Peter Johnstone. Stone Spaces. Cambridge University Press, Cambridge, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....work performed on the formalization of the ccl book is the result of a team e ort by researchers and students of the University of Bia lystok with some contributions from members in Canada and Japan. In the summer of 1995, a seminar devoted to the theory of continuous lattices based on [25] and [30] covered the material to be formalized and in the spring of 1996 the actual work of formalization began. Grzegorz Bancerek volunteered to lead the ccl project from the beginning and has continued this leadership since. The list of all past and current participants comprises 16 authors listed below ....

Peter T. Johnstone. Stone Spaces. Cambridge University Press, Cambridge, London, New York, 1982.

....among them on the fly. So there is no alteration of already existing constraints based on the semantic characterisation, but a satisfiability check and negotiation of constraints when inconsistency is detected. The transgressive adaptation can be compared with the revision in knowledge bases [Grdenfors, 1992] : the addition of a new (adaptation) constraint leads to inconsistency. It is necessary to find a new specification satisfying this constraint and not too different from the source specification. One difference is that adaptation constraints are not always formulas of the specification language. ....

Peter Grdenfors, editor. Belief revision. Cambridge university press, Cambridge (GB), 1992.

....cluster contains the communicational belief cluster, which on its turn contains the default belief cluster. Hence the credibility of a belief is inversely proportional with the size of the cluster on which the belief is interpreted. Note furthermore that from the point of view of belief revision [11, 12], expansions of the various belief sets correspond to shrinkings of the associated belief clusters and contractions of the belief sets correspond to extensions of the clusters (cf. 29] 3.3. Definition. The Kripke models given in Definition 2.3 are modified as follows: the function B is ....

....otherwise in order to maintain consistency of the agent s belief set some of the old beliefs of the agent are deleted before including the new formula. The revision implemented by the actions that we present validates the (well known and by now standard) AGM postulates for belief revision [1, 11, 12, 29]. To deal adequately with the classification of the agents information, the low level revision action is defined to stretch over the various information classes. To emphasize the distinction between the high and the low level informative actions, we introduce in addition to the set of rational ....

P. Gardenfors, editor. Belief Revision. Cambridge University Press, 1992.

....the programmers often are not even professional programmers, but rather users of numerical computing like theoretical physicists, engineers, or meteorologists. Notice that this problem is not restricted to RWL descriptions. Action Semantics, for example, has its operational semantics de ned in [29] with the Structured Operational Semantics method [32] and a programmer will probably won t buy this document in order to better understand the programming language he s using, as the notation is intuitive enough (by its very purpose) The point is that, like Action Semantics or Abstract State ....

Peter D. Mosses. Action Semantics. Cambridge University Press, 1992. CTCS 26.

....natural given the prominence of probability theory in various scienti c disciplines, more e ort is needed to understand the basic principles underlying qualitative decision making. The use of qualitative For example, work on qualitative notions of knowledge and belief [28, 35] belief revision [24], nonmonotonic reasoning [27] planning [1] and qualitative physical models [21] decision tools is likely to come with a price in terms of decision quality, and it is important to develop a better understanding of the basic properties of di erent qualitative decision making approaches. Our aim ....

P. Gardenfors. Belief Revision. Cambridge University Press, 1992.

....natural given the prominence of probability theory in various scientific disciplines, more effort is needed to understand the basic principles underlying qualitative decision making. The use of qualitative For example, work on qualitative notions of knowledge and belief [28, 35] belief revision [24], nonmonotonic reasoning [27] planning [1] and qualitative physical models [21] decision tools is likely to come with a price in terms of decision quality, and it is important to develop a better understanding of the basic properties of different qualitative decision making approaches. Our aim ....

P. Gardenfors. Belief Revision. Cambridge University Press, 1992.

....of X, written x 0 . We say that x X is regular if 3 x = x 00 . Obviously, x x 0 = Hence, if x is open, then x x 00 . The following well known theorem underlies the importance of the regular sets to mereotopology. We state it here without proof. See, e.g. Johnstone [21], section 1.13. Theorem 1 Let X be a topological space. Then the set of regular sets in X forms a Boolean algebra with top and bottom defined by 1 = X and 0 = and Boolean operations defined by x:y = x y, x y = x [ y) 00 and Gammax = x 0 . Accordingly, we shall sometimes use the ....

Peter Johnstone. Stone Spaces. Cambridge University Press, Cambridge, 1982.

....extra topological structure that is not categorical. In general, this category has little categorical structure, lacking in general most limits and colimits. However, a very important exception is that it has all filtered colimits. I don t want to define these in detail (see, e.g. Johnstone [5]) but they are the categorical generalization of directed joins, and I shall describe two particular cases. There are some general points to remember. First, they are constructed set theoretically: a filtered colimit of models is carried by the set theoretic filtered colimits of the carriers. ....

....further and also showed how to generalize the upper powerdomain. Third, it gave an ilustration of the use of the well known categorical generalization of algebraicity, replacing ideal completions of posets by ind completions of categories (i.e. free categories with all filtered colimits see [5]) Topical Categories of Domains This work is still in preparation, though a preliminary account was given in Vickers [11] It exploits the fact that theories of information systems used to present domains (there are various flavours) are geometric: so there are toposes classifying information ....

Peter Johnstone, Stone Spaces, Cambridge University Press, 1982.

....to develop highperformance executable environments for other formal speci cation languages with much less e ort and much greater exibility, maintainability, and extensibility than what would be required in conventional implementations. For example, an executable environment for Action Semantics [52] is currently being considered, and it would be quite interesting to explore Maude implementations, for example, for a next generation CafeOBJ [24] and for CASL [23] Therefore, before discussing in detail the executable speci cation of Full Maude in Maude, we explain the more general methodology ....

Peter Mosses. Action Semantics. Cambridge University Press, 1992.

....ML(CZF) can accomodate reinterpretations of the logic. We focus our attention on reinterpretations of the logic as determined by an operator j on the type P that satis es a type theoretic version of the properties of a Lawvere Tierney topology in an elementary topos [16] or of a nucleus on a frame [14]. We will call such an operator j a topology. The reinterpretation of logic determined by j will be called the j interpretation. In discussing j interpretations, it seems appropriate to consider ML(CZF ) initially, and ML(CZF) at a later stage. There are two main reasons for doing so. A rst ....

Peter T. Johnstone, Stone Spaces, (Cambridge University Press, Cambridge, 1982).

....1 Freedom of Abstraction It is well known that general abstraction principles are needed to cope with the complexity of large systems. For data structures the algebraic specification approach (see [33] shows a way to deal with abstract data types; for actions the action semantics approach (see [30]) proposes a scheme for constructing complex operations out of basic components. Evolving algebras offer the possibility to choose both, the data and the basic actions, at any level of abstraction and independently of each other. The way how this is done is very simple and corresponds to common ....

Peter D. Mosses. Action Semantics. Cambridge University Press, 1992.

.... values and objects, and hence is more in line with traditional formal semantics, and which consequently goes against the everything is an object philosophy known from informal descriptions of object oriented languages [4, in particular] The description is using the formalism Action Semantics [11, 12]. It is still under construction, though. The generalization part has to do with the type system, particularly inheritance or specialization, as it is normally designated in the Scandinavian OO tradition. Normally, specialization is an operational mechanism, in the sense that it supports the ....

Peter D. Mosses. Action Semantics. Cambridge University Press, Cambridge, GB, 1992.

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Gardenfors P. Belief Revision. Cambridge University Press, 1992.

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Gardenfors P. Belief Revision. Cambridge University Press, 1992.

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Peter Johnstone. Stone Spaces. Cambridge University Press, Cambridge, 1982.

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Peter T. Johnstone. Stone Spaces. Cambridge University Press, Cambridge, 1986. Reprint of the 1982 edition.

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P. Gardenfors, Belief Revision, Cambridge University Press, 1992.

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Peter T. Johnstone. Stone spaces. Cambridge University Press, Cambridge, 1986.

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Peter T. Johnstone. Stone spaces. Cambridge University Press, Cambridge, 1986. Reprint of the 1982 edition.

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Peter Jephson Cameron. Combinatorics: topics, techniques, algorithms. Cambridge University Press, Cambridge, U.K., 1994.

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Peter D. Mosses. Action Semantics. Cambridge University Press, 1992.

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Peter J. Cameron. Combinatorics. Cambridge University Press, Cambridge, 1994.

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Peter T. Johnstone. Stone Spaces. Cambridge University Press, Cambridge, 1986. Reprint of the 1982 edition.

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Peter T. Johnstone. Stone spaces. Cambridge University Press, Cambridge, 1986.

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Peter Gardenfors, editor. Belief revision. Cambridge University Press, 1992.

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