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An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
We present a neurosymbolic approach, i.e., combining symbolic and subsymbolic artificial intelligence, to validating offer documents in regulated public institutions. We employ a language model to extract information and then aggregate with…
Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal…
The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
Tree-structured recursive neural networks (TreeRNNs) for sentence meaning have been successful for many applications, but it remains an open question whether the fixed-length representations that they learn can support tasks as demanding as…
Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…
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…
Transformers, as the fundamental deep learning architecture, have demonstrated great capability in reasoning. This paper studies the generalizable first-order logical reasoning ability of transformers with their parameterized knowledge and…
Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…
Transformers have been shown to be able to perform deductive reasoning on a logical rulebase containing rules and statements written in natural language. Recent works show that such models can also produce the reasoning steps (i.e., the…
Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs,…
Probabilistic programming combines general computer programming, statistical inference, and formal semantics to help systems make decisions when facing uncertainty. Probabilistic programs are ubiquitous, including having a significant…
Herewith, a fairly old concept is published for the first time and named "Lucas Interpretation". This has been implemented in a prototype, which has been proved useful in educational practice and has gained academic relevance with an…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
This paper studies interpretable and fair artificial intelligence architectures for understanding English reading. Introduced transformer-based models, integrating advanced attention mechanisms and gradient-based feature attribution. The…
Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation…