Related papers: Investigations into Proof Structures
The difficulties of automatic extraction of definitions and methods from scientific documents lie in two aspects: (1) the complexity and diversity of natural language texts, which requests an analysis method to support the discovery of…
Large language models (LLMs) have been increasingly used to analyze text. However, they are often plagued with contextual reasoning limitations when analyzing long documents. When long documents are processed sequentially, early or dominant…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent…
To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…
The most important problems for society are describable only in vague terms, dependent on subjective positions, and missing highly relevant data. This thesis is intended to revive and further develop the view that giving non-trivial,…
Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
As LLMs make their way into many aspects of our lives, one place that warrants increased scrutiny with LLM usage is scientific research. Using LLMs for generating or analyzing data for research purposes is gaining popularity. But when such…
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…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Friedmann-Lemaitre universe. We explain and employ some basic concepts such as Dirac observables, Dirac brackets, gauge-fixing…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models…
We introduce a new approach to image forensics: placing physical refractive objects, which we call totems, into a scene so as to protect any photograph taken of that scene. Totems bend and redirect light rays, thus providing multiple,…
This methods article presents a reproducible calibration workflow for prompt-based large language models (LLMs) in structured evidence-synthesis tasks. The method separates the rules that define the scientific task from the mutable prompt…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Urban and Bierman introduced a calculus of proof terms for the sequent calculus LK with a strongly normalizing reduction relation. We extend this calculus to simply-typed higher-order logic with inferences for induction and equality, albeit…
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…