This dissertation presents a unifying approach to process (recursive) queries and updates in a deductive database. To improve query performance, a combined top-down and bottom-up evaluation method is used to compile rules into iterative programs that contain relational algebra operators. This method is based on the lemma resolution that retains previous results to guarantee termination.

Due to locality in database processing, it is desirable to materialize frequently used queries against views of the database. Unfortunately, if updates are allowed, maintaining materialized view tables becomes a major problem. We propose to materialize views incrementally, as queries are being answered. Hence views in our approach are only partially materialized. For such views, we design algorithms to perform updates only when the underlying view tables are actually affected.

We compare our approach to two conventional methods for dealing with views: total materialization and query-modification. The first method materializes the entire view when it is defined while the second recomputes the view on the fly without maintaining any physical view tables. We demonstrate that our approach is a compromise between these two methods and performs better than either one in many situations.

It is also desirable to be able to update views just like updating base tables. However, view updates are inherently ambiguous and the semantics of update propagation on recursively defined views were not well understood in the past. Using dynamic logic programming and lemma resolution, we are able to define the semantics of recursive view updates. These are expressed in the form of update translators specified by the database administrator when the view is defined. To guarantee completeness, we identify a subset of safe update translators. We prove that this subset of translators always terminate and are complete.

We present an efficient scheme to terminate infinite recursion in function-free Horn logic. In [BW84], Brough and Walker show that a preorder linear resolution with a goal termination strategy is incomplete, i.e. it must miss some answers. Their theory is true if left-recursion is allowed. The crucial assumption underlying Brough and Walker's theory is that the order of literals in a clause should not be altered. This assumption, however, is not necessary in programs that do not contain any extra-logical features such as the 'cut' symbol of Prolog. This is because the order of literals does not affect the correctness of such programs, only their efficiency. In this paper, we show that left-recursion can always be eliminated. The idea is to transform loops of the input set into safe loops, that are left-recursion free. Consequently, the goal termination strategy guarantees to always terminate properly with all possible answers; thus, it is complete in the domain of safe loops. We further show that all rules in a safe loop can be transformed into rules that begin with a base literal. This permits the implementation of a simple scheme to carry out the goal termination strategy more efficiently. The basic idea of this scheme is to distribute the history containing all executed goals over assertions, rather than maintaining it as a centralized data structure. This reduces the amount of work performed during execution.

First-order Horn logic is a useful formalism to design knowledge-based systems. When implemented on a sequential von Neumann computer, the main limitation of such systems is performance. We present a message-driven model for function-free Horn logic, where the knowledge base is represented as a network of logical processing elements communicating with one another exclusively through messages. The lack of centralized control and centralized memory makes this model suitable to implementation on a highly-parallel asynchronous computer architecture.

The primary contribution of this paper is a performance analysis of this message-driven system and a comparison with a sequential resolution scheme using backtracking. For both approaches, closed form expressions for the performance results are derived and compared.