Related papers: Automated Theorem Proving in Intuitionistic Propos…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Although traditional symbolic reasoning methods are highly interpretable, their application in knowledge graph link prediction is limited due to their low computational efficiency. In this paper, we propose a new neural symbolic reasoning…
Background & Objectives: In the last decade, Machine learning research has grown rapidly, but large models are reaching their soft limits demonstrating diminishing returns and still lack solid reasoning abilities. These limits could be…
Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the…
Enhancing reasoning capabilities remains a central focus in the LLM reasearch community. A promising direction involves requiring models to simulate code execution step-by-step to derive outputs for given inputs. However, as code is often…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
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…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
In structural proof theory, designing and working on large calculi make it difficult to get intuitions about each rule individually and as part of a whole system. We introduce two novel tools to help working on calculi using the approach of…
The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers…
Automated penetration testing (AutoPT) based on reinforcement learning (RL) has proven its ability to improve the efficiency of vulnerability identification in information systems. However, RL-based PT encounters several challenges,…
This study presents the first examination of the ability of Large Language Models (LLMs) to follow reasoning strategies that are used to guide Automated Theorem Provers (ATPs). We evaluate the performance of GPT4, GPT3.5 Turbo and Google's…
While knowledge representation and reasoning are considered the keys for human-level artificial intelligence, connectionist networks have been shown successful in a broad range of applications due to their capacity for robust learning and…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
Argument Mining (AM) helps in automating the extraction of complex argumentative structures such as Argument Components (ACs) like Premise, Claim etc. and Argumentative Relations (ARs) like Support, Attack etc. in an argumentative text. Due…
This paper proposes a new architecture - Attentive Tensor Product Learning (ATPL) - to represent grammatical structures in deep learning models. ATPL is a new architecture to bridge this gap by exploiting Tensor Product Representations…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
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…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…