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A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 41 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
Once Upon a Polymorphic Type
, 1998
"... We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approxim ..."
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Cited by 38 (5 self)
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We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approximate, or defined over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type polymorphism, an essential feature of typed functional programming languages. Secondly, we include general Haskellstyle userdefined algebraic data types. Thirdly, we explain and solve the `poisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchburystyle operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation, and we are currently integrating the system into the Glasgow Haskell Compiler.
HigherOrder, Linear, Concurrent Constraint Programming
, 1992
"... We present a very simple and powerful framework for indeterminate, asynchronous, higherorder computation based on the formulaasagent and proofascomputation interpretation of (higherorder) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constrai ..."
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Cited by 30 (5 self)
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We present a very simple and powerful framework for indeterminate, asynchronous, higherorder computation based on the formulaasagent and proofascomputation interpretation of (higherorder) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constraint programming paradigm [Sar89] in two fundamental ways: (1) by allowing for the consumption of information by agents it permits a direct modelling of (indeterminate) state change in a logical framework, and (2) by admitting simplytyped terms as dataobjects, it permits the construction, transmission and application of (abstractions of) programs at runtime. Much more dramatically, however, the framework can be seen as presenting higherorder (and if desired, constraintenriched) versions of a variety of other asynchronous concurrent systems, including the asynchronous ("input guarded") fragment of the (firstorder) ßcalculus, Hewitt's actors formalism, (abstract forms of) Gelernter's Lin...
A Logic for Characterizing Multiple Bounded Agents
, 2000
"... We describe a metalogic for characterizing the evolving internal reasoning of various families of agents. We view the reasoning of agents as ongoing processes rather than as fixed sets of conclusions. Our approach utilizes a strongly sorted calculus, distinguishing the application language, time ..."
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Cited by 19 (3 self)
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We describe a metalogic for characterizing the evolving internal reasoning of various families of agents. We view the reasoning of agents as ongoing processes rather than as fixed sets of conclusions. Our approach utilizes a strongly sorted calculus, distinguishing the application language, time, and various syntactic sorts. We have established soundness and completeness results corresponding to various families of agents. This allows for useful and intuitively natural characterizations of such agents' reasoning abilities. We discuss and contrast consistency issues as in the work of Montague and Thomason. We also show how to represent the concept of focus of attention in this framework. This material is based upon work supported by the National Science Foundation under Grant No. IIS9907482. We wish to thank the referees for their valuable comments and suggestions. 1 Keywords: logics of knowledge and beliefs, bounded agents, realtime reasoning, multiple agents. 1 Introduct...
A typed foundation for directional logic programming
 In Proc. Workshop on Extensions to Logic Programming
, 1992
"... Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and d ..."
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Abstract. A long standing problem in logic programming is how to impose directionality on programs in a safe fashion. The benefits of directionality include freedom from explicit sequential control, the ability to reason about algorithmic properties of programs (such as termination, complexity and deadlockfreedom) and controlling concurrency. By using Girard’s linear logic, we are able to devise a type system that combines types and modes into a unified framework, and enables one to express directionality declaratively. The rich power of the type system allows outputs to be embedded in inputs and vice versa. Type checking guarantees that values have unique producers, but multiple consumers are still possible. From a theoretical point of view, this work provides a “logic programming interpretation ” of (the proofs of) linear logic, adding to the concurrency and functional programming interpretations that are already known. It also brings logic programming into the broader world of typed languages and typesaspropositions paradigm, enriching it with static scoping and higherorder features.
A Classical Linear λcalculus
, 1997
"... This paper proposes and studies a typed λcalculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natu ..."
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This paper proposes and studies a typed λcalculus for classical linear logic. I shall give an explanation of a multipleconclusion formulation for classical logic due to Parigot and compare it to more traditional treatments by Prawitz and others. I shall use Parigot's method to devise a natural deduction formulation of classical linear logic. This formulation is compared in detail to the sequent calculus formulation. In an appendix I shall also demonstrate a somewhat hidden connexion with the paradigm of control operators for functional languages which gives a new computational interpretation of Parigot's techniques.
A Static Analysis of a Classical Linear Logic Programming Language
"... Proof Graph . . . . . . . . . . . . . . . . . . . . . . . . . 32 6.3 Refinement of Abstract Proof Graph . . . . . . . . . . . . . . . . . 37 1 7 Performance Measurements 42 7.1 The Sorting Program . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.2 A Petri Net for ProducerConsumer System . ..."
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Cited by 1 (1 self)
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Proof Graph . . . . . . . . . . . . . . . . . . . . . . . . . 32 6.3 Refinement of Abstract Proof Graph . . . . . . . . . . . . . . . . . 37 1 7 Performance Measurements 42 7.1 The Sorting Program . . . . . . . . . . . . . . . . . . . . . . . . . . 42 7.2 A Petri Net for ProducerConsumer System . . . . . . . . . . . . . 45 7.3 A ProducerConsumer Program . . . . . . . . . . . . . . . . . . . . 46 8 Conclusion 48 A A Lemma of the Leveled I/O model 54 B A Proof of the Equivalence of the the Leveled I/O model and L ## 56 2 Abstract In this thesis, we propose a new static analysis method which is applicable for a classical linear logic programming language. Andreoli et al. proposed a static analysis method for the classical linear logic programming language LO, but their method did not cover the multiplicative conjunction which is the most important connective for a resourcesensitive feature of linear logic. Our method, in contrast, covers the multiplicative conjunction in addition to the multiplicative disjunction and linear implication. In classical linear logic programming language, such as Forum, the execution of a program is sometimes highly nondeterministic. For example, the execution time of a sorting program written in Forum rises hyperexponentially with list length. The reason is that most of the execution time is spent for trying to prove unprovable sequents. Therefore, it is very important to find unprovable sequents before the execution of programs, and this is realizable by a static analysis performing an abstract proof search on an abstract proof. In order to develop abstract proof search in linear logic, we need to map the sequents into finite sets. we introduce a finite monoid #M,+, 0# homomorphic to N (a set of natural numbers including 0) t...
Using Linear Logic Planning to Make Knowledge Bases Reactive
, 2001
"... . As both, reasoning and knowledge bases, have an important role while planning, we propose a new model where a fusion of all of these concepts is useda Reactive Knowledge Base (RKB). The aim of the RKB is to embed reactive planning [13], knowledge base (often called as a model of a domain) and ..."
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. As both, reasoning and knowledge bases, have an important role while planning, we propose a new model where a fusion of all of these concepts is useda Reactive Knowledge Base (RKB). The aim of the RKB is to embed reactive planning [13], knowledge base (often called as a model of a domain) and the world model. The openness of that structure makes it attractive for robot planning, especially when we are designing a robot control system like described in [4]. The planning process is based on the proof search for linear logic expressions (representing RKB relations) using a subset of linear logic rules. We also discuss algorithms of planning using linear logic formulas and present an idea to use simulation on Coloured Petri nets [17] to generate plans for simultaneous goals. Keywords: Knowledge Base, Linear Logic, AI Planning, Petri Nets. 1