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A Linear Logical Framework
, 1996
"... We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF c ..."
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Cited by 217 (44 self)
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We present the linear type theory LLF as the forAppeared in the proceedings of the Eleventh Annual IEEE Symposium on Logic in Computer Science  LICS'96 (E. Clarke editor), pp. 264275, New Brunswick, NJ, July 2730 1996. mal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of MiniML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cutelimination. 1 Introduction A logical framework is a formal system desig...
Higherorder logic programming
 HANDBOOK OF LOGIC IN AI AND LOGIC PROGRAMMING, VOLUME 5: LOGIC PROGRAMMING. OXFORD (1998
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Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree 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 [15], provide for various forms of abstraction (modules, abstract data types, and higherorder program ..."
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Cited by 85 (11 self)
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The theory of cutfree 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 [15], provide for various forms of abstraction (modules, abstract data types, and higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.
Efficient resource management for linear logic proof search
 Proceedings of the 5th International Workshop on Extensions of Logic Programming
, 1996
"... The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf). Among these, the problem of efficiently managing the li ..."
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Cited by 54 (11 self)
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The design of linear logic programming languages and theorem provers opens a number of new implementation challenges not present in more traditional logic languages such as Horn clauses (Prolog) and hereditary Harrop formulas (λProlog and Elf). Among these, the problem of efficiently managing the linear context when solving a goal is of crucial importance for the use of these systems in nontrivial applications. This paper studies this problem in the case of Lolli [HM94], though its results have application to other systems. We first give a prooftheoretic presentation of the operational semantics of this language as a resolution calculus. We then present a series of resource management systems designed to eliminate the nondeterminism in the distribution of linear formulas that undermines the efficiency of a direct implementation of this system. 1
Structural Cut Elimination  I. Intuitionistic and Classical Logic
 Information and Computation
, 2000
"... this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced b ..."
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Cited by 53 (17 self)
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this paper we present new proofs of cut elimination for intuitionistic and classical sequent calculi and give their representations in the logical framework LF [HHP93] as implemented in the Elf system [Pfe91]. Multisets are avoided altogether in these proofs, and termination measures are replaced by three nested structural inductions. Parameters are treated as variables bound in derivations, thus naturally capturing occurrence conditions. A starting point for the proofs is Kleene's sequent system G 3 [Kle52], which we derive systematically from the point of view that a sequent calculus should be a calculus of proof search for natural deductions. It can easily be related to Gentzen's original and other sequent calculi. We augment G 3 with proof terms that are stable under weakening. These proof terms enable the structural induction and furthermore form the basis of the representation of the proof in LF. The most closely related work on cut elimination is MartinLo# f 's proof of admissibility [ML68]. In MartinLo# f 's system the cut rule incorporates aspects of both weakening and contraction which enables a structural induction argument closely related to ours. However, without the introduction of proof terms, the implicit weakening in the cut rule makes it difficult to implement this proof directly. Herbelin [Her95] restates this proof and proceeds by assigning proof terms only to restricted sequent calculi LJT and LKT which correspond more immediately to
Programming in Lygon: An Overview
 ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY
, 1996
"... Recently, there has been much interest in the derivation of logic programming languages based on linear logic, a logic of resourceconsumption. Such languages provide a notion of resourceoriented programming, often leading to programs that are more elegant and concise than their equivalents in la ..."
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Cited by 40 (18 self)
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Recently, there has been much interest in the derivation of logic programming languages based on linear logic, a logic of resourceconsumption. Such languages provide a notion of resourceoriented programming, often leading to programs that are more elegant and concise than their equivalents in languages, such as Prolog, based on classical logics. We discuss, with examples, the design, implementation and applications of Lygon, a linear logic programming language. Lygon is based on a prooftheoretic analysis of which occurrences of the linear connectives provide an adequate basis for programming. In common with other linear logic programming languages, Lygon allows clauses to be used exactly once in a computation, thereby avoiding the need for the explicit resourcecounting often necessary in Prologlike languages. Indeed, it appears that resourcesensitivity leads to significant differences between the natural programming methodologies in Lygon and Prolog. Just as linear logic...
Modality in Dialogue: Planning, Pragmatics and Computation
, 1998
"... Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the ..."
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Cited by 36 (9 self)
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Natural language generation (NLG) is first and foremost a reasoning task. In this reasoning, a system plans a communicative act that will signal key facts about the domain to the hearer. In generating action descriptions, this reasoning draws on characterizations both of the causal properties of the domain and the states of knowledge of the participants in the conversation. This dissertation shows how such characterizations can be specified declaratively and accessed efficiently in NLG. The heart of this dissertation is a study of logical statements about knowledge and action in modal logic. By investigating the prooftheory of modal logic from a logic programming point of view, I show how many kinds of modal statements can be seen as straightforward instructions for computationally manageable search, just as Prolog clauses can. These modal statements provide sufficient expressive resources for an NLG system to represent the effects of actions in the world or to model an addressee whose knowledge in some respects exceeds and in other respects falls short of its own. To illustrate the use of such statements, I describe how the SPUD sentence planner exploits a modal knowledge base to
A Linear Spine Calculus
 Journal of Logic and Computation
, 2003
"... We present the spine calculus S ##&# as an efficient representation for the linear #calculus # ##&# which includes unrestricted functions (#), linear functions (#), additive pairing (&), and additive unit (#). S ##&# enhances the representation of Church's simply typed #calculus by enforcing ..."
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Cited by 33 (5 self)
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We present the spine calculus S ##&# as an efficient representation for the linear #calculus # ##&# which includes unrestricted functions (#), linear functions (#), additive pairing (&), and additive unit (#). S ##&# enhances the representation of Church's simply typed #calculus by enforcing extensionality and by incorporating linear constructs. This approach permits procedures such as unification to retain the efficient head access that characterizes firstorder term languages without the overhead of performing #conversions at run time. Applications lie in proof search, logic programming, and logical frameworks based on linear type theories. It is also related to foundational work on term assignment calculi for presentations of the sequent calculus. We define the spine calculus, give translations of # ##&# into S ##&# and viceversa, prove their soundness and completeness with respect to typing and reductions, and show that the typable fragment of the spine calculus is strongly normalizing and admits unique canonical, i.e. ##normal, forms.
Objects in Forum
 In Proceedings of the International Logic Programming Symposium
, 1995
"... A logical characterization of the typical features of objectoriented languages could yield a clear semantical counterpart of their operational meaning and, at the same time, it could allow to define a logic programming language in which it is possible to reason over highlycomplex data structures. ..."
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Cited by 24 (9 self)
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A logical characterization of the typical features of objectoriented languages could yield a clear semantical counterpart of their operational meaning and, at the same time, it could allow to define a logic programming language in which it is possible to reason over highlycomplex data structures. Many approaches to this problem have been proposed in the last years. Classical logic turned out to be unsuitable to model complex mechanisms, such as the dynamic modifications of the state of the objects, in a satisfactory way. Girard's Linear Logic [5] provides the means to handle many operational aspects of programming languages from a proof theoretical perspective as shown by Andreoli and Pareschi in [2]. In the paper Forum [11], a presentation of higherorder linear logic, is specialized to deal with statebased systems according to the proof as computation perspective. In this setting it is possible to represent a concrete notion of object assigning a logical meaning to features like ...
A Logical View Of Concurrent Constraint Programming
, 1995
"... . Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent ..."
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Cited by 23 (4 self)
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. Concurrent Constraint Programming (CCP) has been the subject of growing interest as the focus of a new paradigm for concurrent computation. Like logic programming it claims close relations to logic. In fact CCP languages are logics in a certain sense that we make precise in this paper. In recent work it was shown that the denotational semantics of determinate concurrent constraint programming languages forms a fibred categorical structure called a hyperdoctrine, which is used as the basis of the categorical formulation of firstorder logic. What this shows is that the combinators of determinate CCP can be viewed as logical connectives. In this paper we extend these ideas to the operational semantics of such languages and thus make available similar analogies for a much broader variety of languages including indeterminate CCP languages and concurrent blockstructured imperative languages. CR Classification: F3.1, F3.2, D1.3, D3.3 Key words: Concurrent constraint programming, simula...