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

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There has been considerable work aimed at enhancing the expressiveness of logic programming languages. To this end logics other than classical first order logic have been considered, including intuitionistic, relevant, temporal, modal and linear logic. Girard's linear logic has formed the basis of a number of logic programming languages. These languages are successful in enhancing the expressiveness of (pure) Prolog and have been shown to provide natural solutions to problems involving concurrency, natural language processing, database processing and various resource oriented problems. One of the richer linear logic programming languages is Lygon. In this paper we investigate the implementation of Lygon. Two significant problems that arise are the division of resources between sub-branches of the proof and the selection of the formula to be decomposed. We present solutions to both of these problems.

The adoption of the Dolev-Yao model, an abstraction of security protocols that supports symbolic reasoning, is responsible for many successes in protocol analysis. In particular, it has enabled using logic effectively to reason about protocols. One recent framework for expressing the basic assumptions of the Dolev-Yao model is given by strand spaces, certain directed graphs whose structure reflects causal interactions among protocol participants. We represent strand constructions as relatively simple formulas in first-order linear logic, a refinement of traditional logic known for an intrinsic and natural accounting of process states, events, and resources. The proposed encoding is shown to be sound and complete. Interestingly, this encoding differs from the multiset rewriting definition of the Dolev-Yao model, which is also based on linear logic. This raises the possibility that the multiset rewriting framework may differ from strand spaces in some subtle way, although the two settings are known to agree on the basic secrecy property. 1 Introduction In recent years, a variety of methods have been developed for analyzing and reasoning about protocols based on cryptographic primitives. Although there are many differences among these proposals, most current formal approaches use the so-called "Dolev-Yao" model of adversary capabilities, which appears to be drawn from positions taken in [34] and from a simplified model presented in [11]. In this idealized setting, a protocol adversary is allowed to nondeterministically choose among possible actions. Messages are composed of indivisible abstract values, not sequences of bits, and encryption is modeled in an idealized way. The adversary may only send messages comprised of data it "knows" as the result of overhearing past transmissions.

We begin with a review of intuitionistic non-commutative linear logic (INCLL), a refinement of linear logic with an inherent notion of order proposed by the authors in prior work. We then develop a logic programming interpretation for INCLL in two steps: (1) we give a system of ordered uniform derivations which is sound and complete with respect to INCLL, and (2) we present a model of resource consumption which removes non-determinism from ordered resource allocation during search for uniform derivations. We also illustrate the expressive power of the resulting ordered linear logic programming language through some examples, including programs for merge sort, insertion sort, and natural language parsing. 1 The authors can be reached at jpolakow@cs.cmu.edu and fp@cs.cmu.edu. This work was sponsored NSF Grants CCR-9804014 and CCR-9619584. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, ei...

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...

Abstract We propose the monadic linear logic programming language Lol-liMon as a new foundation for the specification of distributed trust

dale 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, Prolog and its linear logic re nement, Lolli [13], provide for various forms of abstraction (modules, abstract data types, and higher-order programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. Forum is a logic programming presentation of all of linear logic that modularly extends Prolog, Lolli, and LO. This language, therefore, allows speci cations to incorporate both abstractions and concurrency. The motivation for Forum. Below are several examples of logic programming languages. Here we use linear logic connectives as in [9], with the addition of) for intuitionistic implication: A) B denotes! A, B. 1. Horn clauses, the logical foundation of Prolog, are formulas of the form 8x(G) A) where G may contain occurrences of & and>. (Weshall use x