Related papers: A Sequent Calculus For Trace Formula Implication
Background: Establishing traceability from requirements documents to downstream artifacts early can be beneficial as it allows engineers to reason about requirements quality (e.g. completeness, consistency, redundancy). However, creating…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
Provenance for database queries or scientific workflows is often motivated as providing explanation, increasing understanding of the underlying data sources and processes used to compute the query, and reproducibility, the capability to…
Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof…
Runtime verification (RV) consists in dynamically verifying that the event traces generated by single runs of a system under scrutiny (SUS) are compliant with the formal specification of its expected properties. RML (Runtime Monitoring…
Traceability, the ability to trace relevant software artifacts to support reasoning about the quality of the software and its development process, plays a crucial role in requirements and software engineering, particularly for…
Modern software projects include automated tests written to check the programs' functionality. The set of functions invoked by a test is called the trace of the test, and the action of obtaining a trace is called tracing. There are many…
We introduce a cyclic proof system for the two-way alternation-free modal $\mu$-calculus. The system manipulates one-sided Gentzen sequents and locally deals with the backwards modalities by allowing analytic applications of the cut rule.…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
We present a new approach to the global fairness verification of tree-based classifiers. Given a tree-based classifier and a set of sensitive features potentially leading to discrimination, our analysis synthesizes sufficient conditions for…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
The problem of writing a specification which accurately reflects the intent of the developer has long been recognized as fundamental. We propose a method and a supporting tool to write and check a specification and an implementation using a…
Compiler correctness is, in its simplest form, defined as the inclusion of the set of traces of the compiled program into the set of traces of the original program, which is equivalent to the preservation of all trace properties. Here…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
The refinement calculus for logic programs is a framework for deriving logic programs from specifications. It is based on a wide-spectrum language that can express both specifications and code, and a refinement relation that models the…
The existence of trace links between artifacts of the software development life cycle can improve the efficiency of many activities during software development, maintenance and operations. Unfortunately, the creation and maintenance of…
We specify the operational semantics and bisimulation relations for the finite pi-calculus within a logic that contains the nabla quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…