Related papers: Formal Semantics and Formally Verified Validation …
This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for…
Isabelle is a generic theorem prover, designed for interactive reasoning in a variety of formal theories. At present it provides useful proof procedures for Constructive Type Theory, various first-order logics, Zermelo-Fraenkel set theory,…
The use of autonomous vehicles in real-world applications is often precluded by the difficulty of providing safety guarantees for their complex controllers. The simulation-based testing of these controllers cannot deliver sufficient safety…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis,…
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,…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We…
Previous work in the context of natural language querying of temporal databases has established a method to map automatically from a large subset of English time-related questions to suitable expressions of a temporal logic-like language,…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
Temporal logics are an obvious high-level descriptive companion formalism to dynamical systems which model behavior as deterministic evolution of state over time. A wide variety of distinct temporal logics applicable to dynamical systems…
In this paper we present a formal computational framework for modeling manipulation actions. The introduced formalism leads to semantics of manipulation action and has applications to both observing and understanding human manipulation…
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic.…
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We…
In previous work, summarized in this paper, we proposed an operation of parallel composition for rewriting-logic theories, allowing compositional specification of systems and reusability of components. The present paper focuses on…
Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…
Large language models (LLM), such as Google's Minerva and OpenAI's GPT families, are becoming increasingly capable of solving mathematical quantitative reasoning problems. However, they still make unjustified logical and computational…
Recently, a growing number of researchers have applied machine learning to assist users of interactive theorem provers. However, the expressive nature of underlying logics and esoteric structures of proof documents impede machine learning…
Virtually all verification techniques using formal methods rely on the availability of a formal specification, which describes the design requirements precisely. However, formulating specifications remains a manual task that is notoriously…
Proof assistants offer tactics to facilitate inductive proofs. However, it still requires human ingenuity to decide what arguments to pass to those induction tactics. To automate this process, we present smart_induct for Isabelle/HOL. Given…
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…