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13
Observational logic
 IN ALGEBRAIC METHODOLOGY AND SOFTWARE TECHNOLOGY (AMAST'98
, 1999
"... We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required ..."
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Cited by 55 (10 self)
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We present an institution of observational logic suited for statebased systems specifications. The institution is based on the notion of an observational signature (which incorporates the declaration of a distinguished set of observers) and on observational algebras whose operations are required to be compatible with the indistinguishability relation determined by the given observers. In particular, we introduce a homomorphism concept for observational algebras which adequately expresses observational relationships between algebras. Then we consider a flexible notion of observational signature morphism which guarantees the satisfaction condition of institutions w.r.t. observational satisfaction of arbitrary firstorder sentences. From the proof theoretical point of view we construct a sound and complete proof system for the observational consequence relation. Then we consider structured observational specifications and we provide a sound and complete proof system for such specifications by using a general, institutionindependent result of [6].
On the integration of observability and reachability concepts
 Foundations of Software Science and Computation Structures, LNCS
, 2002
"... 2 Institut f"ur Informatik, LudwigMaximiliansUniversit"at M"unchen, Germany ..."
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Cited by 22 (2 self)
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2 Institut f&quot;ur Informatik, LudwigMaximiliansUniversit&quot;at M&quot;unchen, Germany
Observational Logic, ConstructorBased Logic, and their Duality
, 2002
"... Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this p ..."
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Cited by 7 (1 self)
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Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability. Then we develop in a completely analogous way the constructorbased logic institution which formalizes a novel treatment of reachability. Both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view. We show that there is a methodological and even formal duality between both frameworks. In particular, we establish a correspondence between observer operations and datatype constructors, observational and constructorbased algebras, fully abstract and reachable algebras, and observational and inductive consequences of specifications. The formal duality between the observability and reachability concepts is established in a categorytheoretic setting.
Brzozowski’s algorithm (co)algebraically
"... Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctn ..."
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Cited by 6 (1 self)
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Abstract. We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. 1
Dialgebraic Specification and Modeling
"... corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube ..."
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Cited by 4 (4 self)
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corecursive functions COALGEBRA state model constructors destructors data model recursive functions reachable hidden abstraction observable hidden restriction congruences invariants visible abstraction ALGEBRA visible restriction!e Swinging Cube
A AlgebraCoalgebra Duality in Brzozowski’s Minimization Algorithm
"... We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simpl ..."
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Cited by 1 (0 self)
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We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algorithms to obtain minimal, language equivalent automata from Moore, nondeterministic and weighted automata.
Towards Behavioral Maude: Behavioral Membership Equational Logic Jos'e Meseguer 1
"... Maude's underlying equational logic, membership equational logic, generalizes and increases the expressive power of manysorted and ordersorted equational logics. We develop a hiddensorted extension of membership equational logic, and give conditions under which theories have both an algebrai ..."
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Maude's underlying equational logic, membership equational logic, generalizes and increases the expressive power of manysorted and ordersorted equational logics. We develop a hiddensorted extension of membership equational logic, and give conditions under which theories have both an algebraic and a coalgebraic semantics, including final (co)algebras. We also discuss the language design of BMaude, based on such an extended logic and using categorical notions in and across the different institutions involved. We also explain how Maude's reflective semantics provides a systematic method to extend Maude to BMaude within Maude, including module composition operations, evaluation, and automated proof methods. Key words: Membership and hidden algebra, coalgebra, Maude.
On the Integration of Observability and . . .
 FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES, LNCS
, 2002
"... This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software ..."
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This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software systems. Thereby the underlying paradigm is that the semantics of a specification should be as loose as possible to capture all its correct realizations. We also consider the socalled "idealized models" of a specication which are useful to study the behavioral properties a user can observe when he/she is experimenting with the system. Finally, we present sound and complete proof systems that allow us to derive behavioral properties from the axioms of a given specification.
On the Integration of Observability and Reachability Concepts
, 2002
"... This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software s ..."
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This paper focuses on the integration of reachability and observability concepts within an algebraic, institutionbased framework. We develop the essential notions that are needed to construct an institution which takes into account both the generation and observationoriented aspects of software systems. Thereby the underlying paradigm is that the semantics of a specification should be as loose as possible to capture all its correct realizations. We also consider the socalled "idealized models" of a specification which are useful to study the behavioral properties a user can observe when he/she is experimenting with the system. Finally, we present sound and complete proof systems that allow us to derive behavioral properties from the axioms of a given specification.