Related papers: Compositional pre-processing for automated reasoni…
Inference tasks such as answer sentence selection (AS2) or fact verification are typically solved by fine-tuning transformer-based models as individual sentence-pair classifiers. Recent studies show that these tasks benefit from modeling…
This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
This work studies the applicability of automatic AI agent optimization methods to real-world agents in formal verification settings, focusing on automated theorem proving in Rocq as a representative and challenging domain. We evaluate how…
Autoresearch offers a flexible paradigm for automating scientific tasks, in which an AI agent proposes, implements, evaluates, and refines candidate solutions against a quantitative objective. Here, we use composition-based…
Evidence-based reasoning is at the core of many problem-solving and decision-making tasks in a wide variety of domains. Generalizing from the research and development of cognitive agents in several such domains, this paper presents progress…
Dependently-typed proof assistants furnish expressive foundations for mechanised mathematics and verified software. However, automation for these systems has been either modest in scope or complex in implementation. We aim to improve the…
The design of a complex system warrants a compositional methodology, i.e., composing simple components to obtain a larger system that exhibits their collective behavior in a meaningful way. We propose an automaton-based paradigm for…
Auto-active verifiers provide a level of automation intermediate between fully automatic and interactive: users supply code with annotations as input while benefiting from a high level of automation in the back-end. This paper presents…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
I introduce an approach for automated reasoning in first order set theories that are not finitely axiomatizable, such as $ZFC$, and describe its implementation alongside the automated theorem proving software E. I then compare the results…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…
This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
This book is about conformal prediction and related inferential techniques that build on permutation tests and exchangeability. These techniques are useful in a diverse array of tasks, including hypothesis testing and providing uncertainty…
We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…
Goal-conditioned reinforcement learning is a powerful way to control an AI agent's behavior at runtime. That said, popular goal representations, e.g., target states or natural language, are either limited to Markovian tasks or rely on…