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Specification of RealTime and Hybrid Systems in Rewriting Logic
, 1999
"... This paper explores the application of rewriting logic to the executable formal modeling of realtime and hybrid systems. We give general techniques by which such systems can be specified as ordinary rewrite theories, and show that a wide range of realtime and hybrid system models, including object ..."
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Cited by 33 (17 self)
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This paper explores the application of rewriting logic to the executable formal modeling of realtime and hybrid systems. We give general techniques by which such systems can be specified as ordinary rewrite theories, and show that a wide range of realtime and hybrid system models, including objectoriented systems, timed automata [4], hybrid automata [2], timed and phase transition systems [28], and timed extensions of Petri nets [1,37], can indeed be expressed in rewriting logic quite naturally and directly. Since rewriting logic is executable and is supported by several language implementations, our approach complements propertyoriented methods and tools less well suited for execution purposes. The relationships with the timed rewriting logic approach of Kosiuczenko and Wirsing [24,25] are also studied. 1 Introduction This paper explores the application of rewriting logic to the executable formal modeling of realtime and hybrid systems. The general conceptual advantage of using...
Formalising Ontologies and Their Relations
 In Proceedings of DEXA’99
, 1999
"... . Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledg ..."
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Cited by 28 (1 self)
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. Ontologies allow the abstract conceptualisation of domains, but a given domain can be conceptualised through many different ontologies, which can be problematic when ontologies are used to support knowledge sharing. We present a formal account of ontologies that is intended to support knowledge sharing through precise characterisations of relationships such as compatibility and refinement. We take an algebraic approach, in which ontologies are presented as logical theories. This allows us to characterise relations between ontologies as relations between their classes of models. A major result is cocompleteness of specifications, which supports merging of ontologies across shared subontologies. 1 Introduction Over the last decade ontologies  best characterised as explicit specifications of a conceptualisation of a domain [17]  have become increasingly important in the design and development of knowledge based systems, and for knowledge representations generally. They...
A Formalization of Objects Using Equational Dynamic Logic
, 1991
"... Ordersorted equational logic is extended with dynamic logic to a specification language for dynamic objects. Special attention is paid to different concepts of encapsulation that play a role in objectorientation. It is argued that the resulting language, CMSL, meets those requirements of the ob ..."
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Cited by 24 (9 self)
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Ordersorted equational logic is extended with dynamic logic to a specification language for dynamic objects. Special attention is paid to different concepts of encapsulation that play a role in objectorientation. It is argued that the resulting language, CMSL, meets those requirements of the objectoriented database system manifesto [6] that are applicable to objectoriented conceptual models (as opposed to OO databases).
Algebraic Approaches to Nondeterminism  an Overview
 ACM Computing Surveys
, 1997
"... this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University ..."
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Cited by 23 (3 self)
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this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSLTR95664, Stanford University
A NATURAL AXIOMATIZATION OF COMPUTABILITY AND PROOF OF CHURCH’S THESIS
"... Abstract. Church’s Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turingcomputable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally e ..."
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Cited by 23 (10 self)
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Abstract. Church’s Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turingcomputable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church’s Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing’s Thesis, characterizing the effective string functions, and—in particular—the effectivelycomputable functions on string representations of numbers.
Ready Simulation, Bisimulation, and the Semantics of CCSLike Languages
, 1993
"... The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively sim ..."
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Cited by 21 (3 self)
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The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively simple case of core languages for concurrency, such as the kernel language of Milner's CCS. We introduce some criteria for judging notions of program comparison. Our basic notion is that of a congruence: two programs are equivalent with respect to a language L and a set of observations O iff they cannot be distinguished by any observation in O in any context of L. Bisimulation, the notion of program equivalence ordinarily used with CCS, is finer than CCS congruence: there are two programs which are not bisimilar, but cannot be told apart by CCS contexts. We explore the possibility of making bisimulation into a congruence. We CCS is defined by a set of structured operational rules. We introduc...
From Total Equational to Partial First Order Logic
, 1998
"... The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to pa ..."
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Cited by 19 (8 self)
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The focus of this chapter is the incremental presentation of partial firstorder logic, seen as a powerful framework where the specification of most data types can be directly represented in the most natural way. Both model theory and logical deduction are described in full detail. Alternatives to partiality, like (variants of) error algebras and ordersortedness are also discussed, showing their uses and limitations. Moreover, both the total and the partial (positive) conditional fragment are investigated in detail, and in particular the existence of initial (free) models for such restricted logical paradigms is proved. Some more powerful algebraic frameworks are sketched at the end. Equational specifications introduced in last chapter, are a powerful tool to represent the most common data types used in programming languages and their semantics. Indeed, Bergstra and Tucker have shown in a series of papers (see [BT87] for a complete exposition of results) that a data type is semicompu...
Specification and Analysis of RealTime and Hybrid Systems in Rewriting Logic
, 2000
"... 2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4 ..."
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Cited by 10 (3 self)
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2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4
Meadows and the equational specification of division
, 901
"... The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of equational specifications of data types cannot use field theory in ap ..."
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Cited by 6 (5 self)
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The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of equational specifications of data types cannot use field theory in applications to number systems based upon rational, real and complex numbers. We study a new axiomatic concept for number systems with division that uses only equations: a meadow is a commutative ring with a total inverse operator satisfying two equations which imply 0 −1 = 0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms for inverse, we start the development of a theory of meadows. We give a general representation theorem for meadows and find, as a corollary, that the conditional equational theory of meadows coincides with the conditional equational theory of zero totalized fields. We also prove representation results for meadows of finite characteristic.
The Data Type Variety of Stack Algebras
, 1995
"... We define and study the class of all stack algebras as the class of all minimal algberas in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we show that the initial model of the variety is computable, that its equational theory is decidable, but t ..."
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Cited by 5 (5 self)
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We define and study the class of all stack algebras as the class of all minimal algberas in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we show that the initial model of the variety is computable, that its equational theory is decidable, but that its equational deduction problem is undecidable. We show that it cannot be finitely axiomatised by equations, but it can be axiomatised by equations with a hidden sort and functions. This class of all stack algebras, together with its specifications, can be used to survey the many models in the literature on stacks in a systematic way, and hence give the study of the stack some mathematical coherence. KEY WORDS & PHRASES : stacks, equational specifications with hidden functions, complete term rewriting systems, many sorted algebras, computable algebras, equational theories, equational deduction problem. 2 To Dirk van Dalen 1 INTRODUCTION A stack is a structure that stores data. Its sta...