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An Axiomatic Approach to Structuring Specifications
"... In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions, which means two levels of institution independence. This abstract axiomatic app ..."
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In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract institutions, which means two levels of institution independence. This abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators, and moreover it unifies the theory and the model oriented approaches. Within this framework we develop concepts and results about ‘abstract structured specifications ’ such as colimits, model amalgamation, compactness, interpolation, sound and complete proof theory, and pushoutstyle parameterization with sharing, all of them in a top down manner dictated by the upper level of institution independence. 1.
Semantics of the Distributed Ontology Language: Institutes and Institutions
"... The Distributed Ontology Language (DOL) is a recent development within the ISO standardisation initiative 17347 Ontology Integration and Interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology lang ..."
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The Distributed Ontology Language (DOL) is a recent development within the ISO standardisation initiative 17347 Ontology Integration and Interoperability (OntoIOp). In DOL, heterogeneous and distributed ontologies can be expressed, i.e. ontologies that are made up of parts written in ontology languages based on various logics. In order to make the DOL metalanguage and its semantics more easily accessible to the wider ontology community, we have developed a notion of institute which are like institutions but with signature partial orders and based on standard settheoretic semantics rather than category theory. We give an institutebased semantics for the kernel of DOL and show that this is compatible with institutional semantics. Moreover, as it turns out, beyond their greater simplicity, institutes have some further surprising advantages over institutions.
Institutional semantics for manyvalued logics
"... We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our ..."
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We develop manyvalued logic, including a generic abstract model theory, over a fully abstract syntax. We show that important manyvalued logic model theories, such as traditional firstorder manyvalued logic and fuzzy multialgebras, may be conservatively embedded into our abstract framework. Our development is technically based upon the socalled theory of institutions of Goguen and Burstall and may serve as a template for defining at hand manyvalued logic model theories over various concrete syntaxes or, from another perspective, to combine manyvalued logic with other logical systems. We also show that our generic manyvalued logic abstract model theory enjoys a couple of important institutional model theory properties that support the development of deep model theory methods. Key words: institutions, manyvalued logic 1.
On the Algebra of the Structured Specifications
"... We develop module algebra for structured specifications with model oriented denotations. Our work extends the existing theory with specification building operators for nonprotecting importation modes and with new algebraic rules (most notably for initial semantics) and upgrades the pushoutstyle se ..."
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We develop module algebra for structured specifications with model oriented denotations. Our work extends the existing theory with specification building operators for nonprotecting importation modes and with new algebraic rules (most notably for initial semantics) and upgrades the pushoutstyle semantics of parameterized modules to capture the (possible) sharing between the body of the parameterized modules and the instances of the parameters. We specify a set of sufficient abstract conditions, smoothly satisfied in the actual situations, and prove the isomorphism between the parallel and the serial instantiation of multiple parameters. Our module algebra development is done at the level of abstract institutions, which means that our results are very general and directly applicable to a wide variety of specification and programming formalisms that are rigorously based upon some logical system. 1.
Under consideration for publication in Math. Struct. in Comp. Science Encoding Hybridised Institutions into First Order Logic
, 2013
"... A ‘hybridisation ’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridised institutions ..."
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A ‘hybridisation ’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridised institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridised institutions into (manysorted) first order logic (abbreviated FOL) as a ‘hybridisation ’ process of abstract encodings of institutions into FOL, which may be seen as an abstraction of the well known standard translation of modal logic into first order logic. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover we consider the socalled theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accommodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridisation process, which provides the possibility to shift a formal verification process from the hybridised institution to FOL. 1.
SERVICEORIENTED LOGIC PROGRAMMING
"... Abstract. We develop formal foundations for notions and mechanisms needed to support serviceoriented computing. Our work builds on recent theoretical advancements in the algebraic structures that capture the way services are orchestrated and in the processes that formalize the discovery and binding ..."
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Abstract. We develop formal foundations for notions and mechanisms needed to support serviceoriented computing. Our work builds on recent theoretical advancements in the algebraic structures that capture the way services are orchestrated and in the processes that formalize the discovery and binding of services to given client applications by means of logical representations of required and provided services. We show how the denotational and the operational semantics specific to conventional logic programming can be generalized using the theory of institutions to address both static and dynamic aspects of serviceoriented computing. Our results rely upon a strong analogy between the discovery of a service that can be bound to an application and the search for a clause that can be used for computing an answer to a query; they explore the manner in which requests for external services can be described as service queries, and explain how the computation of their answers can be performed through serviceoriented derivatives of unification and resolution, which characterize the binding of services and the reconfiguration of applications. 1.
Parchments for CafeOBJ logics? Till Mossakowski1, Wies law Paw lowski2, Donald Sannella3
"... Abstract. This paper addresses issues arising in the systematic construction of large logical systems. We rely on a modeltheoretic view of logical systems, captured by institutions that are in turn presented by parchments. We define their categories, and study constructions that may be carried out ..."
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Abstract. This paper addresses issues arising in the systematic construction of large logical systems. We rely on a modeltheoretic view of logical systems, captured by institutions that are in turn presented by parchments. We define their categories, and study constructions that may be carried out in these categories. In particular we show how limits of parchments may be used to combine features involved in various logical systems, sometimes necessarily augmenting the universal construction by additional systematic adjustments. We illustrate these developments by sketching how the logical systems that form the logical foundations of CafeOBJ may be built in this manner. 1
Graded consequence: an institution theoretic study
"... We develop a general study of graded consequence (of manyvalued logic) in an institution theoretic (in the sense of Goguen and Burstall) style. This means both syntax and semantics are considered fully abstract, as well as the satisfaction between them. Our approach contrasts to other approaches on ..."
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We develop a general study of graded consequence (of manyvalued logic) in an institution theoretic (in the sense of Goguen and Burstall) style. This means both syntax and semantics are considered fully abstract, as well as the satisfaction between them. Our approach contrasts to other approaches on manyvalued logic in that it is a multisignature one, in the spirit of institution theory. We consider graded consequence at three different conceptual levels: entailment, semantic, and closure operators, and explore several interpretations between them. We also study logical connectors and quantifiers both at the entailment and semantic level, compactness and soundness properties. 1.
On the Existence of Translations of Structured Specifications
"... We provide a set of sufficient conditions for the existence of translations of structured specifications across specification formalisms. The most basic condition is the existence of a translation between the logical systems underlying the specification formalisms, which corresponds to the unstructu ..."
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We provide a set of sufficient conditions for the existence of translations of structured specifications across specification formalisms. The most basic condition is the existence of a translation between the logical systems underlying the specification formalisms, which corresponds to the unstructured situation. Our approach is based upon institution theory and especially upon a recent abstract approach to structured specifications in which both the underlying logics and the structuring systems are treated fully abstractly. Hence our result is applicable to a wide range of actual specification formalisms that may employ different logics as well as different structuring systems, and is very relevant within the context of the fastly developing heterogeneous specification paradigm. 1.