Continuous queries over data streams may suffer from blocking operations
and/or unbound wait, which may delay answers until some relevant input arrives
through the data stream. These delays may turn answers, when they arrive,
obsolete to users who sometimes have to make decisions with no help whatsoever.
Therefore, it can be useful to provide hypothetical answers – “given the
current information, it is possible that X will become true at time t” –
instead of no information at all.

In this paper we present a semantics for queries and corresponding answers
that covers such hypothetical answers, together with an online algorithm for
updating the set of facts that are consistent with the currently available
information.

Continuous queries over data streams can be complex and challenging due to the potential for blocking operations and unbound wait times. These issues can lead to delays in providing answers to users, making the information potentially obsolete by the time it arrives. This can be problematic, especially in scenarios where users need timely information to make informed decisions.

One approach to address this problem is to provide hypothetical answers to users based on the current information available. By presenting hypothetical answers such as “given the current information, it is possible that X will become true at time t,” users can at least have some guidance or direction when making decisions.

This paper introduces a semantics for queries and answers that incorporates these hypothetical answers. By considering possible future scenarios based on the available information, this approach helps to mitigate the negative impact of delays in continuous queries over data streams.

In addition to the theoretical framework, the paper also presents an online algorithm for updating the set of facts that are consistent with the currently available information. This algorithm enables the system to dynamically adapt and incorporate new information as it becomes available, ensuring that the hypothetical answers remain relevant and accurate.

This research brings together concepts from multiple disciplines, including data management, stream processing, and decision-making. The multi-disciplinary nature of the concepts presented in this paper highlights the need for collaborative efforts and cross-disciplinary approaches to tackle complex problems in data analysis and decision support systems.

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