Related papers: From Qualitative to Quantitative Proofs of Securit…
We introduce First-Order Coalition Logic ($\mathsf{FOCL}$), which combines key intuitions behind Coalition Logic ($\mathsf{CL}$) and Strategy Logic ($\mathsf{SL}$). Specifically, $\mathsf{FOCL}$ allows for arbitrary quantification over…
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…
Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…
Assurance arguments provide a clear and structured way to explain why stakeholders should trust that a system satisfies certain properties, yet widely used notations, e.g.Goal Structuring Notation (GSN), typically lack an operational…
Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e.,…
This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We introduce an infinitary first order linear logic with least and greatest fixed points. To ensure cut elimination, we impose a validity condition on infinite derivations. Our calculus is designed to reason about rich signatures of…
The one-variable fragment of a first-order logic may be viewed as an "S5-like" modal logic, where the universal and existential quantifiers are replaced by box and diamond modalities, respectively. Axiomatizations of these modal logics have…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
First Order Logic (FOL) is a powerful reasoning tool for program verification. Recent work on Ivy shows that FOL is well suited for verification of parameterized distributed systems. However, specifying many natural objects, such as a ring…
Many privacy-type properties of security protocols can be modelled using trace equivalence properties in suitable process algebras. It has been shown that such properties can be decided for interesting classes of finite processes (i.e.,…
Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…
In process algebras, security properties are expressed as equivalences between processes, but which equivalence is suitable is not clear. This means that there is a gap between an intuitive security notion and the formulation. Appropriate…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…