Adam Grove. Two Modellings for Theory Change. The Journal of Philosophical Logic, 17:157--170, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on #. It is the two last ones (R5) and (R6) that allow to state the below representation theorem, which says that a revision operator corresponds to a family of pre orders on interpretations. The theorem is due to Katsuno and Mendelzon, but the idea can be directly traced back to Grove [10]. But first we need the following: Definition 2 (Faithful assignment) A function that maps each belief set B to a pre order on interpretations is called a faithful assignment if and only if the following holds: B, then # B, then # B # # 3. If B 1 = B 2 , then #B1 =#B2 ....

A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17(157-180), 1988.

....(K a) If a K then (K a) a = K (I( 7) a) n ) a (K S) If K (a ) then K (a ) There are a number of different methods for con structing AGM contraction operations. We briefly describe a model theoretic semantic method which uses total preorders on V. From results by Grove [7] and Katsuno and Mendelzon [11] AGM contraction can be characterised semantically by a set of total preorders (i.e. connected, reflexive, transitive relations) on V. For any total preorder on V, we say that x W V is minimal in W iff for every y W, x y, and we denote the set of ....

Adam Grove. Two modellings for theo- ry change. Journal of Philosophical Logic, 17:157-170, 1988.

....Internet Customer s Station Customer s Station Customer s Station Figure 1: The CESM Architecture The frequency of the collection of soft measurements is determined by analysing the previous results and evaluating the results stored in the CESM database. Using belief revision techniques [18], we are then able to estimate the appropriate time to retrieve the new soft data sample. 4 The CESM Tool The CESM tool is comprised of three components: QD (Questionnaire Designer) an application where the author designs questionnaires for each . WP (Web Page) of each questionnaire, which ....

Grove A. Two modellings for theory change . Journal of Philosophical Logic. 17, 157-170, 1988.

....in order to accommodate some new fact, the less entrenched belief will be relinquished, while the more entrenched persists. Semantically, an entrenchment relation (hence a revision function) can be modeled by associating with each set of possible worlds a plausibility, in any of a number of ways [5, 10, 17, 20]. For the purposes of this paper, we adopt Spohn s ordinal conditional functions or rankings [ 19, 31] A function W N U oo assigns to each world a ranking reflecting its plausibility: if (w) v) then w is more plausible than v. We insist that (0) 3, so that maximally plausible worlds ....

....anc I( the inconsistent belief set) It is normally assumed that [ N W 5k( 3 for every satisfiable thus every satisfiable proposition is accorded some degree of plausibility. It is wellknown that this type of model induces the class of revision functions sanctioned by the AGM postulates [5, 19, 20]. We define conditional plausibility, for U, V C W and (U) 5k( as: VlU) A U) Intuitively, this denotes the degree to which F would be considered plausible if U were believed. These notions are strongly reminiscent of standard concepts from probability theory. Indeed, the role of q ....

A. Grove. Two modellings for theory change. J. Phil. Logic, 17:157-170, 1988.

....meet contraction function over K if and only if 8) over K. The respective revision operation defined via the Levi identity satisfies postulates (K 8) It can also be shown that requiring to be connected does not lead to further contraction postulates. Grove s Sphere Semantics Grove [39] developed a sphere semantics for the AGM framework inspired by Lewis [67] semantics for counterfactual reasoning. He concentrated on revision functions although the idea is easily extended to deal with contraction (via the Harper Identity) and expansion. Grove views maximally consistent ....

....and defined as [ff] fffg] i.e. ff] fm 2 M L : ff 2 mg) We also define a function th : 2 K mapping sets of possible worlds to belief sets. For any X M L we have (Def th) th(X) fm 2 Xg for X M L and X 6= K if X = We reproduce the following properties, listed by Grove [39], for reference. Lemma 2.2.14 Properties of th [39] i) th( K] K for all belief sets (i.e. theories) K if the underlying logic is compact (ii) th(X) 6= K if and only if X is nonempty Grove s idea can be viewed as a semantics insofar as it gives a picture for AGM belief change. ....

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Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

....these options) satisfy a certain set of axioms. Grove s approach also begins with a natural model of theory choice, and then proves that we can think of an agent as revising her theories in this way just in case her choice of a new theory (her belief revision function) satisfles certain axioms (Grove 1988). It is easiest to describe Grove s model of belief change in terms of possible worlds. Aside from formal convenience, this approach will also provide an opportunity to illustrate a technique for passing from a syntactic to a semantic setting that is often useful in formal logic. 26 Oliver ....

Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic 17, 157-170.

.... for inconsistent belief bases has been studied in an alternative approach by Brewka [4] paraconsistent belief revision is explored by Tanaka [34] while Restall and Slaney [31] have developed a paraconsistent semantical representation based on the revision of models approach 21 suggested in Grove [16]. The investigation of complexity procedures in Nebel [27] via a ne grained set of complexity classes, has shown that the complexity of base revision procedures satisfying AGM postulates is that of ordinary propositional derivability. Nebel s comparison of di erent revision methods shows that ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-170, 1988.

....own logical closure. Definition 4.2 The knowledge base extracted from a total preorder on is some sentence QF such that XQF K d . The intuition is in line with the typical minimal model semantics approach in the nonmonotonic reasoning and belief revision literature [7, 11, 10]. Example 4.2 Consider the infobase 8W S K ML0 Lq , N . It is easily verified that g B , g w a , g H Xm k , g H XB k , and thus that F , d . BLm . In other words, the knowledge base extracted from is logically equivalent to 0 . As would be expected, ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

....of its own logical closure. Definition 4.2 The knowledge base extracted from a total preorder on is some sentence T s.t. T . The intuition is in line with the typical minimal model semantics approach in the nonmonotonic reasoning and belief revision literature [Grove, 1988; Kraus et al. 1990; Katsuno and Mendelzon, 1991] Example 4.2 Consider the infobase ; Y2LKJ3]KJAd2L . It is easily verified that drn k F , rn F , 1 Actually, Meyer defines an infobase as a list, or sequence, of sentences. However, the reason for this is to allow for ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

....is therefore also possible. Definition 4.2 The knowledge base extracted from a total preorder on is some sentence V B s.t. V X 0 . The intuition is in line with the typical minimal model semantics approach in the nonmonotonic reasoning and belief revision literature [9, 14, 13]. Example 4.2 Consider the infobase 1 727G 1 . It is easily verified that , f ] S , l S , f k] S , and thus that 0 I7u k . In other words, the knowledge base extracted from s is logically equivalent to 2 . As would be expected, knowledge ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-- 170, 1988.

....include contraction and revision operations) as functions from IB L to IB, where IB is the set of all infobases. We shall also frequently assume the existence of a fixed infobase IB, and consider infobase IB change operations as functions from L to IB. From results by Grove [7] and Katsuno et al. 9] AGM theory change can be characterised by a set of total preorders (i.e. connected, reflexive, transitive relations) on U . For a total preorder # on U , we say that x # V # U is # minimal in V i# for every y # V , x # y, and we denote the set of # minimal ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

....criteria bounding the properties of any revision function. There have been various modellings of these postulates, including that of the epistemic entrenchment of sentences in a language [ GM88 ] In this paper we will be most concerned with a modelling of revision, due to Adam Grove [ Gro88 ] that is based on Lewis system of spheres semantics for counterfactuals [ Lew73 ] In this paper I am concerned with fundamental notions of belief revision. The question addressed is a familiar one: given a knowledge base and sentence by which the knowledge base is to be revised, what can ....

....state can be modelled by a set of complete and consistent descriptions of how the world might be, assuming that the system s beliefs are true. I will refer to this latter characterisation, in terms of possible worlds, as a knowledge base. This second characterisation is used for example in [ Gro88 ] Given these precedents, I will use both belief sets (in specifying postulates) and knowledge bases (in the modelling) in this paper. These notions are easily interdefinable. Roughly speaking, for belief state K and knowledge base jKj (where the notation will be made clear later) and for ....

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-- 170, 1988.

....be clear that postulates (K 1) to (K 8) aim to characterize only one of the unary functions Gamma K , or equivalently, consider for a fixed, given theory K. We turn now to a semantic characterization of the AGM revision function. Among the alternative presentations of the AGM theory, Grove s [4] provides a possible worlds semantics via his constructions based on systems of spheres. A system of spheres S K for a theory K is a subset of P(W ) containing W , totally ordered under set inclusion, such that [K] is the minimal element of S K . A system S K should validate the Limit ....

....S K (notated as c K (A) with non empty intersection with [A] A system S K determines a revision function for K in the sense that for every formula A 2 L and every w 2 W , w 2 [K A] iff w 2 [A] and w 2 c K (A) Grove proves the following representation result. Observation 2. 2 (Grove, [4]) The following are equivalent: i) The revision operation satisfies (K 1) K 8) ii) There exists a system of spheres S K such that for all formulas A 2 L, K A = Th(c K (A) A] A system of spheres S K is well founded if establishes a well founded relation on S K . The class of ....

Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-- 170, 1988.

....with respect to the intersection and union of theories, and they present some properties of multiple contractions. Following this idea we elaborate upon the de nition of an iterable function for each of the ve AGM presentations: postulates [ Alchourr on et al. 1985 ] systems of spheres [ Grove, 1988 ] meet functions [ Alchourr on and Makinson, 1982 ] epistemic entrenchments [ G ardenfors and Makinson, 1988 ] and safe hierarchies [ Alchourr on and Makinson, 1985 ] 4 CARLOS ARECES VER ONICA BECHER In this work we assume knowledge of the AGM model as well as basic knowledge of ....

....s L is transitively relational. 3.3 Extended Systems of Spheres In this section we develop a de nition of an iterable contraction function based on Systems of Spheres, which turns out to be equivalent to an early unpublished result of Makinson 2 . We rst turn to Grove s original framework [ Grove, 1988 ] A system of spheres S for a theory K is a set of sets of possible worlds that veri es the properties S1. If U; V 2 S then U V or V U . Totally Ordered. S2. For every U 2 S, K] U . Minimum. S3. M 2 S. Maximum. S4. For every sentence such that there is a sphere U in S with ....

A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-170, 1988.

.... modification of oe consistent with the above procedure for calculating B(oe E) That is, world states in min oe (E) are brought to the bottom of the revised order, leaving the ordering over all other world states unaffected: w oe ME w 0 , w 2 min oe (E) w oe w 0 ) 2 Adam Grove [10] showed that any method satisfying the axioms presented in [5] can be so represented. It should be mentioned, however, that an alternative approach to revision called updating [13] proceeds differently. 2 The lexicographic method L , presented by Spohn [28] and generalized by Nayak [24] ....

Adam Grove (1988) "Two Modellings for Theory Change", Journal of Philosohical Logic 17: 157-170.

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Adam Grove. Two Modellings for Theory Change. The Journal of Philosophical Logic, 17:157--170, 1988.

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-- 170, 1988.

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Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

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Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-- 170, 1988.

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

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A. Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157--170, 1988.

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Grove, A. (1988) `Two Modellings for Theory Change', Journal of Philosophical Logic, Vol. 17, pp. 157-70

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Adam Grove. Two modellings for theory change. Journal of Philosophical Logic, 17:157-170, 1988.

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