Related papers: Hammering Higher Order Set Theory
LLMs have demonstrated strong mathematical reasoning abilities by leveraging reinforcement learning with long chain-of-thought, yet they continue to struggle with theorem proving due to the lack of clear supervision signals when solely…
Quite often, verification tasks for distributed systems are accomplished via counter abstractions. Such abstractions can sometimes be justified via simulations and bisimulations. In this work, we supply logical foundations to this practice,…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…
The program Reverse Mathematics in the foundations of mathematics seeks to identify the minimal axioms required to prove theorems of ordinary mathematics. One always assumes the base theory, a logical system embodying computable…
We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics. We propose a two stage approach for this task that yields good results…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Subatomic logic is a recent innovation in structural proof theory where atoms are no longer the smallest entity in a logical formula, but are instead treated as binary connectives. As a consequence, we can give a subatomic proof system for…
Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI…
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.
We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…
Classical automata theory is far more capable of modeling complex digital systems than is widely acknowledged in the ``formal methods'' literature. This paper takes a second look at automata theory methods that were mostly developed in the…
Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…
Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation…
This paper shows how the use of Structural Operational Semantics (SOS) in the style popularized by the process-algebra community can lead to a more succinct and useful construction for building finite automata from regular expressions. Such…
Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplication, etc. We observe that fast-growing hierarchies can be…
In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on…
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…