Related papers: Making Relational Hoare Logic Alignment Complete
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…
While reachability analysis is one of the most promising approaches for formal verification of dynamic systems, a major disadvantage preventing a more widespread application is the requirement to manually tune algorithm parameters such as…
Constraint Handling Rules (CHR) is both an effective concurrent declarative constraint-based programming language and a versatile computational formalism. While conceptually simple, CHR is distinguished by a remarkable combination of…
Constraint Handling Rules (CHR) is a rule-based programming language which is typically embedded into a general-purpose language. There exists a plethora of implementations of CHR for numerous host languages. However, the existing…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
This paper investigates the relationship between the Logical Algorithms language (LA) of Ganzinger and McAllester and Constraint Handling Rules (CHR). We present a translation schema from LA to CHR-rp: CHR with rule priorities, and show…
We examine the relationships between axiomatic and cyclic proof systems for the partial and total versions of Hoare logic and those of its dual, known as reverse Hoare logic (or sometimes incorrectness logic). In the axiomatic proof systems…
Abstract interpretation, Hoare logic, and incorrectness (or reverse Hoare) logic are powerful techniques for static analysis of computer programs. All of them have been successfully extended to the quantum setting, but largely developed in…
Constraint Handling Rules is an effective concurrent declarative programming language and a versatile computational logic formalism. CHR programs consist of guarded reactive rules that transform multisets of constraints. One of the main…
Focus in Explainable AI is shifting from explanations defined in terms of low-level elements, such as input features, to explanations encoded in terms of interpretable concepts learned from data. How to reliably acquire such concepts is,…
Incorrectness Separation Logic (ISL) is a proof system designed to automate verification and detect bugs in programs manipulating heap memories. In this study, we extend ISL to support variable-length array predicates and pointer…
In search for a foundational framework for reasoning about observable behavior of programs that may not terminate, we have previously devised a trace-based big-step semantics for While. In this semantics, both traces and evaluation…
Coherence is an essential property of well-written texts, that refers to the way textual units relate to one another. In the era of generative AI, coherence assessment is essential for many NLP tasks; summarization, generation, long-form…
We consider the decidability of the verification problem of programs \emph{modulo axioms} --- that is, verifying whether programs satisfy their assertions, when the functions and relations it uses are assumed to interpreted by arbitrary…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
We consider enhancing large language models (LLMs) for complex planning tasks. While existing methods allow LLMs to explore intermediate steps to make plans, they either depend on unreliable self-verification or external verifiers to…
The introduction of machine learning methods has led to significant advances in automation, optimization, and discoveries in various fields of science and technology. However, their widespread application faces a fundamental limitation: the…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
This paper introduces a model theory for resolution on Higher Order Hereditarily Harrop formulae (HOHH), the logic underlying the Lambda-Prolog programming language, and proves soundness and completeness of resolution. The semantics and the…