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Topic: Conservative extension

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	Conservative extension - Wikipedia, the free encyclopedia
		Extensions by unconstrained predicate or function symbols are conservative.
		Extensions by predicate or function symbols that are axiomatized by a Horn theory are conservative.
		The importance of conservative extensions for the foundations of mathematics
	en.wikipedia.org /wiki/Conservative_extension (299 words)

	Antimeta: Conservative Extensions Are Permissible, But Non-Conservative Ones Can Be Mandatory (Site not responding. Last check: 2007-10-23)
		On the face of it, Hartry Field's insistence that the conservativity of mathematics (together with the existence of acceptable nominalistic scientific theories) means that we shouldn't believe in numbers flies in the face of mathematical history.
		The established conservativity of the complex numbers means that they are a consistent extension that is conservative over the nominalistic physical theory we already have, and therefore it is just as acceptable to talk about complex numbers as it is to talk about real numbers.
		The parts of our physical theories that talk about subatomic particles are not conservative over the nicely formulated parts that don't, but we must accept them and their implied entities anyway.
	www.antimeta.org /blog/archives/2005/03/conservative_ex.html (419 words)

	Conservative Partial Definitions
		Conservative partial definitions specify defining axioms that are conservative extensions of the language.
		However, the arbitrary sentences that can be included in partial definitions are not in general conservative extensions of the language and therefore must be transformed into a conditional form of defining axiom that is guaranteed to be conservative.
		The third form of conservative partial definition of a relation constant provides for the specification of necessary conditions for the relation to hold and optionally provides an arbitrary sentence to be included in the constant's conditional defining axiom.
	logic.stanford.edu /kif/Hypertext/node44.html (808 words)

	Wand on final algebra semantics
		Wand's main theorem is that every standard conservative extension has a maximal base-conservative augment.
		A base-conservative extension of an extension T0->T1 is an extension of T1 which conservatively extends the base T0 (the composition j;i in the diagram).
		With it in, the extension of the theory T0 of natural numbers to the theory T1 of arrays is standard.
	www.seas.upenn.edu /~sweirich/types/archive/1988/msg00175.html (826 words)

	Antimeta: Fictionalism Archives
		In fact, it's a conservative extension of the original language, and is additionally expressively conservative, in that any sentence at all in the extended language can be proven equivalent to one phrased in the restricted language.
		In "Conservativeness and Incompleteness" (from 1983), Stewart Shapiro attacks Field's program for nominalizing physics (and eliminating mathematics) by showing that the addition of ZFC to the nominalistic theory of gravity that he gives is in fact deductively non-conservative.
		Conservativity is the (testable) claim that there are no observational or purely concrete claims in, say, physics that are decided by the addition of mathematical axioms making reference to a separate class of non-observable entities.
	www.ocf.berkeley.edu /~easwaran/blog/fictionalism (7500 words)

	PlanetMath: von Neumann-Bernays-Gödel set theory
		NBG and ZFC are very closely related and are in fact equiconsistent, NBG being a conservative extension of ZFC.
		It is also not too difficult to show that NBG without global choice is a conservative extension of ZFC.
		This is equivalent to showing that NBG with global choice is conservative over NBG with only local choice.
	planetmath.org /encyclopedia/VonNeumannBernausGodelSetTheory.html (801 words)

	T-8 -- 2 What are the consequences for CASL? (Site not responding. Last check: 2007-10-23)
		The question arises which definition of conservative extension should be chosen to allow for optimal tool support.
		The definition of mt-conservative extensions is independent of the underlying logic.
		Switching to pt-conservative extensions would not be of any practical help as the definition postulates a property of all (usually infinitely many) sentences of a theory.
	homepages.inf.ed.ac.uk /dts/CoFI/Notes/T-8/index_2.html (380 words)

	Theravada as the Conservative Extension of the Buddha's Teachings: The arhant Ideal.
		Theravada as the Conservative Extension of the Buddha's Teachings: The arhant Ideal.
		Theravada is the more conservative tradition, inasmuch as it has consciously tried to maintain Buddhist practice among the members of the Sangha (the order of monks) in precisely the form that the historical Buddha first taught.
		Thus, the Theravada schools of Buddhism teach that the Buddha was a highly attained human being (not a god), and that monks who follow the rules of discipline (vinaya) are able to attain arhant (or arahat, arhat) status and reach the same state as the Buddha himself.
	www.humboldt.edu /~wh1/6.Buddhism.OV/6.Theravada.html (1165 words)

	Re: Wand on final algebra semantics
		Since "standard conservative" is a bit of a mouthful how about "biconservative" for "standard conservative?" Wand's theorem in its elementary (noncategorical) form then reads as follows.
		Also it seems reasonable to generalize "base-conservative augment of an extension" to mean one that makes no identifications of base terms other than those already made by the extension* itself*.
		together with the observation that when the extension is standard there is a greatest such augment and it coincides with the optimal one.
	www.cis.upenn.edu /~bcpierce/types/archives/1988/msg00176.html (357 words)

	Publications
		Their conservative extension with means to define control-structures or modes have been a long-term research topic and several solutions have emerged.
		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 preserved.
		The extension proposed here is conservative with respect to the fundamental properties of the initial language: reactivity (i.e, execution in bounded memory and time) and referential transparency are kept.
	www.lri.fr /~pouzet/bib/bib.html (2727 words)

	9. Theory Interpretations
		Model conservative extensions are safe extensions since they add new machinery without compromising the old machinery.
		The most important model conservative extensions are definitional extensions which introduce new symbols that are defined in terms of old vocabulary.
		Then instances of the model conservative extension type are obtained by instantiating the theory.
	imps.mcmaster.ca /manual/node14.html (2483 words)

	Abstract: Did I Damage my Ontology? A Case for Conservative Extensions in Description Logics. (Site not responding. Last check: 2007-10-23)
		We argue that, after performing such modifications, it is important to know whether the resulting ontology is a conservative extension of the original one.
		In this paper, we propose and investigate new reasoning problems based on the notion of conservative extension, assuming that ontologies are formulated as TBoxes in the description logic ALC.
		If the extension of an ontology is not conservative, our algorithm is capable of computing a concept that witnesses non-conservativeness.
	lat.inf.tu-dresden.de /~clu/papers/abstracts/kr06a.html (258 words)

	logicandlanguage.net: Dummett on Harmony, Conservative Extensions and Local Reduction/Normalisation
		This post will be a brief discussion of a family of related concepts - local reduction/normalisation, conservative extension and harmony - in the light of Dummett's "Circularity, Consistency and Harmony" in The Logical Basis of Metaphysics....
		And then: "A conservative extension in the logicians' sense is conservative with respect to formal provability.
		And, as noted earlier, he thinks that the rules governing a connective are in harmony with respect to a proof system just in case adding that connective to a proof system results in a conservative extension.
	www.logicandlanguage.net /archives/2005/04/dummett_on_harm.html (1436 words)

	Conservative Extension in Positive/Negative Conditional Term Rewriting with Applications to Software Renovation ... (Site not responding. Last check: 2007-10-23)
		We transpose a conservative extension theorem from structural operational semantics to conditional term rewriting.
		Fokkink, W.J., and Verhoef, C. (1998), "Conservative Extension in Positive /Negative Conditional Term Rewriting with Applications to Software Renovation Factories", Report P9802, University of Amsterdam.
		5 An SOS message: conservative extension for higherorder posit..
	citeseer.ist.psu.edu /17648.html (928 words)

	Conservativity theorem - Wikipedia, the free encyclopedia
		In mathematical logic, the conservativity theorem states the following: Suppose that a closed formula
		is a conservative extension of T, which means that the theory T
		In a more general setting, the conservativity theorem is formulated for extensions of a first-order theory by introducing a new functional symbol:
	en.wikipedia.org /wiki/Conservativity_theorem (165 words)

	[No title]
		I also show that adding all the "disquotational" T-sentences, " 'A' is true iff A" always yields a conservative extension.
		I define a deflationary theory of truth to be one which generates conservative extensions.
		I define an adequate theory of truth to be one which allows you to prove "T is true" from T. It follows that only a non-conservative theory of truth could be adequate.
	users.ox.ac.uk /~jrlucas/Godel/ketland.html (677 words)

	Aggregate Functions, Conservative Extension, and Linear Orders (Site not responding. Last check: 2007-10-23)
		If a query language possesses the conservative extension property, then the class of functions having certain input and output heights (that is, the maximal depth of nesting of sets in the input and output) definable in the language is independent of the height of intermediate data used.
		This paper shows that the nested relational calculus endowed with simple arithmetic and a summation operation has the conservative extension property.
		Grumbach and Vianu and Hull and Su proved that the presence of powerset destroys conservativity in the basic nested relational language.
	www.cis.upenn.edu /~db/abstracts/dbpl93b.html (186 words)

	Left gets nod from right on copyright law \| CNET News.com
		During a lecture organized by the American Enterprise Institute and the Brookings Institution., Posner criticized a 1998 law extending the duration of U.S. copyrights.
		Posner's critique is significant because up to now much of the attack on the steady expansion of intellectual-property rights has come from the left, and the Seventh Circuit judge is a darling of the conservative movement.
		In his speech, Posner warned that Hollywood studios and other entertainment companies that lobbied for the 1998 Copyright Term Extension Act could be fouling their own industry by reducing materials in the public domain.
	news.com.com /2100-1023-966595.html (589 words)

	Conservative Extension in Structural Operational Semantics (Site not responding. Last check: 2007-10-23)
		A question that arises naturally is whether or not the original and the extended TSS induce the same transitions in the original domain.
		Usually it is desirable that an extension is operationally conservative, meaning that the provable transitions for an original term are the same both in the original and in the extended TSS.
		This paper contains an exposition of existing conservative extension formats for Structural Operational Semantics, and their applications with respect to term rewriting systems and completeness of axiomatizations
	www.brics.dk /BRICS/RS/99/24 (123 words)

	Corrigenda to Mind 1999
		Then T È DT is a conservative extension of T. Proof.
		So, T È DT is a conservative extension of T (for L-sentences).
		Theorem 1: Let T extend K. Then T È DT is conservative* extension of T. Proof.
	homepages.ed.ac.uk /jketland/corrigendum.html (342 words)

	Conservative Extension in Structural Operational Semantics (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		SOS generates a labelled transition system, whose states are the closed terms over an algebraic signature, and whose transitions are supplied with labels.
		13 A general conservative extension theorem (context) - D'Argenio, Verhoef - 1997
		13 A general conservative extension theorem (context) - D'Argenio - 1995
	citeseer.ist.psu.edu /265260.html (701 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		In this paper we consider a conservative extension of the Euler equations for gas dynamics to describe a two-component compressible flow in Cartesian coordinates.
		It is well known that classical shock-capturing schemes applied to conservative models are oscillatory near the interface between the two gases.
		We solve directly this conservative model by a flux-split algorithm, due to the first author (see[J. Comput.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20390780 (316 words)

	Scientific Papers :: Downloads (Site not responding. Last check: 2007-10-23)
		A Conservative Extension of Synchronous Dataflow with State Machines
		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 la SyncChart.
		A Conservative Extension of Synchronous Dataflow with State Machines [245 KB]
	www.esterel-technologies.com /technology/scientific-papers (746 words)

	HOST pedigree (Site not responding. Last check: 2007-10-23)
		Robin Milner invents a simple form of polymorphism for typed lambda cacluli in the course of implementing a proof tool for Scott's Logic for Computable Functions (LCF).
		Mike Gordon combines Church's STT with Milner polymorphism and conservative extension features in his LCF derived implementation of HOL.
		Jean Raymond Abrial elaborates ZF set theory into the Z specification language which is used with freewheeling axiomatic extension and no apparent regard for conservative extension.
	www.rbjones.com /rbjpub/logic/log013.htm (142 words)

	Logic [Science]
		All the questions are related to a single topic, so I would like to draw 4 conclusions from the tendency, the 4 conclusions are: improving, descending, fluctuate, stable.
		Herman Rubin wrote: > As was already mentioned, NBG is a conservative extension > of ZF.
		This means that any theorem of ZF can be proved in > NBG if and only if it can be proved in ZF.
	www.adras.com /Logic.s94-50.html (432 words)

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