Related papers: A Generalized Hybrid Hoare Logic
In probabilistic reasoning, the traditionally discrete domain has been elevated to the hybrid domain encompassing additionally continuous random variables. Inference in the hybrid domain, however, usually necessitates to condone trade-offs…
Split learning (SL) enables collaborative training of large language models (LLMs) between resource-constrained edge devices and compute-rich servers by partitioning model computation across the network boundary. However, existing SL…
Distributed system theory literature often argues for correctness using an informal, Hoare-like style of reasoning. While these arguments are intuitive, they have not all been foolproof, and whether they directly correspond to formal proofs…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
The $tock$-CSP encoding embeds a rich and flexible approach to modelling discrete timed behaviours in CSP where the event $tock$ is interpreted to mark the passage of time. The model checker FDR provides tailored support for $tock$-CSP,…
This paper presents a study of operational and type-theoretic properties of different resolution strategies in Horn clause logic. We distinguish four different kinds of resolution: resolution by unification (SLD-resolution), resolution by…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant…
Answer Set Programming (ASP) is a powerful tool for solving real-world problems. However, many problems involve numeric values and complex constraints beyond the capabilities of standard ASP solvers. Hybrid solvers like CLINGCON and…
The Epistemic Halpern-Shoham logic (EHS) is a temporal-epistemic logic that combines the interval operators of the Halpern-Shoham logic with epistemic modalities. The semantics of EHS is based on interpreted systems whose labelling function…
We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…
The automation of High-Level Context (HLC) reasoning across intelligent systems at scale is imperative because of the unceasing accumulation of contextual data, the trend of the fusion of data from multiple sources (e.g., sensors,…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program…
We have previously published the Isabelle/HOL formalization of a general theory of syntax with bindings. In this companion paper, we instantiate the general theory to the syntax of lambda-calculus and formalize the development leading to…
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we…
Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time…
The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak…