The theory of cut-free sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [12], provide data types, higher-order programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends the languages λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. As a meta-language, Forum greatly extends the expressiveness of these other logic programming languages. To illustrate its expressive strength, we specify in Forum a sequent calculus proof system and the operational semantics of a functional programming language that incorporates such nonfunctional features as counters and references. 1

A proof procedure is presented for a class of formulas in intuitionistic logic. These formulas are the so-called goal formulas in the theory of hereditary Harrop formulas. Proof search inintuitionistic logic is complicated by the non-existence of a Herbrand-like theorem for this logic: formulas cannot in general be preprocessed into a form such as the clausal form and the construction of a proof is often sensitive to the order in which the connectives and quantifiers are analyzed. An interesting aspect of the formulas we consider here is that this analysis can be carried out in a relatively controlled manner in their context. In particular, the task of finding a proof can be reduced to one of demonstrating that a formula follows from a set of assumptions with the next step in this process being determined by the structure of the conclusion formula. An acceptable implementation of this observation must utilize unification. However, since our formulas may contain universal and existential quantifiers in mixed order, care must be exercised to ensure the correctness of unification. One way of realizing this requirement involves labelling constants and variables and then using these labels to constrain unification. This form of unification is presented and used in a proof procedure for goal formulas in a first-order version of hereditary Harrop formulas. Modifications to this procedure for the relevant formulas in a higher-order logic are also described. The proof procedure that we present has a practical value in that it provides the basis for an implementation of the logic programming language lambdaProlog.

In this paper we present a modal extension of logic programming, which provides reasoning capabilities in a multiagent situation. The language contains embedded implications, modal operators [a i ] to represent agent beliefs, together with a kind of "common knowledge" operator. In this language we can also define modules, compose them in several ways, and, also, we can perform hypothetical reasoning. 1 Introduction The problem of extending logic programming languages with modal operators, has been studied by several researchers. In particular, in [4] an extension of Prolog with modal operators, called MOLOG, is proposed, and a resolution procedure, close to Prolog resolution, is defined for modal Horn clauses in the logic S5 which contain universal modal operators of the form Know(a). Another modal extension of logic programming is the temporal logic programming language TEMPLOG introduced in [1]. Moreover, in [20] a logic language extended with a modal operator assume is define...