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The need for formal definition of the very basis of mathematics arose in the last century. The scale and complexity of mathematics, along with discovered paradoxes, revealed the danger of accumulating errors across theories. Although,…
Set theory is foundational to mathematics and, when sets are finite, to reasoning about the world. An intelligent system should perform set operations consistently, regardless of superficial variations in the operands. Initially designed…
Agentic theorem provers often introduce intermediate lemmas, proof sketches, or subgoal decompositions before returning to tactic-level search. This can look like an expensive detour: if proving lemmas is itself hard, why should a learned…
Artificial intelligence is reshaping science and industry, yet many users still regard its models as opaque "black boxes". Conventional explainable artificial-intelligence methods clarify individual predictions but overlook the upstream…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
The AI community is increasingly focused on merging logic with deep learning to create Neuro-Symbolic (NeSy) paradigms and assist neural approaches with symbolic knowledge. A significant trend in the literature involves integrating axioms…
Most existing prompting methods suffer from the issues of generalizability and consistency, as they often rely on instance-specific solutions that may not be applicable to other instances and lack task-level consistency across the selected…
There have been several research works proposing new Explainable AI (XAI) methods designed to generate model explanations having specific properties, or desiderata, such as fidelity, robustness, or human-interpretability. However,…
The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising…
We introduce OpSets, an executable framework for specifying and reasoning about the semantics of replicated datatypes that provide eventual consistency in a distributed system, and for mechanically verifying algorithms that implement these…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…
Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…
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…
Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…
Graphical user interface (GUI) agents powered by large vision-language models (VLMs) have shown remarkable potential in automating digital tasks, highlighting the need for high-quality trajectory data to support effective agent training.…
Large Language Models (LLMs) have emerged as powerful tools for generating coherent text, understanding context, and performing reasoning tasks. However, they struggle with temporal reasoning, which requires processing time-related…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…