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40
Kleene Algebra with Domain
, 2003
"... We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We ..."
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Cited by 42 (29 self)
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We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and wellfoundedness. Second, an algebraic reconstruction of propositional Hoare logic.
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...
Synthesizing Distributed Constrained Events from Transactional Workflow Specifications
 In Proceedings of the 12th International Conference on Data Engineering (ICDE
, 1996
"... Workflows are the semantically appropriate composite activities in heterogeneous computing environments. Such environments typically comprise a great diversity of locally autonomous databases, applications, and interfaces. Much good research has focused on the semantics of workflows, and how to capt ..."
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Cited by 40 (11 self)
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Workflows are the semantically appropriate composite activities in heterogeneous computing environments. Such environments typically comprise a great diversity of locally autonomous databases, applications, and interfaces. Much good research has focused on the semantics of workflows, and how to capture them in different extended transaction models. Here we address the complementary issues pertaining to how workflows may be declaratively specified, and how distributed constraints may be derived from those specifications to enable local control, thus obviating a centralized scheduler. Previous approaches to this problem were limited and often lacked a formal semantics. 1 Introduction Workflows are composite, semantically appropriate activities that execute in heterogeneous environments. In such environments, extremely common in practice, the challenge is to interoperate properly without violating the autonomy of the components. Workflows address this challenge [5]. Transactional workfl...
Semantical considerations on workflows: An algebra for intertask dependencies
 In Proceedings of the International Workshop on Database Programming Languages
, 1995
"... Workflows are composite multitransaction activities occurring in heterogeneous environments. They relax the semantic properties of traditional transactions to accommodate the demands of such environments. It is important that workflows be specified declaratively, reasoned about formally, and schedul ..."
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Cited by 31 (0 self)
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Workflows are composite multitransaction activities occurring in heterogeneous environments. They relax the semantic properties of traditional transactions to accommodate the demands of such environments. It is important that workflows be specified declaratively, reasoned about formally, and scheduled automatically. Declarative approaches based on intertask dependencies are prominent in the literature. However, extant approaches often lack a formal semantics, or fail to meet other important criteria. Also, they do not carefully distinguish event types from instances, a distinction that is crucial when the constraint that tasks are loopfree is relaxed. We propose an approach that gives a rigorous formal semantics for dependencies and meets the above conditions. Our approach uses algebraic expressions to represent dependencies and uses symbolic reasoning to take scheduling decisions. It can form the basis of a programming language for workflows. 1
The Stone gamut: A coordinatization of mathematics
 In Logic in Computer Science
, 1995
"... We give a uniform representation of the objects of mathematical practice as Chu spaces, forming a concrete selfdual bicomplete closed category and hence a constructive model of linear logic. This representation distributes mathematics over a twodimensional space we call the Stone gamut. The Stone ..."
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Cited by 30 (13 self)
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We give a uniform representation of the objects of mathematical practice as Chu spaces, forming a concrete selfdual bicomplete closed category and hence a constructive model of linear logic. This representation distributes mathematics over a twodimensional space we call the Stone gamut. The Stone gamut is coordinatized horizontally by coherence, ranging from −1 for sets to 1 for complete atomic Boolean algebras (CABA’s), and vertically by complexity of language. Complexity 0 contains only sets, CABA’s, and the inconsistent empty set. Complexity 1 admits noninteracting setCABA pairs. The entire Stone duality menagerie of partial distributive lattices enters at complexity 2. Groups, rings, fields, graphs, and categories have all entered by level 16, and every category of relational structures and their homomorphisms eventually appears. The key is the identification of continuous functions and homomorphisms, which puts StonePontrjagin duality on a uniform basis by merging algebra and topology into a simple common framework. 1 Mathematics from matrices We organize much of mathematics into a single category Chu of Chu spaces, or games as Lafont and Streicher have called them [LS91]. A Chu space is just a matrix that we shall denote =, but unlike the matrices of linear algebra, which serve as representations of linear transformations, Chu spaces serve as representations of the objects of mathematics, and their essence resides in how they transform. This organization permits a general twodimensional classification of mathematical objects that we call the Stone gamut 1, distributed horizontally by ∗This work was supported by ONR under grant number N0001492J1974. 1 “Spectrum, ” the obvious candidate for this appliction, already has a standard meaning in Stone duality, namely the representation of the dual space of a lattice by its prime ideals. “A
Merging without mystery, variables in dynamic semantics
, 1993
"... In this paper we discuss the treatment ofvariables in dynamic semantics. Referent systems are introduced as a exible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which wemanipulate themtheir namesand from th ..."
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Cited by 26 (0 self)
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In this paper we discuss the treatment ofvariables in dynamic semantics. Referent systems are introduced as a exible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which wemanipulate themtheir namesand from the information that we store in themtheir values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with the familiar formalisms in dynamic semantics, DRT and DPL.
Rewriting Extended Regular Expressions
, 1993
"... We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion ..."
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Cited by 19 (1 self)
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We concider an extened algebra of regular events (languages) with intersection besides the usual operations. This algebra has the structure of a distributive lattice with monotonic operations; the latter property is crucial for some applications. We give a new complete Horn equational axiomatiztion of the algebra and develop some termrewriting techniques for constructing logical inferences of valid equations. A shorter version of this paper is to appear in the proceedings of Developments in Language Theory, Univ. of Turku, July 1993, published by World Scientific. The present version has been submitted for publication elsewhere. 1 Introduction In this paper we consider an extended algebra of regular events (languages) on a given alphabet with intersection besides the usual operations (union, concatenation, Kleene star, empty, and the regular unit). This algebra has the structure of a distributive lattice (join is union, meet is intersection) with only monotonic operations. The latte...
The Duality of Time and Information
 In Proc. of CONCUR'92, LNCS 630
, 1992
"... The states of a computing system bear information and change time, while its events bear time and change information. We develop a primitive algebraic model of this duality of time and information for rigid local computation, or straightline code, in the absence of choice and concurrency, where time ..."
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Cited by 17 (7 self)
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The states of a computing system bear information and change time, while its events bear time and change information. We develop a primitive algebraic model of this duality of time and information for rigid local computation, or straightline code, in the absence of choice and concurrency, where time and information are linearly ordered. This shows the duality of computation to be more fundamental than the logic of computation for which choice is disjunction and concurrency conjunction. To accommodate flexible distributed computing systems we then bring in choice and concurrency and pass to partially ordered time and information, the formal basis for this extension being BirkhoffStone duality. A degree of freedom in how this is done permits a perfectly symmetric logic of computation amounting to Girard's full linear logic, which we view as the natural logic of computation when equal importance is attached to choice and concurrency. We conclude with an assessment of the prospects for ex...
The State of Change: A Survey
, 1998
"... . Updates are a crucial component of any database programming language. Even the simplest database transactions, such as withdrawal from a bank account, require updates. Unfortunately, updates are not accounted for by the classical Horn semantics of logic programs and deductive databases, which limi ..."
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Cited by 9 (2 self)
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. Updates are a crucial component of any database programming language. Even the simplest database transactions, such as withdrawal from a bank account, require updates. Unfortunately, updates are not accounted for by the classical Horn semantics of logic programs and deductive databases, which limits their usefulness in realworld applications. As a shortterm practical solution, logic programming languages have resorted to handling updates using ad hoc operators without a logical semantics. A great many works have been dedicated to developing logical theories in which the state of the underlying database can evolve with time. Many of these theories were developed with specific applications in mind, such as reasoning about actions, database transactions, program verification, etc. As a result, the different approaches have different strengths and weaknesses. In this survey, we review a number of these works, discuss their application domains, and highlight their strong and weak points...