users to…
Using Reinforcement Learning with Verifiable Rewards (RLVR) to optimize Large Language Models (LLMs) can be conceptualized as progressively editing a query's `Reasoning Tree'. This process involves exploring nodes (tokens) and dynamically…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
This chapter, which is an extended and revised version of the conference paper 'Predator: Byte-Precise Verification of Low-Level List Manipulation', concentrates on a detailed description of the algorithms behind the Predator shape analyser…
Recent improvements of the LEO-II theorem prover are presented. These improvements include a revised ATP interface, new translations into first-order logic, rule support for the axiom of choice, detection of defined equality, and more…