Related papers: A Complete Axiomatisation for Quantifier-Free Sepa…
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…
Quantitative separation logic (QSL) is an extension of separation logic (SL) for the verification of probabilistic pointer programs. In QSL, formulae evaluate to real numbers instead of truth values, e.g., the probability of memory-safe…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
We construct a complex entire function with arbitrary number of variables which has the following property: The infinite set consisting of all the values of all its partial derivatives of any orders at all algebraic points, including zero…
A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Algebraic approach to quantum non - separability is applied to the case of two qubits. It is based on the partition of the algebra of observables into independent subalgebras and the tensor product structure of the Hilbert space is not…
We investigate the complexity consequences of adding pointer arithmetic to separation logic. Specifically, we study extensions of the points-to fragment of symbolic-heap separation logic with various forms of Presburger arithmetic…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…
We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding…
For over two decades Separation Logic has been arguably the most popular framework for reasoning about heap-manipulating programs, as well as reasoning about shared resources and permissions. Separation Logic is often extended to include…
The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
This paper introduces a dynamic logic extension of separation logic. The assertion language of separation logic is extended with modalities for the five types of the basic instructions of separation logic: simple assignment, look-up,…
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…