Topic
Conservative extension
About: Conservative extension is a research topic. Over the lifetime, 421 publications have been published within this topic receiving 8083 citations.
Papers published on a yearly basis
Papers
TL;DR: This paper introduces the notions of conservative extension, safety and module for a very general class of logic-based ontology languages, and provides the notion of a safety class, which characterizes any sufficient condition for safety, and identifies a family of safety classes-called locality--which enjoys a collection of desirable properties.
Abstract: In this paper, we propose a set of tasks that are relevant for the modular reuse of ontologies. In order to formalize these tasks as reasoning problems, we introduce the notions of conservative extension, safety and module for a very general class of logic-based ontology languages. We investigate the general properties of and relationships between these notions and study the relationships between the relevant reasoning problems we have previously identified. To study the computability of these problems, we consider, in particular, Description Logics (DLs), which provide the formal underpinning of the W3C Web Ontology Language (OWL), and show that all the problems we consider are undecidable or algorithmically unsolvable for the description logic underlying OWL DL. In order to achieve a practical solution, we identify conditions sufficient for an ontology to reuse a set of symbols "safely"--that is, without changing their meaning. We provide the notion of a safety class, which characterizes any sufficient condition for safety, and identify a family of safety classes-called locality--which enjoys a collection of desirable properties. We use the notion of a safety class to extract modules from ontologies, and we provide various modularization algorithms that are appropriate to the properties of the particular safety class in use. Finally, we show practical benefits of our safety checking and module extraction algorithms.
436 citations
27 Jul 1996
TL;DR: The linear type theory LLF is presented as the formal basis for a conservative extension of the LF logical framework and can be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination.
Abstract: We present the linear type theory LLF as the formal basis for a conservative extension of the LF logical framework. LLF combines the expressive power of dependent types with linear logic to permit the natural and concise representation of a whole new class of deductive systems, namely those dealing with state. As an example we encode a version of Mini-ML with references including its type system, its operational semantics, and a proof of type preservation. Another example is the encoding of a sequent calculus for classical linear logic and its cut elimination theorem. LLF can also be given an operational interpretation as a logic programming language under which the representations above can be used for type inference, evaluation and cut-elimination.
208 citations
TL;DR: The notion of π-institution is proposed as an alternative to the notion of institution, replacing the notions of model and satisfaction by a primitive consequence operator in the definition of a logic.
Abstract: Building on the work of Goguen and Burstall on institutions and on Tarski's notion of deductive system, a categorial framework for manipulating theories in an arbitrary logic is presented. Its main contribution is the formalisation of the semantics of theory-building operations on top of a consequence relation. For that purpose, the notion of π-institution is proposed as an alternative to the notion of institution, replacing the notions of model and satisfaction by a primitive consequence operator in the definition of a logic. The resulting approach to the semantics of specification languages is intrinsically different from the original one in the sense that the ultimate denotation of a specification is taken herein to be a class of theories (sets of formulae closed for the consequence relation) and not a class of models of that logic. Adopting this point of view, the semantics of Clear-like specification building operations is analysed.
136 citations
18 Sep 2005
TL;DR: The central idea of the paper is to base this extension of a synchronous data-flow language such as Lustre with imperative features expressed in terms of powerful state machine à la SyncChart on the use of clocks, translating imperative constructs into well clocked data- flow programs from the basic language.
Abstract: This paper presents an extension of a synchronous data-flow language such as Lustre with imperative features expressed in terms of powerful state machine a laSyncChart This extension is fully conservative in the sense that all the programs from the basic language still make sense in the extended language and their semantics is preservedFrom a syntactical point of view this extension consists in hierarchical state machines that may carry at each hierarchy level a bunch of equations This proposition is an alternative to the joint use of Simulink and Stateflow but improves it by allowing a fine grain mix of both stylesThe central idea of the paper is to base this extension on the use of clocks, translating imperative constructs into well clocked data-flow programs from the basic language This clock directed approach is an easy way to define a semantics for the extension, it is light to implement in an existing compiler and experiments show that the generated code compete favorably with ad-hoc techniques The proposed extension has been implemented in the ReLuC compiler of Scade/Lustre and in the Lucid Synchrone compiler
136 citations
TL;DR: It is proved that dWPHP(PV) is (over S21) equivalent to a statement asserting the existence of a family of Boolean functions with exponential circuit complexity, and the Nisan–Wigderson construction is formalized in a conservative extension of S21.
128 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 4 |
| 2024 | 2 |
| 2023 | 1 |
| 2022 | 17 |
| 2021 | 10 |