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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 169 (57 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...
A Survey of Abstract Algebraic Logic
 TO APPEAR IN STUDIA LOGICA; (SPECIAL ISSUE ON ABSTRACT ALGEBRAIC LOGIC, PART II)
, 2003
"... ..."
Abstract algebraic logic and the deduction theorem
 Bull. of Symbolic Logic
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Structured theory presentations and logic representations
 ANNALS OF PURE AND APPLIED LOGIC
, 1994
"... The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the ..."
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Cited by 14 (1 self)
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The purpose of a logical framework such as LF is to provide a language for defining logical systems suitable for use in a logicindependent proof development environment. All inferential activity in an object logic (in particular, proof search) is to be conducted in the logical framework via the representation of that logic in the framework. An important tool for controlling search in an object logic, the need for which is motivated by the difficulty of reasoning about large and complex systems, is the use of structured theory presentations. In this paper a rudimentary language of structured theory presentations is presented, and the use of this structure in proof search for an arbitrary object logic is explored. The behaviour of structured theory presentations under representation in a logical framework is studied, focusing on the problem of "lifting" presentations from the object logic to the metalogic of the framework. The topic of imposing structure on logic presentations...
Categorial Fibring of Logics with Terms and Binding Operators
 FRONTIERS OF COMBINING SYSTEMS 2, STUDIES IN LOGIC AND COMPUTATION
, 1998
"... Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison wi ..."
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Cited by 14 (11 self)
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Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison with model theoretic parchments is included.
Formal Interoperability
, 1998
"... this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss: ..."
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Cited by 13 (3 self)
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this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss:
Synchronization of Logics
 Studia Logica
, 1996
"... Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, onestep derivation systems and theory spaces, as well as their functorial ..."
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Cited by 12 (9 self)
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Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, onestep derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequence systems. Key words: combination of logics, synchronization on formulae, sync...
Parameterisation of Logics
 Recent trends in algebraic development techniques Selected papers
, 1999
"... . Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [9]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual pa ..."
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Cited by 11 (6 self)
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. Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [9]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual parameter) logic. We provide a categorial characterisation of parameterisation and illustrate it with an example. Under reasonable assumptions, we show that the result logic is a conservative extension of both the parameterised and parameter logics and also that soundness, completeness and decidability are transferred. 1 Introduction We need to work with evermore complex systems. The challenge is to identify abstractions that may lead to a modular and integrated management of this complexity. One such approach is the combination of logics. In practice, it is geared by the need for integrating heterogeneous platforms and tools. Theoretically, the study of logics for combined structures has bee...
On the Role of Category Theory in the Area of Algebraic Specifications
 In LNCS , Proc. WADT11
, 1996
"... . The paper summarizes the main concepts and paradigms of category theory and explores some of their applications to the area of algebraic specifications. In detail we discuss different approaches to an abstract theory of specification logics. Further we present a uniform framework for developing pa ..."
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Cited by 10 (3 self)
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. The paper summarizes the main concepts and paradigms of category theory and explores some of their applications to the area of algebraic specifications. In detail we discuss different approaches to an abstract theory of specification logics. Further we present a uniform framework for developing particular specification logics. We make use of `classifying categories', to present categories of algebras as functor categories and to obtain necessary basic results for particular specification logics in a uniform manner. The specification logics considered are: equational logic for total algebras, conditional equational logic for partial algebras, and rewrite logic for concurrent systems. 1 Category Theory and Applications in Computer Science Category theory has been developed as a mathematical theory over 50 years and has influenced not only almost all branches of structural mathematics but also the development of several areas of computer science. It is the aim of this paper to review t...