No Arabic abstract
Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different styles, one based on abstract executions and the other based on dependency graphs. The choice between these styles has been made according to intended applications: the former has been used to specify and verify the implementation of these databases, and the latter to prove properties of programs running on top of the databases. In this paper, we present a set of novel algebraic laws (i.e. inequations) that connect these two styles of specifications; the laws relate binary relations used in a specification based on abstract executions, to those used in a specification based on dependency graphs. We then show that this algebraic connection gives rise to so called robustness criteria, conditions which ensures that a program running on top of a weakly-consistent database does not exhibit anomalous behaviours due to this weak consistency. These criteria make it easy to reason about programs running on top of these databases, and may become a basis for dynamic or static program analyses. For a certain class of consistency models specifications, we prove a full abstraction result that connects the two styles of specifications.
Motivated by recent work on weak distributive laws and their applications to coalgebraic semantics, we investigate the algebraic nature of semialgebras for a monad. These are algebras for the underlying functor of the monad subject to the associativity axiom alone-the unit axiom from the definition of an Eilenberg-Moore algebras is dropped. We prove that if the underlying category has coproducts, then semialgebras for a monad M are in fact the Eilenberg-Moore algebras for a suitable monad structure on the functor id + M , which we call the semifree monad M^s. We also provide concrete algebraic presentations for semialgebras for the maybe monad, the semigroup monad and the finite distribution monad. A second contribution is characterizing the weak distributive laws of the form M T $Rightarrow$ T M as strong distributive laws M^s T $Rightarrow$ T M^s subject to an additional condition.
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or by the throw of dice. This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabilities to these possible worlds. We present a novel syntax and semantics for such system, and show that they generalise Modal Logic. We also give a sound and complete calculus for reasoning in the base semantics, and a sound calculus for the full modal semantics, that we conjecture to be complete. Finally we discuss some application to reasoning about game playing agents.
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (ECNTL) and Nested Metric Temporal Logic (NMTL). The logic ECNTL is an extension of both the logic CARET (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of ECNTL and visibly model-checking of Visibly Pushdown Timed Automata VPTA against ECNTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to ECNTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete.
We study a variant of the Ackermann encoding $mathbb{N}(x) := sum_{yin x}2^{mathbb{N}(y)}$ of the hereditarily finite sets by the natural numbers, applicable to the larger collection $mathsf{HF}^{1/2}$ of the hereditarily finite hypersets. The proposed variation is obtained by simply placing a `minus sign before each exponent in the definition of $mathbb{N}$, resulting in the expression $mathbb{R}(x) := sum_{yin x}2^{-mathbb{R}(y)}$. By a careful analysis, we prove that the encoding $mathbb{R}_{A}$ is well-defined over the whole collection $mathsf{HF}^{1/2}$, as it allows one to univocally assign a real-valued code to each hereditarily finite hyperset. We also address some preliminary cases of the injectivity problem for $mathbb{R}_{A}$.
Spatial and spatio-temporal model checking techniques have a wide range of application domains, among which large scale distributed systems and signal and image analysis. We explore a new domain, namely (semi-)automatic contouring in Medical Imaging, introducing the tool VoxLogicA which merges the state-of-the-art library of computational imaging algorithms ITK with the unique combination of declarative specification and optimised execution provided by spatial logic model checking. The result is a rapid, logic based analysis development methodology. The analysis of an existing benchmark of medical images for segmentation of brain tumours shows that simple VoxLogicA analysis can reach state-of-the-art accuracy, competing with best-in-class algorithms, with the advantage of explainability and replicability. Furthermore, due to a two-orders-of-magnitude speedup compared to the existing general-purpose spatio-temporal model checker topochecker, VoxLogicA enables interactive development of analysis of 3D medical images, which can greatly facilitate the work of professionals in this domain.