Related papers: Abstract Completion, Formalized
For engineering software with formal correctness proofs it is crucial that proofs can be efficiently reused in case the software or its specification is changed. Unfortunately, in reality even slight changes in the code or its specification…
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
Summaries are important when it comes to process huge amounts of information. Their most important benefit is saving time, which we do not have much nowadays. Therefore, a summary must be short, representative and readable. Generating…
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
Completion is a well-known transformation that captures the stable model semantics of logic programs by turning a program into a set of first-order definitions. Stable models are models of the completion, but not all models of the…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
This essay examines how automation has reconfigured mathematical proof and labor, and what might happen in the future. It discusses practical standards of proof, distinguishes between prominent forms of automation in research, provides…
Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel…
Software model checkers based on under-approximations and SMT solvers are very successful at verifying safety (i.e. reachability) properties. They combine two key ideas -- (a) "concreteness": a counterexample in an under-approximation is a…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Contextual refinement and separation logics are successful verification techniques that are very different in nature. First, the former guarantees behavioral refinement between a concrete program and an abstract program while the latter…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Work in progress concerning alternative formalizations of arithmetic.
In a recent paper by Harrison et al., the concept of program completion is extended to a large class of programs in the input language of the ASP grounder gringo. We would like to automate the process of generating and simplifying…
We propose an abstraction-based model checking method which relies on refinement of an under-approximation of the feasible behaviors of the system under analysis. The method preserves errors to safety properties, since all analyzed…
We describe a derivational approach to abstract interpretation that yields novel and transparently sound static analyses when applied to well-established abstract machines for higher-order and imperative programming languages. To…
We provide a literature review about Automatic Text Summarization (ATS) systems. We consider a citation-based approach. We start with some popular and well-known papers that we have in hand about each topic we want to cover and we have…