Related papers: Formalization of PAL$\cdot$S5 in Proof Assistant
We introduce a framework for reasoning about the security of computer systems using modal logic. This framework is sufficiently expressive to capture a variety of known security properties, while also being intuitive and independent of…
Modal logics allow reasoning about various modes of truth: for example, what it means for something to be possibly true, or to know that something is true as opposed to merely believing it. This report describes embeddings of propositional…
Legal reasoning requires both precise interpretation of statutory language and consistent application of complex rules, presenting significant challenges for AI systems. This paper introduces a modular multi-agent framework that decomposes…
General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in…
Large Language Models (LLMs) have been successful in mathematical reasoning tasks such as formal theorem proving when integrated with interactive proof assistants like Lean. Existing approaches involve training or fine-tuning an LLM on a…
The provability logic of a theory $T$ captures the structural behavior of formalized provability in $T$ as provable in $T$ itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
The companion paper introduced a four-level verification lattice on agent-skill manifests (unverified, declared, tested, formal) and left the top level aspirational. This paper closes that gap. We give a precise semantics for skill…
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers. The following has been done (and in this order): A detailed natural deduction…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
We develop a proof-theoretic semantics -- in particular, a base-extension semantics -- for multi-agent S5 modal logic (and hence also for the usual unindexed S5). Following the inferentialist interpretation of logic, this gives us a…
In this paper we introduce {\em global and local announcement logic} (GLAL), a dynamic epistemic logic with two distinct announcement operators -- $[\phi]^+_A$ and $[\phi]^-_A$ indexed to a subset $A$ of the set $Ag$ of all agents -- for…
Information about the powers and abilities of acting entities is used to coordinate their actions in societies, either physical or digital. Yet, the commonsensical meaning of an acting entity being deemed able to do something is still…
The present dissertation introduces the research project on HOLMS (\textbf{HOL} Light Library for \textbf{M}odal \textbf{S}ystems), a growing modular framework for modal reasoning within the HOL Light proof assistant. To provide an…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO and have made significant progress. This paper focuses on formal verification,…