This paper presents a logic framework for modeling the interaction among deductive databases in a P2P (Peer to Peer) environment. Each peer joining a P2P system provides or imports data from its neighbors by using a set of mapping rules, i.e. a set of semantic correspondences to a set of peers belonging to the same environment. Two different types of mapping rules are defined: mapping rules allowing to import a maximal set of atoms not leading to inconsistency (called maximal mapping rules) and mapping rules allowing to import a minimal set of atoms needed to restore consistency (called minimal mapping rules). Implicitly, the use of maximal mapping rules states it is preferable to import as long as no inconsistencies arise; whereas the use of minimal mapping rules states that it is preferable not to import unless a inconsistency exists. The paper presents three different declarative semantics of a P2P system: (i) the Max Weak Model Semantics, in which mapping rules are used to import as much knowledge as possible from a peer's neighborhood without violating local integrity constraints; (ii) the Min Weak Model Semantics, in which the P2P system can be locally inconsistent and the information provided by the neighbors is used to restore consistency, that is to only integrate the missing portion of a correct, but incomplete database; (iii) the Max-Min Weak Model Semantics that unifies the previous two different perspectives captured by the Max Weak Model Semantics and Min Weak Model Semantics. This last semantics allows to characterize each peer in the neighborhood as a resource used either to enrich (integrate) or to fix (repair) the knowledge, so as to define a kind of integrate-repair strategy for each peer. Under consideration in Theory and Practice of Logic Programming (TPLP).
------------------------- In @cite_6 several techniques for optimizing the reformulation of queries in a PDMS are presented. In particular the paper presents techniques for pruning semantic paths of mappings in the reformulation process and for minimizing the reformulated queries. The design of optimization methods for query processing over a network of semantically related data is investigated in @cite_40 . ------------------------------------------------------------
@cite_40 @cite_6
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Peer data management systems (PDMS) offer a flexible architecture for decentralized data sharing. In a PDMS, every peer is associated with a schema that represents the peer's domain of interest, and semantic relationships between peers are provided locally between pairs (or small sets) of peers. By traversing semantic paths of mappings, a query over one peer can obtain relevant data from any reachable peer in the network. Semantic paths are traversed by reformulating queries at a peer into queries on its neighbors.Naively following semantic paths is highly inefficient in practice. We describe several techniques for optimizing the reformulation process in a PDMS and validate their effectiveness using real-life data sets. In particular, we develop techniques for pruning paths in the reformulation process and for minimizing the reformulated queries as they are created. In addition, we consider the effect of the strategy we use to search through the space of reformulations. Finally, we show that pre-computing semantic paths in a PDMS can greatly improve the efficiency of the reformulation process. Together, all of these techniques form a basis for scalable query reformulation in PDMS.To enable our optimizations, we developed practical algorithms, of independent interest, for checking containment and minimization of XML queries, and for composing XML mappings. Search logs contain examples of frequently occurring patterns of user reformulations of queries. Intuitively, the reformulation "San Francisco" -- "San Francisco 49ers" is semantically similar to "Detroit" -- "Detroit Lions". Likewise, "London" -- "things to do in London" and "New York" -- "New York tourist attractions" can also be considered similar transitions in intent. The reformulation "movies" -- "new movies" and "york" -- "New York", however, are clearly different despite the lexical similarities in the two reformulations. In this paper, we study the distributed representation of queries learnt by deep neural network models, such as the Convolutional Latent Semantic Model, and show that they can be used to represent query reformulations as vectors. These reformulation vectors exhibit favourable properties such as mapping semantically and syntactically similar query changes closer in the embedding space. Our work is motivated by the success of continuous space language models in capturing relationships between words and their meanings using offset vectors. We demonstrate a way to extend the same intuition to represent query reformulations. Furthermore, we show that the distributed representations of queries and reformulations are both useful for modelling session context for query prediction tasks, such as for query auto-completion (QAC) ranking. Our empirical study demonstrates that short-term (session) history context features based on these two representations improves the mean reciprocal rank (MRR) for the QAC ranking task by more than 10 over a supervised ranker baseline. Our results also show that by using features based on both these representations together we achieve a better performance, than either of them individually. We critically evaluate the current state of research in multiple query opGrnization, synthesize the requirements for a modular opCrnizer, and propose an architecture. Our objective is to facilitate future research by providing modular subproblems and a good general-purpose data structure. In rhe context of this archiuzcture. we provide an improved subsumption algorithm. and discuss migration paths from single-query to multiple-query oplimizers. The architecture has three key ingredients. First. each type of work is performed at an appropriate level of abstraction. Segond, a uniform and very compact representation stores all candidate strategies. Finally, search is handled as a discrete optimization problem separable horn the query processing tasks. 1. Problem Definition and Objectives A multiple query optimizer (h4QO) takes several queries as input and seeks to generate a good multi-strategy, an executable operator gaph that simultaneously computes answers to all the queries. The idea is to save by evaluating common subexpressions only once. The commonalities to be exploited include identical selections and joins, predicates that subsume other predicates, and also costly physical operators such as relation scans and SOULS. The multiple query optimization problem is to find a multi-strategy that minimizes the total cost (with overlap exploited). Figure 1 .l shows a multi-strategy generated exploiting commonalities among queries Ql-Q3 at both the logical and physical level. To be really satisfactory, a multi-query optimization algorithm must offer solution quality, ejjiciency, and ease of Permission to copy without fee all a part of this mataial is granted provided that the copies are nut made a diitributed for direct commercial advantage, the VIDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Da Blse Endowment. To copy otherwise. urturepublim identify many kinds of commonalities (e.g., by predicate splitting, sharing relation scans); and search effectively to choose a good combination of l-strategies. Efficiency requires that the optimization avoid a combinatorial explosion of possibilities, and that within those it considers, redundant work on common subexpressions be minimized. ‘Finally, ease of implementation is crucial an algorithm will be practically useful only if it is conceptually simple, easy to attach to an optimizer, and requires relatively little additional soft- The purpose of semantic query optimization is to use semantic knowledge (e.g., integrity constraints) for transforming a query into a form that may be answered more efficiently than the original version. In several previous papers we described and proved the correctness of a method for semantic query optimization in deductive databases couched in first-order logic. This paper consolidates the major results of these papers emphasizing the techniques and their applicability for optimizing relational queries. Additionally, we show how this method subsumes and generalizes earlier work on semantic query optimization. We also indicate how semantic query optimization techniques can be extended to databases that support recursion and integrity constraints that contain disjunction, negation, and recursion.