Related papers: Towards Automated Proof Strategy Generalisation
Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…
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…
We study the generalization abilities of language models when translating natural language into formal specifications with complex semantics. In particular, we fine-tune language models on three datasets consisting of English sentences and…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
Recent approaches to goal recognition have progressively relaxed the assumptions about the amount and correctness of domain knowledge and available observations, yielding accurate and efficient algorithms. These approaches, however, assume…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
Humans readily generalize, applying prior knowledge to novel situations and stimuli. Advances in machine learning and artificial intelligence have begun to approximate and even surpass human performance, but machine systems reliably…
We study whether automatically-induced prompts that effectively extract information from a language model can also be used, out-of-the-box, to probe other language models for the same information. After confirming that discrete prompts…
We present a method to estimate the provability of a mathematical formula. We adapt the tactical theorem prover TacticToe to factor in these estimations. Experiments over the HOL4 library show an increase in the number of theorems re-proven…
The advancement of Large Language Models (LLMs) has greatly improved our ability to process complex language. However, accurately detecting logical fallacies remains a significant challenge. This study presents a novel and effective prompt…
Automata learning is a technique that has successfully been applied in verification, with the automaton type varying depending on the application domain. Adaptations of automata learning algorithms for increasingly complex types of automata…
We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
Task-oriented dialogue is difficult in part because it involves understanding user intent, collecting information from the user, executing API calls, and generating helpful and fluent responses. However, for complex tasks one must also…
Recently, research efforts have gained pace to cater to varied user preferences while generating text summaries. While there have been attempts to incorporate a few handpicked characteristics such as length or entities, a holistic view…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for…