Higher-order logic and infinitary logic are two extensions of first-order logic that allow greater expressivity. Both features have not been investigated together yet. In this paper, we define a higher-order infinitary logic, based on an extension of simple type theory. The resulting logic features higher-order quantifiers, infinite conjunctions and infinite disjunctions. We establish results at both the syntactic and the semantic level. We introduce a sound notion of model, and we show a strong version of completeness that entails the cut-elimination theorem for natural deduction. Moreover, we prove an extension of Barr’s theorem, allowing us to constructivize classical proofs of a particular fragment of higher-order infinitary logic.

In this paper, we present a general strategy that enables the translation of tableau proofs using different Skolemization rules into machine-checkable proofs. It is part of a framework that enables (i) instantiation of the strategy into algorithms for different sets of tableau rules (e.g., different logics) and (ii) easy soundness proof which relies on the local extensibility of user-defined rules. Furthermore, we propose an instantiation of this strategy for first-order tableaux that handles notably pre-inner Skolemization rules, which is, as far as the authors know, the first one in the literature. This deskolemization strategy has been implemented in the Goéland [17] automated theorem prover, enabling an export of its proofs to Coq [8] and Lambdapi [2]. Finally, we have evaluated the algorithm performances for inner and pre-inner Skolemization rules through the certification of proofs from some categories of the TPTP [39] library.

Identifying the root cause and impact of a system intrusion remains a foundational challenge in computer security. Digital provenance provides a detailed history of the flow of information within a computing system, connecting suspicious events to their root causes. Although existing provenance-based auditing techniques provide value in forensic analysis, they assume that such analysis takes place only retrospectively. Such post-hoc analysis is insufficient for realtime security applications; moreover, even for forensic tasks, prior provenance collection systems exhibited poor performance and scalability, jeopardizing the timeliness of query responses. We present CamQuery, which provides inline, realtime provenance analysis, making it suitable for implementing security applications. CamQuery is a Linux Security Module that offers support for both userspace and in-kernel execution of analysis applications. We demonstrate the applicability of CamQuery to a variety of runtime security applications including data loss prevention, intrusion detection, and regulatory compliance. In evaluation, we demonstrate that CamQuery reduces the latency of realtime query mechanisms, while imposing minimal overheads on system execution. CamQuery thus enables the further deployment of provenance-based technologies to address central challenges in computer security.

Concern about data leakage is holding back more widespread adoption of cloud computing by companies and public institutions alike. To address this, cloud tenants/applications are traditionally isolated in virtual machines or containers. But an emerging requirement is for cross-application sharing of data, for example, when cloud services form part of an IoT architecture. Information Flow Control (IFC) is ideally suited to achieving both isolation and data sharing as required. IFC enhances traditional Access Control by providing continuous, data-centric, cross-application, end-to-end control of data flows. However, large-scale data processing is a major requirement of cloud computing and is infeasible under standard IFC. We present a novel, enhanced IFC model that subsumes standard models. Our IFC model supports `Big Data' processing, while retaining the simplicity of standard IFC and enabling more concise, accurate and maintainable expression of policy.

We introduce INICheck, a translation tool from a new programming language called INI, which combines both rule-based and event-based programming styles into Promela, the language of the model-checker SPIN. INI allows the definitions of rules that can be triggered by events, that are implemented in a multithreaded way. This makes it suitable for many types of applications such as embedded applications and self-adaptive software. Moreover, by using INICheck, programmers can verify constraints, which need to be satisfied in their INI programs.

Two main lines have been adopted to prove the cut elimination theorem: the syntactic one, that studies the process of reducing cuts, and the semantic one, that consists in interpreting a sequent in some algebra and extracting from this interpretation a cut-free proof of this very sequent. A link between those two methods was exhibited by studying in a semantic way, syntactical tools that allow to prove (strong) normalization of proof-terms, namely reducibility candidates. In the case of deduction modulo, a framework combining deduction and rewriting rules in which theories like Zermelo set theory and higher order logic can be expressed, this is obtained by constructing a reducibility candidates valued model. The existence of such a pre-model for a theory entails strong normalization of its proof-terms and, by the usual syntactic argument, the cut elimination property. In this paper, we strengthen this gate between syntactic and semantic methods, by providing a full semantic proof that the existence of a pre-model entails the cut elimination property for the considered theory in deduction modulo. We first define a new simplified variant of reducibility candidates à la Girard, that is sufficient to prove weak normalization of proof-terms (and therefore the cut elimination property). Then we build, from some model valued on the pre-Heyting algebra of those WN reducibility candidates, a regular model valued on a Heyting algebra on which we apply the usual soundness/strong completeness argument. Finally, we discuss further extensions of this new method towards normalization by evaluation techniques that commonly use Kripke semantics.

Olivier Hermant, James Lipton; Completeness and Cut-elimination in the Intuitionistic Theory of Types—Part 2, Journal of Logic and Computation, Volume 20,