Related papers: Generating Theorems by Generating Proof Structures
Mathematical reasoning demands two critical, complementary skills: constructing rigorous proofs for true statements and discovering counterexamples that disprove false ones. However, current AI efforts in mathematics focus almost…
Large pre-trained language models (LMs) have been shown to perform surprisingly well when fine-tuned on tasks that require commonsense and world knowledge. However, in end-to-end architectures, it is difficult to explain what is the…
Sentence Embedding stands as a fundamental task within the realm of Natural Language Processing, finding extensive application in search engines, expert systems, and question-and-answer platforms. With the continuous evolution of large…
Recent Large Language Models (LLMs) have demonstrated remarkable capabilities in generating text that closely resembles human writing across wide range of styles and genres. However, such capabilities are prone to potential abuse, such as…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
Event Extraction bridges the gap between text and event signals. Based on the assumption of trigger-argument dependency, existing approaches have achieved state-of-the-art performance with expert-designed templates or complicated decoding…
When developing text classification models for real world applications, one major challenge is the difficulty to collect sufficient data for all text classes. In this work, we address this challenge by utilizing large language models (LLMs)…
Verification proofs encode complete program behavior, yet we discard them after checking correctness. We present compiling by proving, a paradigm that transforms these proofs into optimized execution rules. By constructing All-Path…
The work relates to the automatic generation of logical specifications, considered as sets of temporal logic formulas, extracted directly from developed software models. The extraction process is based on the assumption that the whole…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and…
Generating metaphors is a difficult task as it requires understanding nuanced relationships between abstract concepts. In this paper, we aim to generate a metaphoric sentence given a literal expression by replacing relevant verbs. Guided by…
Decision-making usually takes five steps: identifying the problem, collecting data, extracting evidence, identifying pro and con arguments, and making decisions. Focusing on extracting evidence, this paper presents a hybrid model that…
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
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…
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This…
Enthymemes are defined as arguments where a premise or conclusion is left implicit. We tackle the task of generating the implicit premise in an enthymeme, which requires not only an understanding of the stated conclusion and premise but…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…