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Logic Programming and MultiAgent Systems: A Synergic Combination for Applications and Semantics
 IN THE LOGIC PROGRAMMING PARADIGM  A 25YEAR PERSPECTIVE
, 1999
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A Linear Logic Calculus of Objects
 Proceedings of the Joint International Conference and Symposium on Logic Programming
, 1996
"... This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an objectoriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have rec ..."
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This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an objectoriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have recently been proposed in the literature. From these proposals, O \Gammaffi inherits the representation of objects as composite data structures, with attribute and method fields, as well as their interpretation as firstclass values. O \Gammaffi also gives a direct logical modeling of the selfapplication semantics of method invocation that justifies the view of objects as elements of recursive types. As such, the design of O \Gammaffi appears interesting, in perspective, as a basis for developing flexible and powerful type systems for logical objectbased languages.
Forum as a Logic Programming Language: Preliminary Report
 Proceedings of the Linear Logic '96 Meeting
, 1996
"... When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in ..."
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When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in the implementation of Lolli can be extended naturally to Forum. Finally, we show two Forum programs in order to demonstrate some of the paradigms that arise in using the language. 1 Introduction Forum, a fragment of Linear Logic introduced by Dale Miller in 1994, is distinguished by two key features. First, it is complete for all of Linear Logic, in the sense that Linear Logic operators that are not part of Forum can be mapped to Forum by a provabilitypreserving translation. Second, a form of goaldirected proof search (as characterized by uniform proofs) is complete. Historically, logics for which uniform proofs are complete, such as Horn Clauses, Hereditary Harrop Formulas, and Linear H...
Object Calculi in Linear Logic
"... Several calculi of objects have been studied in the recent literature, that support the central features of objectbased languages: messages, inheritance, dynamic dispatch, object update and objectextension. We show that a complete semantic account of these features may be given in a fragment of hi ..."
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Cited by 8 (0 self)
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Several calculi of objects have been studied in the recent literature, that support the central features of objectbased languages: messages, inheritance, dynamic dispatch, object update and objectextension. We show that a complete semantic account of these features may be given in a fragment of higherorder linear logic.
An Overview of Linear Logic Programming
 in Computational Logic
, 1985
"... Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequen ..."
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Logic programming can be given a foundation in sequent calculus by viewing computation as the process of building a cutfree sequent proof bottomup. The first accounts of logic programming as proof search were given in classical and intuitionistic logic. Given that linear logic allows richer sequents and richer dynamics in the rewriting of sequents during proof search, it was inevitable that linear logic would be used to design new and more expressive logic programming languages. We overview how linear logic has been used to design such new languages and describe briefly some applications and implementation issues for them.
Lógica Linear E a Especificação De Sistemas Computacionais
, 2001
"... In recent years, intuitionistic logic and type systems have been used in numerous computational logical systems as frameworks for the specification of natural deduction proof systems. As we shall illustrate here, linear logic can be similarly used to specify the more general setting of sequent calcu ..."
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Cited by 6 (2 self)
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In recent years, intuitionistic logic and type systems have been used in numerous computational logical systems as frameworks for the specification of natural deduction proof systems. As we shall illustrate here, linear logic can be similarly used to specify the more general setting of sequent calculus proof systems and provides rich forms of analysis and deduction of properties of the specified systems. We shall present several example encodings of sequent calculus proof systems using the Forum presentation of linear logic: linear logic is a resource conscious logic developed by Girard, and Forum is an abstract logic programming language associated to it, due to Miller. We start by proposing an encoding of sequents, rules and systems. Then a correctness result is proved for these encodings and it is observed that metalevel proofs match closely the objectlevel ones. The encoding of an objectlevel proof system as Forum clauses has certain advantages over encoding them as inference figures. For example, Forum specifications do not deal with context explicitly and instead it only focuses on the formulas that are directly involved in the inference rule. The distinction between making the inference rule additive or multiplicative is achieved in inference rule figures by explicitly presenting contexts and either splitting or copying them. The Forum clause representation achieves the same distinction using metalevel additive or multiplicative connectives. Objectlevel quantifiers can be handled directly using the metalevel quantification. Similarly, the structural rules of contraction and weakening can be captured together using the ? modal. Finally, since the encoding of proof systems is natural and direct, we are able to use the rich metatheory of linear logic to help ...
Proofs as Computations in Linear Logic
, 2000
"... The notions of uniform proof and of resolution represent the foundations of the prooftheoretic characterization of logic programming. The class of Abstract Logic Programming Languages nicely captures these concepts for a wide spectrum of logical systems. In the logic programming setting, however, t ..."
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The notions of uniform proof and of resolution represent the foundations of the prooftheoretic characterization of logic programming. The class of Abstract Logic Programming Languages nicely captures these concepts for a wide spectrum of logical systems. In the logic programming setting, however, the structure of the formulas, e.g. Horn clauses and hereditary Harrop formulas, plays a crucial role in discriminating between programming and theorem proving. In the paper, and in the framework of the proofs as computations interpretation of linear logic, we present an extension of hereditary Harrop formulas and a corresponding logical system which are the foundations of the logic programming language ehhf . The starting point of this study is Forum [26], a presentation of higherorder linear logic in terms of uniform proofs. A subset of its formulas have been isolated and proved to be wellsuited to encode descriptions of various programming paradigms.
A Linear Logic Specification for Chimera
, 1997
"... . Forum [36], a powerful logic formalism based on Higher Order Linear Logic, is particularly suited to specify and reason about complex programs and systems. Ehhf [12], a subset of Forum, models many interesting logic programming extensions towards O.O. and concurrent systems and can be viewed as ..."
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. Forum [36], a powerful logic formalism based on Higher Order Linear Logic, is particularly suited to specify and reason about complex programs and systems. Ehhf [12], a subset of Forum, models many interesting logic programming extensions towards O.O. and concurrent systems and can be viewed as a very high level logic programming specification language. The paper presents some results in this direction, namely the specification in Ehhf of Chimera, an Active, ObjectOriented and Deductive Database System. Keywords: Linear Logic, ObjectOriented and Deductive Databases. 1 Introduction Proof theory and automated deduction have provided relevant contributions to computer science, in particular in the fields of highlevel programming languages and formal verification of software. Many different logics have been proposed and used for these purposes. We will work with Linear logic [22] with the aim to use it as a theoretical foundation for modern and powerful specification language...
Linearity for objects
, 2006
"... Linear type systems guarantee that no copies are made of certain program values. The EGO language is a foundational calculus which adds linearity to object oriented languages. EGO allows changes to be made to the interface of an object, such as the addition or removal of methods, as long as such an ..."
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Linear type systems guarantee that no copies are made of certain program values. The EGO language is a foundational calculus which adds linearity to object oriented languages. EGO allows changes to be made to the interface of an object, such as the addition or removal of methods, as long as such an object is linear, i.e., there exists only one reference to it. However, this linearity constraint is often unwieldy and hard to program with. We extend EGO with a linguistic primitive for temporarily relaxing the linearity guarantee. EGO allows objects to be linear and enforces that only one reference exists such an object. We allow multiple references to linear objects in certain expressions by borrowing references to these objects. Borrowing annotates the type of the reference with a region, which is a unique token indicating where the reference was borrowed. We disallow references with types containing regions that are not currently borrowed. We use this to temporarily make multiple references to an object in a given expression but enforce that outside this expression only one reference exists. This work was supported in part by NASA cooperative agreements NCC21298 and NNA05CS30A and NSF grants CCR