Abstract. Tabled evaluations can incorporate a number of features, including tabled negation, reduction with respect to the well-founded model, tabled constraints and answer subsumption. Many of these features are most efficiently evaluated using the Local evaluation strategy, which fully evaluates each mutually dependent set of tabled subgoals before returning answers to other subgoals outside of that set. In this paper, we introduce a formalism, Concurrent Local SLG by which multiple threads of computation concurrently perform Local evaluation of the well-founded semantics, and which is a framework for multi-threaded tabling in the XSB system. We prove several properties of Local evaluation within single-threaded tabled computation. We then extend SLG to a model of concurrency and show that the completeness and complexity of SLG are retained when computed by multiple threads. Finally, we extend Local evaluation to concurrent SLG, and show that the properties of Local evaluation continue to hold under concurrency.This paper provides an operational semantics for a type of concurrent TLP that relies on a scheduling strategy called Local evaluation [4]. The model of concurrency adopted is one in which threads of computation execute separate subgoals while sharing completed tables. The main idea behind Local evaluation is that it fully evaluates a single mutually dependent set of tabled subgoals before performing operations (such as returning answers) to subgoals outside of that set. Experiments in several implementations have shown that Local evaluation utilizes space efficiently (see e.g. [4,10]) and as a result it has been implemented for several Prologs.Another feature of Local evaluation is shown in an example in [4] in which tabling was used to compute the shortest path between two nodes. When Local evaluation was used the shortest path could be computed in a time proportional to the number of nodes in the graph, while if a non-Local scheduling strategy was used the time was proportional to the number of paths in the graph -i.e. the time was exponential in the number of nodes. Comparing path lengths to compute a shortest path can be considered as an instance of answer subsumption in which answers are retained and propagated only if they are maximal over a partial order or are a monotonic function of answers so far produced.Using SLG resolution [1] as a basis, this paper presents the following results about concurrent and Local evaluations.-As analysis of Local evaluation in the literature has been mostly empirical, Local SLG evaluation is formally defined in Section 2 and shown complete