A Case for Stale Synchronous Distributed Model for Declarative Recursive Computation

A large class of traditional graph and data mining algorithms can be concisely expressed in Datalog, and other Logic-based languages, once aggregates are allowed in recursion. In fact, for most BigData algorithms, the difficult semantic issues raised by the use of non-monotonic aggregates in recursion are solved byPre-Mappability(${\cal P}$reM), a property that assures that for a program with aggregates in recursion there is an equivalent aggregate-stratified program. In this paper we show that, by bringing together the formal abstract semantics of stratified programs with the efficient operational one of unstratified programs,$\[{\cal P}\]$reMcan also facilitate and improve their parallel execution. We prove that$\[{\cal P}\]$reM-optimized lock-free and decomposable parallel semi-naive evaluations produce the same results as the single executor programs. Therefore,$\[{\cal P}\]$reMcan be assimilated into the data-parallel computation plans of different distributed systems, irrespective of whether these follow bulk synchronous parallel (BSP) or asynchronous computing models. In addition, we show that non-linear recursive queries can be evaluated using a hybrid stale synchronous parallel (SSP) model on distributed environments. After providing a formal correctness proof for the recursive query evaluation with$\[{\cal P}\]$reMunder this relaxed synchronization model, we present experimental evidence of its benefits.

Secrecy-Preserving Reasoning and Query Answering in Probabilistic Description Logic Knowledge Bases

In this paper we study Secrecy-Preserving Query Answering problem underthe OpenWorld Assumption (OWA) for Prob-EL>0;=1 Knowledge Bases(KBs). We have designed a tableau procedure to compute a semi model Mover the given KB which eventually is equivalent to a probabilistic modelto KB. Given a secrecy set S, which is a finite set of assertions, wecompute a function E, called an envelope of S, which assigns a set E() ofassertions to each world in the semi modal M. E provides logical protection to the secrecy set S against the reasoning of a querying agent. Once the semi model M and an envelope E are computed, we define the secrecy-preserving semi model ME.Based on the information available in ME, assertional queries with probabilisticoperators can be answered eciently while preserving secrecy. Tothe best of our knowledge, this work is first one studying secrecy-preservingreasoning in description logic augmented with probabilistic operators. Whenthe querying agent asks a query q, the reasoner answers “Yes” if informationabout q is available in ME; otherwise, the reasoner answers “Unknown”. Beingable to answer “Unknown” plays a key role in protecting secrecy underOWA. Since we are not computing all the consequences of the knowledgebase, answers to the queries based on just secrecy-preserving semi modelME could be erroneous. To fix this problem, we further augment our algorithmsby providing recursive query decomposition algorithm to make thequery answering procedure foolproof.1

An Operational Semantics for Network Datalog

Network Datalog (<i>NDlog</i>) is a recursive query language that extends Datalog by allowing programs to be distributed in a network. In our initial efforts to formally specify <i>NDlog</i>'s operational semantics, we have found several problems with the current evaluation algorithm being used, including unsound results, unintended multiple derivations of the same table entry, and divergence. In this paper, we make a first step towards correcting these problems by formally specifying a new operational semantics for <i>NDlog</i> and proving its correctness for the fragment of non-recursive programs. We also argue that if termination is guaranteed, then the results also extend to recursive programs. Finally, we identify a number of potential implementation improvements to <i>NDlog</i>.