Related papers: Deciding KAT and Hoare Logic with Derivatives
We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice…
In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…
Reactive programs are ubiquitous in modern applications, and so verification is highly desirable. We present a verification strategy for reactive programs with a large or infinite state space utilising algebraic laws for reactive relations.…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
We survey the landscape of Hoare logics for quantum programs. We review three papers: "Reasoning about imperative quantum programs" by Chadha, Mateus and Sernadas; "A logic for formal verification of quantum programs" by Yoshihiko Kakutani;…
Despite the impressive performance of large language models (LLMs) pretrained on vast knowledge corpora, advancing their knowledge manipulation-the ability to effectively recall, reason, and transfer relevant knowledge-remains challenging.…
We prove that the equational theory of Kleene algebra with commutativity conditions on primitives (or atomic terms) is undecidable, thereby settling a longstanding open question in the theory of Kleene algebra. While this question has also…
Regular expressions are widely used in software. Various regular expression engines support different combinations of extensions to classical regular constructs such as Kleene star, concatenation, nondeterministic choice (union in terms of…
Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (such as functional correctness). Hoare logic has been…
Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…
We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs $P$ and $Q$ and vocabulary $V$ (set of predicates) the existence of a program $R$ in $V$ such that $P \cup R$ and $P \cup…
We present a formal system for proving the partial correctness of a single-pass instruction sequence as considered in program algebra by decomposition into proofs of the partial correctness of segments of the single-pass instruction…
In this paper, we show that the equational theory of relational Kleene algebra with the \emph{graph loop} operator (a.k.a.~\emph{fixset}) is \textsc{PSpace}-complete. Here, the graph loop is the unary operator that restricts a binary…
Modern software is constantly changing. Researchers and practitioners are increasingly aware that verification tools can be impactful if they embrace change through analyses that are compositional and span program versions. Reasoning about…
Formally specifying, let alone verifying, properties of systems involving multiple programming languages is inherently challenging. We introduce Heterogeneous Dynamic Logic (HDL), a framework for combining reasoning principles from distinct…
Evaluating the capabilities and risks of foundation models is paramount, yet current methods demand extensive domain expertise, hindering their scalability as these models rapidly evolve. We introduce SKATE: a novel evaluation framework in…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of…