Related papers: Compositional Hoare-style Reasoning about Hybrid C…
Language-enabled AI systems can answer complex, multi-hop questions to high accuracy, but supporting answers with evidence is a more challenging task which is important for the transparency and trustworthiness to users. Prior work in this…
We propose a new approach to formally describing the requirement for statistical inference and checking whether a program uses the statistical method appropriately. Specifically, we define belief Hoare logic (BHL) for formalizing and…
Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler…
We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…
We describe a program logic for weak memory (also known as relaxed memory). The logic is based on Hoare logic within a thread, and rely/guarantee between threads. It is presented via examples, giving proofs of many weak-memory litmus tests.…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
Programs must be correct with respect to their application domain. Yet, the program specification and verification approaches so far only consider correctness in terms of computations. In this work, we present a two-tier Hoare Logic that…
Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative to formal methods in…
Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of…
Relational Hoare logics extend the applicability of modular, deductive verification to encompass important 2-run properties including dependency requirements such as confidentiality and program relations such as equivalence or similarity…
We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Concurrent separation logic with fractional permissions (CSLPerm) provides a promising reasoning system to verify most complex sequential and concurrent fine-grained programs. The logic with strong and weak separating conjunctions offers a…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
Languages based on the theory of timed automata are a well established approach for modelling and analysing real-time systems, with many applications both in industrial and academic context. Model checking for timed automata has been…
A simple dynamically-typed, (purely) object-oriented language is defined. A structural operational semantics as well as a Hoare-style program logic for reasoning about programs in the language in multiple notions of correctness are given.…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…
We present a semantic framework for the deductive verification of hybrid systems with Isabelle/HOL. It supports reasoning about the temporal evolutions of hybrid programs in the style of differential dynamic logic modelled by flows or…
Constrained Horn Clauses (CHCs) are an intermediate program representation that can be generated by several verification tools, and that can be processed and solved by a number of Horn solvers. One of the main challenges when using CHCs in…