This paper explores the application of rewriting logic to the executable formal modeling of real-time 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 real-time and hybrid system models, including object-oriented 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 property-oriented 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 real-time and hybrid systems. The general conceptual advantage of using...

. 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 sub-ontologies. 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...

Order-sorted 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 object-orientation. It is argued that the resulting language, CMSL, meets those requirements of the object-oriented database system manifesto [6] that are applicable to object-oriented conceptual models (as opposed to OO databases).

this paper was published as Walicki, M.A. and Meldal, S., 1995, Nondeterministic Operators in Algebraic Frameworks, Tehnical Report No. CSL--TR--95--664, Stanford University

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 order-sortedness 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...

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...

2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4

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 effectively-computable functions on string representations of numbers.

Abstract computable functions are defined by abstract finite deterministic algorithms on manysorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable functions on any many-sorted algebra; (ii) all functions effectively approximable by abstract computable functions on any metric algebra. We show that there exist universal algebraic specifications for all the classically computable functions on the set R of real numbers. The algebraic specifications used are mainly bounded universal equations and conditional equations. We investigate the initial algebra semantics of these specifications, and derive situations where algebraic specifications precisely define the computable functions.

This work investigates the suitability of rewriting logic as a semantic framework for modeling real-time and hybrid systems. We present a general method to specify and symbolically simulate such systems in rewriting logic and illustrate it with a well-known benchmark. We also show how a wide range of real-time and hybrid system models can be naturally expressed and are unified within our approach. The relationships with timed rewriting logic [9,10] are also investigated. 1 Introduction Rewriting logic is a flexible and expressive framework in which many different models of concurrent computation and many different types of systems can be naturally specified [13,16,12,14]. It seems therefore natural to investigate the question of how rewriting logic can be applied to the specification of realtime and hybrid systems. From the semantic point of view this offers the possibility of integrating real-time aspects with other features and models already supported by rewriting logic. The first ...