Belief Semantics of Authorization Logic

Authorization logics have been used in the theory of computer security to reason about access control decisions. In this work, a formal belief semantics for authorization logics is given. The belief semantics is proved to subsume a standard Kripke semantics. The belief semantics yields a direct representation of principals' beliefs, without resorting to the technical machinery used in Kripke semantics. A proof system is given for the logic; that system is proved sound with respect to the belief and Kripke semantics. The soundness proof for the belief semantics, and for a variant of the Kripke semantics, is mechanized in Coq

On the strength of proof-irrelevant type theories

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic. Finally we describe a simple set-theoretic semantics.Comment: 20 pages, Logical Methods in Computer Science, Long version of IJCAR 2006 pape

An Automatic Technique for Checking the Simulation of Timed Systems

International audienceIn this paper, we suggest an automatic technique for checking the timed weak simulation between timed transition systems. The technique is an observation-based method in which two timed transition systems are composed with a timed observer. A μ-calculus property that captures the timed weak simulation is then verified on the result of the composition. An interesting feature of the suggested technique is that it only relies on an untimed μ-calculus model-checker without any specific algorithm needed to analyze the result of the composition. We also show that our simulation relation supports interesting results concerning the trace inclusion and the preservation of linear properties. Finally, the technique is validated using the FIACRE/TINA toolset

A Fully Verified Executable LTL Model Checker

International audienceWe present an LTL model checker whose code has been completely verified using the Isabelle theorem prover. The checker consists of over 4000 lines of ML code. The code is produced using recent Isabelle technology called the Refinement Framework, which allows us to split its correctness proof into (1) the proof of an abstract version of the checker, consisting of a few hundred lines of “formalized pseudocode”, and (2) a verified refinement step in which mathematical sets and other abstract structures are replaced by implementations of efficient structures like red-black trees and functional arrays. This leads to a checker that, while still slower than unverified checkers, can already be used as a trusted reference implementation against which advanced implementations can be tested. We report on the structure of the checker, the development process, and some experiments on standard benchmarks

Formalizing alternating-time temporal logic in the coq proof assistant

This work presents a complete formalization of Alternating-time Temporal Logic (ATL) and its semantic model, Concurrent Game Structures (CGS), in the Calculus of (Co)Inductive Constructions, using the logical framework Coq. Unlike standard ATL semantics, temporal operators are formalized in terms of inductive and coinductive types, employing a fixpoint characterization of these operators. The formalization is used to model a concurrent system with an unbounded number of players and states, and to verify some properties expressed as ATL formulas. Unlike automatic techniques, our formal model has no restrictions in the size of the CGS, and arbitrary state predicates can be used as atomic propositions of ATL. Keywords: Reactive Systems and Open Systems, Alternating-time Temporal Logic, Concurrent Game Structures, Calculus of (Co)Inductive Constructions, Coq Proof Assistant

Verified Decision Procedures for Modal Logics

We describe a formalization of modal tableaux with histories for the modal logics K, KT and S4 in Lean. We describe how we formalized the static and transitional rules, the non-trivial termination and the correctness of loop-checks. The formalized tableaux are essentially executable decision procedures with soundness and completeness proved. Termination is also proved in order to define them as functions in Lean. All of these decision procedures return a concrete Kripke model in cases where the input set of formulas is satisfiable, and a proof constructed via the tableau rules witnessing unsatisfiability otherwise. We also describe an extensible formalization of backjumping and its verified implementation for the modal logic K. As far as we know, these are the first verified decision procedures for these modal logics

Types and verification for infinite state systems

Server-like or non-terminating programs are central to modern computing. It is a common requirement for these programs that they always be available to produce a behaviour. One method of showing such availability is by endowing a type-theory with constraints that demonstrate that a program will always produce some behaviour or halt. Such a constraint is often called productivity. We introduce a type theory which can be used to type-check a polymorphic functional programming language similar to a fragment of the Haskell programming language. This allows placing constraints on program terms such that they will not type-check unless they are productive. We show that using program transformation techniques, one can restructure some programs which are not provably productive in our type theory into programs which are manifestly productive. This allows greater programmer flexibility in the specification of such programs. We have demonstrated a mechanisation of some of these important results in the proof-assistant Coq. We have also written a program transformation system for this term-language in the programming language Haskell

LF+ in Coq for fast-and-loose reasoning

We develop the metatheory and the implementation, in Coq, of the novel logical framework LF+ and discuss several of its applications. LF+ generalises research work, carried out by the authors over more than a decade, on Logical Frameworks conservatively extending LF and featuring lock-type constructors L-P(N:sigma)[center dot]. Lock-types capture monadically the concept of inhabitability up-to. They were originally introduced for factoring-out, postponing, or delegating to external tools the verification of time-consuming judgments, which are morally proof-irrelevant, thus allowing for integrating different sources of epistemic evidence in a unique Logical Framework. Besides introducing LF+ and its "shallow" implementation in Coq, the main novelty of the paper is to show that lock-types are also a very flexible tool for expressing in Type Theory several diverse cognitive attitudes and mental strategies used in ordinary reasoning, which essentially amount to reasoning up-to, as in e.g. Typical Ambiguity provisos or co-inductive Coq proofs. In particular we address the encoding of the emerging paradigm of fast-and-loose reasoning, which trades off efficiency for correctness. This paradigm, implicitly used normally in naive Set Theory, is producing considerable impact also in computer architecture and distributed systems, when branch prediction and optimistic concurrency control are implemented