The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and existential quantifiers are permitted to appear in mixed order in goals, the devices of logic variables and unification that are employed in solving existential goals must be modified to ensure that constraints arising out of the order of quantification are respected. Suitable modifications that are based on attaching numerical tags to constants and variables and on using these tags in unification are described. The resulting devices are amenable to an efficient implementation and can, in fact, be assimilated easily into the usual machinery of the Warren Abstract Machine (WAM). The provision of implications in goals results in the possibility of program clauses being added to the program for the purpose of solving specific subgoals. A naive scheme based on asserting and retracting program clauses does not suffice for implementing such additions for two reasons. First, it is necessary to also support the resurrection of an earlier existing program in the face of backtracking. Second, the possibility for implication goals to be surrounded by quantifiers requires a consideration of the parameterization of program clauses by bindings for their free variables. Devices for supporting these additional requirements are described as also is the integration of these devices into the WAM. Further extensions to the machine are outlined for handling higher-order additions to the language. The ideas presented here are relevant to the implementation of the higher-order logic programming language λProlog.

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SUMMARYTo deal with failures as simply as possible, we propose a new foundation for the core (untyped) C ++ , which is based on a new logic called task logic or imperative logic. We then introduce a sequentialdisjunctive statement of the form S : R. This statement has the following semantics: execute S and R sequentially. It is considered a success if at least one of S , R is a success. This statement is useful for dealing with inessential errors without explicitly catching them.

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This paper proposes a new approach to defining and expressing algorithms: the notion of task logical algorithms. This notion allows the user to define an algorithm for a task T as a set of agents who can collectively perform T . This notion considerably simplifies the algorithm development process and can be seen as an integration of the sequential pseudocode and logical algorithms.This observation requires some changes to algorithm development process. We propose a two-step approach: the first step is to define an algorithm for a task T via a set of agents that can collectively perform T . The second step is to translate these agents into (higher-order) computability logic.