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Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
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Cited by 147 (52 self)
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Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
, 1996
"... . This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency mod ..."
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Cited by 82 (22 self)
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. This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency models, each on its own terms, avoiding any encodings or translations. Bringing very different models under a common semantic framework makes easier to understand what different models have in common and how they differ, to find deep connections between them, and to reason across their different formalisms. It becomes also much easier to achieve in a rigorous way the integration and interoperation of different models and languages whose combination offers attractive advantages. The logic and model theory of rewriting logic are also summarized, a number of current research directions are surveyed, and some concluding remarks about future directions are made. Table of Contents 1 In...
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...
Plans, Affordances, and Combinatory Grammar
, 2002
"... The idea that natural language grammar and planned action are related systems has been implicit in psychological theory for more than a century. However, formal theories in the two domains have have tended to look very different. This article argues that both faculties share the formal character ..."
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Cited by 8 (1 self)
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The idea that natural language grammar and planned action are related systems has been implicit in psychological theory for more than a century. However, formal theories in the two domains have have tended to look very different. This article argues that both faculties share the formal character of applicative systems based on operations corresponding to the same two combinatory operations, namely functional composition and typeraising. Viewing them in this way suggests simpler and more cognitively plausible accounts of both systems, and suggests that the language faculty evolved in the species and develops in children by a rather direct adaptation of a more primitive apparatus for planning purposive action in the world by composing affordances of objects or tools. The knowledge representation that underlies such planning is also reflected in the natural language semantics of tense, mood, and aspect, which the paper begins by arguing provides the key to understanding both systems.
On Linear Logic Planning and Concurrency
"... We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicativ ..."
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Cited by 1 (1 self)
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We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicative exponential linear logic in a way that exhibits a noninterleaving behavioral concurrency semantics. Relying on this fact, we argue that this work is a crucial step for establishing a common language for concurrency and planning that will allow to carry techniques and methods between these two fields.
Theorem Proving with the Inverse Method for Linear Logic
, 2004
"... Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, conc ..."
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Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, concurrent computation, process calculi and games. It accomplishes this unifying view by providing logical connectives whose behaviour is closely tied to the collection of resources, which is free of structural phenomena such as weakening (allowing more resources than necessary) or contraction (using a resource more than once). The usual (nonlinear) logic is embedded in this substructural framework by means of an exponential modal operator. The interaction of the rules for multiplicative, additive and exponential connectives gives rise to a wide and expressive array of behaviours. Various approaches have been taken to produce automated reasoning systems for fragments of linear logic, usually in the form of logic programming engines; but, due to the lack of the full complement of linear connectives, uses of such systems have an idiomatic commitment, for example as serializations or in continuationpassingstyle. This thesis addresses the need for automated reasoning for the complete set of operators for first order intuitionistic linear logic (i.e., ⊗, 1, ❜, &, ⊤, ⊕, 0,!, ∀, ∃), which removes the need for such idiomatic constructions and allows direct logical expression. The particular theorem proving technique used is the inverse method, which performs forward
www.elsevier.com/locate/entcs Playing with Maude ⋆
"... This paper is an introduction to rulebased programming in Maude. We illustrate in particular the use of operator attributes to structure the state of a system, and the difference between equations and rules. We use wellknown mathematical games and puzzles for our examples illustrating the expressi ..."
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This paper is an introduction to rulebased programming in Maude. We illustrate in particular the use of operator attributes to structure the state of a system, and the difference between equations and rules. We use wellknown mathematical games and puzzles for our examples illustrating the expressive power of Maude. Keywords: Rulebased programming, Maude, puzzles.
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"... The idea that to perceive an object is to perceive its affordances—that is, the interactions of the perceiver with the world that the object supports or affords—is attractive from the point of view of theories in cognitive science that emphasize the fundamental role of actions in representing an age ..."
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The idea that to perceive an object is to perceive its affordances—that is, the interactions of the perceiver with the world that the object supports or affords—is attractive from the point of view of theories in cognitive science that emphasize the fundamental role of actions in representing an agent’s knowledge about the world. However, in this general form, the notion has so far lacked a formal expression. This paper offers a representation for objects in terms of their affordances using Linear Dynamic Event Calculus, a formalism for reasoning about causal relations over events. It argues that a representation of this kind, linking objects to the events which they are characteristically involved in, underlies some universal operations of natural language syntactic and semantic composition that are postulated in Combinatory Categorial Grammar (CCG). These observations imply that the language faculty is more directly related to prelinguistic cognitive apparatus used for planning action than formal theories in either domain have previously seemed to allow.