Related papers: Towards Automated Proof Strategy Generalisation
When mathematicians present proofs they usually adapt their explanations to their didactic goals and to the (assumed) knowledge of their addressees. Modern automated theorem provers, in contrast, present proofs usually at a fixed level of…
This paper presents new methods for analyzing and evaluating generalized plans that can solve broad classes of related planning problems. Although synthesis and learning of generalized plans has been a longstanding goal in AI, it remains…
We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…
We propose a new framework for discovering landmarks that automatically generalize across a domain. These generalized landmarks are learned from a set of solved instances and describe intermediate goals for planning problems where…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
As the first part of the treatise on A General Theory of Concept Lattice (I-V), this work develops the general concept lattice for the problem concerning categorization of objects according to their properties. Unlike the conventional…
Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…
When an autonomous robot learns how to execute actions, it is of interest to know if and when the execution policy can be generalised to variations of the learning scenarios. This can inform the robot about the necessity of additional…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
A goal of artificial intelligence is to construct an agent that can solve a wide variety of tasks. Recent progress in text-guided image synthesis has yielded models with an impressive ability to generate complex novel images, exhibiting…
Providing plausible responses to why questions is a challenging but critical goal for language based human-machine interaction. Explanations are challenging in that they require many different forms of abstract knowledge and reasoning.…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
Many prediction problems, such as those that arise in the context of robotics, have a simplifying underlying structure that, if known, could accelerate learning. In this paper, we present a strategy for learning a set of neural network…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further…
Grounded language models use external sources of information, such as knowledge graphs, to meet some of the general challenges associated with pre-training. By extending previous work on compositional generalization in semantic parsing, we…
We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…