M. Ginsberg and W. Harvey. Iterative broadening. Artificial Intelligence, pages 367--383, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....completion, we were made aware of an system that generated constraint satisfaction problems as subproblems, and thus required a search engine to solve these problems efficiently. The system, called COPS [14] implements a newly developed approach to generative planning, called approximate planning [13]. This approach is based on refining two planset descriptions, one describing those plans that can be guaranteed to succeed and another describing those plans that may succeed. If the first set can be shown to contain a member, that plan is a solution, where as if the second set can be shown to be ....

Matthew L. Ginsberg. Approximate planning. Artificial Intelligence, 76:89--123, 1995.

....methods provide better results than depth first search for a given time limit. We distinguish four approaches: Iterative weakening methods solve the same problem repeatedly with some search restrictions progressively relaxed at each iteration. See, for instances, iterative broadening (IB) [11] which uses an artificial breadth cuto#, limited discrepancy search (LDS) 17] which uses a maximum number of discrepancies along all the search paths and depth bounded discrepancy search (DDS) 32] which allows discrepancies high in the tree by means of an iteratively increasing depth bound. ....

....explorations based on the same search tree following the ordered tuning policy from the first greedy combination to the last complete one. The primitive increasedScope implements this strategy. We describe several iterative weakening methods using this primitive: IB: iterative broadening [11] In practice, the increasing property is verified if the policy contains monotonically increasing parameter values. increasedScope(p, list(0, 1, 2, nodelimit(p, order, st) LDS: limited discrepancy search [17] increasedScope(p, list(0, 1, 2, pathlimit(p, sum(order) st) ....

M.L. Ginsberg and W.D. Harvey. Iterative broadening. Artificial Intelligence, 55:367--383, 1992.

....The main drawback of these methods is the fact that each iteration revisits all the interior nodes of the previous iteration, except when a better upper bound has been found. We give four examples of iterative methods using a decreasing degree of incompleteness. Iterative Broadening [9] Iterative Broadening controls the search algorithm incompleteness by using a cardinality condition (Inc) limiting domain enumeration. This condition evolves from one to the maximum domain size (MaxCard) FOR(1,MaxCard) L Inc ) where prune ) solution cont Some iterative ....

M.L. Ginsberg and W.D. Harvey. Iterative broadening. Artificial Intelligence, 55:367--383, 1992.

....(RCL) and explore the subproblem generated only by 6 RCLs for each variable. This method provides in general a good starting point for performing local search. Our ranking method could be in principle applied to GRASP like algorithms. Another connection can be made with iterative broadening [15], where one can view the breadth cuto# as corresponding to the cardinality of our good sets. The first generated subproblem of both approaches is then the same. However, iterative broadening behaves di#erently on backtracking (it gradually restarts increasing the breadth cuto#) 3.1 Linear ....

M.L. Ginsberg and W.D. Harvey. Iterative broadening. Artificial Intelligence, 55(2):367--383, 1992.

....some initial solution of the subproblem, and try to improve it by performing problem dependent local moves . The resulting approach is not complete . 4 Comparison with other approaches This section compares DBS with similar approaches to traverse a search tree, namely Iterative Broadening (IB) [2] and Limited Discrepancy Search (LDS) 5] Note the distinction between LDS as sole search strategy (single valued) and LDS as component of DBS to generate subproblems (multi valued) For our comparison we make the following assumptions. DBS, IB and LDS are applied to the same search tree with ....

....a higher probability of being successful than LDS under certain conditions. Finally, we show experimental behaviour of LDS and DBS on the whole search tree, given a number of probability distributions among the branches being successful. 4. 1 Iterative Broadening Iterative Broadening (IB) see [2]) introduces a breadth cut o# c 0 which is the maximum branch width to explore in a Depth First Search (DFS) tree. First c 0 is set to some initial value, and the corresponding search tree is traversed in a DFS manner. After that, we increase c 0 and traverse the extended search tree. Typically c ....

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M.L. Ginsberg and W.D. Harvey. Iterative broadening. Artificial Intelligence, 55(2):367--383, 1992.

....to which the body of knowledge should change as little as possible if new information is incorporated. A well known knowledge change approach is the Set Of Theories approach, a formula based change method first defined in [16] in the context of databases and considered for AI applications e.g. in [22, 38]. This method works as follows. Assume that the sentence p must be incorporated into the knowledge base T , which is a finite set of sentences. If T is consistent with p, then p is simply added to T ; otherwise, is provable from T . In this case, a set R of sentences is removed from T such ....

....edges of Tr(T , P ) Formally, let T = f 1 , fn be a finite set of satisfiable sentences and let p be a satisfiable sentence in a suitable logic. Then, define = p , T R = T , E) R E , W # p W ; p) p) denotes the possible worlds [22], which are with respect to set inclusion maximal subsets of T in which the sentence p may be true. It is easily verified that ; p) is the collection of all maximal independent sets of the hypergraph = T , E) i.e. the maximal sets (under set inclusion) W T such that S W for every ....

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M. L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....to Levi identity, the revision functions are obtained by adding the new data to the output of the contraction functions. The main idea is that of simple base contraction, using B#a. Contraction is defined as the intersection of all subsets in B#a. We modify the original notion given in [3] [9], 14] in order to retain the finiteness of the base) A di#erent approach was introduced in [1] for belief sets, but may be easily adapted to belief bases. The safe contraction is the base obtained deleting all possible minimal subsets implying a. Deleting the elements of an incision on B#a ....

Ginsberg, M.L., Counterfactuals. Artificial Intelligence 30(1), pp. 35-79, (1986)

....strict order on Omega will be denoted by ) and a function r : V 7 Omega (the ranking function) such that s OE t iff r(s) r(t) The proof is simple and will not be given. A partial order satisfying any of the conditions of Lemma 14 will be called modular (this terminology is proposed in [12] as an extension of the notion of modular lattice of [13] Definition 14 A ranked model W is a preferential model hV; l; OEi for which the strict partial order OE is modular. 19 Those models are called ranked since the effect of function r of property 4 of Lemma 14 is to rank the states: a ....

Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....to Levi identity, the revision functions are obtained by adding the new data to the output of the contraction function. The main idea is that of simple base contraction, using B#a. Contraction is defined as the intersection of all subsets in B#a. We modify the original notion given in [3] [9], 14] in order to retain the finiteness of the base) A different approach was introduced by [1] for belief sets, but may be easily adapted to belief bases. The safe contraction is the base obtained deleting all possible minimal subsets implying a. Last, deleting the elements of an incision on ....

Ginsberg, M.L., Counterfactuals. Artificial Intelligence 30(1), pp. 35-79, (1986)

....rules to decide if a node should be expanded, while iterative sampling makes that choice randomly. Iterative state space reduction is a combination of heuristic node pruning and iterative weakening [39] Iterative weakening directly follows iterative deepening [24] and iterative broadening [15]. These iterative methods all repeatedly apply a search process, but with stronger or weaker parameters in different passes. It has been shown that a given set of search policies should be applied in an increasing order of the search complexities that these policies incur [39] Iterative ....

....but with stronger or weaker parameters in different passes. It has been shown that a given set of search policies should be applied in an increasing order of the search complexities that these policies incur [39] Iterative state space reduction bears a close similarity to iterative broadening [15]. Briefly, iterative broadening first carries out a search with a breadth limit of two. If it fails, the algorithm repeats the search with breadth limit of three, and so on, until it finds a solution. Early passes of both algorithms comb through the state space for better solutions, and they ....

M. L. Ginsberg and W. D. Harvey. Iterative broadening. Artificial Intelligence, 55:367-- 383, 1992.

..... The set that is associated with is defined as follows: KB = f 2KB j ( t and A( I( KB) g: 1 Keeping this semantical correspondence to the original information is one of the main differences between the present formalism and some other formalisms for restoring consistency (see, e.g. [5, 6, 9]) The set KB corresponds to the (maximal) fragment of KB that can be interpreted in a consistent way by . Elimination of pieces of inadequate information in order to get a more robust representation of the intended knowledge is a common method in belief revision and argumentative ....

....corresponds to the (maximal) fragment of KB that can be interpreted in a consistent way by . Elimination of pieces of inadequate information in order to get a more robust representation of the intended knowledge is a common method in belief revision and argumentative reasoning (see, e.g. [5, 6, 9]) Proposition 2. 1] Every set that is associated with a model of KB is a recovered knowledge base of KB. Proposition 2 implies that usually there will be a lot of ways to recover a given inconsistent knowledge base. By what we have noted above, plausible candidates of being the best ....

M.Ginsberg. Counterfactuals. Artificial Intelligence 30(1), pages 35--79, 1986.

....This process has been called belief revision and the result of revising T with P is denoted as T # P . This minimal change assumption was followed by the introduction of a large number of specific revision operators. Among the others, we mention Fagin, Ullman and Vardi [FUV83] Ginsberg [Gin86] and Dalal [Dal88] A general framework for belief revision has been proposed by Alchourron, Gardenfors and Makinson [AGM85, Gar88] A close variant of revision is update. The general framework for update has been studied by Katsuno and Mendelzon [KM89, KM91] and specific operators have been ....

....with the revising formula P : W (T, P ) T # # T T # # P # = #, #U : T # # U # T, U # P # = # The set W (T, P ) contains all the plausible subsets of T that we may retain when inserting P . 3 Ginsberg. Fagin, Ullman and Vardi in [FUV83] and, independently, Ginsberg in [Gin86] define the revised knowledge base as a set of theories: T # G P . T # # P T # # W (T, P ) That is, the result of revising T is the set of all maximal subsets of T consistent with P , plus P . Logical consequence in the revised knowledge base is defined as logical consequence in ....

M. L. Ginsberg. Conterfactuals. Artificial Intelligence, 30:35--79, 1986.

....entailment, and then, conclude only the sentences which are in the intersection of all the closures. Many semantics use this cautious principle. This includes notably the framework of Rescher and Manor [26] which has been recommended in the areas of belief update [13] belief base revision [16,24], and combined knowledge [2,17] If all pieces of information in the environment are equally reliable, this principle can be specified by a mapping 4, which we call cautious scheme, from finite sets of sentences of LW to sentences of LW and defined as follows: 4(A) T max(fB A : B is ....

....as follows: A j= p OE iff 4 p (A) j= OE: 4.2 Approximate reasoning Now, we turn to the formalization of approximate reasoning. From this point of view, it is interesting to notice that cautious reasoning, possibly prioritized, corresponds neatly to revising a knowledge base, in the sence of [16,24], with the sentence true , which indeed eliminates inconsistency. However, it has been recently proved that deciding whether a sentence belongs to such a revised knowledge base is a Pi P 2 complete problem in the propositional case [11] In other words, it seems impossible to solve it by a ....

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M. L. Ginsberg. Counterfactuals. Artificial Intelligence, 30(1):35--79, 1986.

....It must be noted that there are several correct, i.e. satisfying the Gardenfors postulates, ways to revise a knowledge base. That is, the Gardenfors postulates do not specify the revision process unambiguously. Of the possible revision schemes, as described in the literature, we discuss Ginsberg s [Gin86], which is also independently developed by Fagin, Ullman and Vardi [FUV83] The main reason for presenting this scheme here, is that it is relatively straightforward to explain and it is more or less easily extended towards the incorporation of domain specific information as will be described in ....

....way. Next, we will discuss the relationship between belief revision and diagnosis. To do this, we will introduce a notion related to belief revision systems: counterfactuals. Counterfactuals A counterfactual is a conditional statement as If p, then q , where p is known or expected to be false [Gin86]. Counterfactuals were introduced by Lewis [Lew73] to overcome the problem with material implication if the antecedent is false. For example, the absurd 1 statement if pigs fly, then elephants have 5 legs is logically valid if it is encoded as material implication. Encoded as a counterfactual ....

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Mathew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....submitted to AAAI 96. This work was supported by a William T. Fontaine Fellowship at the University of Pennsylvania. 1 Introduction In recent years tools belonging to formal systems that model aspects of information change have been the subject of a great deal of interest (see, for example, [8, 9, 10, 16, 44, 12, 1, 31, 5]) The relation between these frameworks and counterfactual reasoning originates in a proposal known as the Ramsey Test[36] To evaluate the counterfactual OE (read: if OE had been the case, would have been the case ) given a set of beliefs, S, add OE to S while at the same time making ....

....modifications to S in order to maintain consistency. If holds in the resulting belief state then the counterfactual is true. Competing approaches under this paradigm include those in which beliefs are represented as models [3, 17, 44] and those in which beliefs are represented by formulas [8, 32, 21]. An advantage of the former is insensitivity to the syntax of beliefs whereas the latter, because of its sensitivity to syntax, can support reason maintenance [32] The technical problems surrounding each approach involve which beliefs to discard or add to S in order to maintain consistency with ....

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Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....case we would say that my pulling the door was the method I employed to open the door. These cases are handled as follows. First define the transitive closure of counterfactual dependence, This is necessary as counterfactuals are inherently nonmonotonic and, hence, not generally transitive [ Ginsberg, 1986 ] Definition 3.1 (Transitive closure of counterfactual dependence) The transitive closure, of is defined by: j= OE iff either w j= OE or there is some s.t. w j= OE and w j= 3 In the remainder of this paper, upper case symbols will stand for constants and lower ....

....; 1) L(w 0 ; 1) Causal judgments are made relative to WD Omega . Notice that occurs(unlock obj(Rear) exit obj(Rear) 1) is not included in WD Omega as it will follow from rationality postulate 13.3; this is necessary in syntactic approaches to belief change and counterfactual reasoning [ Ginsberg, 1986; Ortiz, 1999 ] the idea is that if an agent s beliefs are represented by the logical closure of A = fp; p oe qg, then the withdrawal of belief in p is represented by first removing p from A and then taking the logical closure; q will then no longer follow. Given this description, the following ....

Ginsberg, Matthew L. 1986. Counterfactuals. Artificial Intelligence 30:35--79.

....E to fall at the same time followed by the remainder of the dominos in each of those branches, followed by G and H . 2.2. 1 The preference problem for counterfactuals Ginsberg s work on counterfactuals was the first major attempt at investigating the role of counterfactuals to problems in AI [ Ginsberg, 1986a ] Though he termed his approach a possible worlds approach, it was really an application of the Ramsey test. His suggestion is the following. Let T be a satisfiable set of sentences in some logical language and let: W (p; T ) fT 0 T j T 0 6j= p; T 0 ae U T ) U j= pg (1) This is ....

....two conditions (under the present scheme this would be expressed as two distinct rules) would then have the same ab qualification and would therefore not serve the purpose of localizing the effect of the causal rule. The negation of the ab predicates (over all ground atoms) is initially assumed [ Ginsberg, 1986a ] as a sort of closed world assumption, and given lowest priority under . This illustrates the need for functional terms corresponding to the logical connectives present within holds statements: consider a causal law with the antecedent of the form holds( OE; t) in which the ab predicate ....

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Ginsberg, Matthew L. 1986a. Counterfactuals. Artificial Intelligence 30:35--79.

....be defined) partial order if C is rational. This result is crucial in the proof of the representation result of Section 8.5. Lemma 8.3 If OE is a partial order on a set V , the following conditions are equivalent. A partial order satisfying them is called modular (this terminology is proposed in [9] as an extension of the notion of modular lattice of [10] 1. for any x; y; z 2 V such that x 6OE y, y 6OE x and z OE x, then z OE y, 2. for any x; y; z 2 V such that x OE z, either x OE y or y OE z, 3. the relation 6OE is transitive, 4. there is a totally ordered set Omega (the strict ....

Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....hypothesis, to what it really is, then fi would be true. For us ff fi means that ff is a good enough reason to believe fi, or that fi is a plausible consequence of ff. The main difference is that conditional logic refers implicitly to the actual state of the world whereas we do not. M. Ginsberg s [14] proposal to harness conditional logic to nonmonotonic reasoning was clearly set with the former semantics in mind, and that explains our disagreements concerning the desirability of certain rules, e.g. the rule of Rational Monotonicity (see equation (25) One of the logical systems, P, studied ....

Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....rg. We shall therefore presume that q holds and we shall not presume that d def = q r :q :r holds. This is the common wisdom and the present perspective subscribes to it. Suppose now that our specific information is c :d, or, equivalently, p q :r :p :q r. The common wisdom, defended in [4], would like to convince us that we should not presume q to be true. The position defended here, presumes that q is true (and also p and :r) because this situation violates only one default ( r) whereas the other possible situation: p :q r violates two defaults. The reader may suspect that ....

Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

....paper are assumed to hold for every model and world time pair. All unbound variables are further assumed to be universally quantified. gen(ff; fi) j gen1(ff; fi) 2) 9fl:gen1(ff; fl) gen(fl; fi) This inductive definition is needed because counterfactual dependence is not generally transitive (Ginsberg 1986). The first axiom states that ff and fi must be distinct (this enforces ireflexivity) and that fi counterfactually depends on both ff and intend(i; fi) The second axiom simply states that two actions are related by generation just in case there is a chain of counterfactual dependencies between ....

....dependencies between the pair. This approach depends on a body of basic generation knowledge of the form: happens(i; t; fl) c oe happens(i; t; ffi ) where these axioms can be separately qualified (Ginsberg Smith 1988) It also depends on a more restrictive treatment of along the lines of (Ginsberg 1986) so that if, for example, the arm extension (ff) had not occurred then one only considers possible worlds that must follow from this revision and causal knowledge: alternative means of signally will not be considered since the causal factor (intention) has been retracted 5 . In order to ensure ....

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Ginsberg, M. L. 1986. Counterfactuals. Artificial Intelligence 30:35--79.

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M. Ginsberg and W. Harvey. Iterative broadening. Artificial Intelligence, pages 367--383, 1992.

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Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

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M. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35--79, 1986.

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Matthew L. Ginsberg. Counterfactuals. Artificial Intelligence, 30:35-- 79, 1986.

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