14387948
Axiomatic Aspects of Default Inference
This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called a default structure. We study axioms for the nonmonotonic consequence relation derived from extensions as in Reiter's default logic, using skeptical reasoning, but extensions are now used for the construction of possible worlds in a default information structure. 
In previous work we showed that skeptical reasoning arising from default-extensions obeys a well-behaved set of axioms including the axiom of cautious cut. We show here that, remarkably, the converse is also true: any consequence relation obeying this set of axioms can be represented as one constructed from skeptical reasoning. We provide representation theorems to relate axioms for nonmonotonic consequence relation and properties about extensions, and provide one-to-one correspondence between nonmonotonic systems which satisfies the law of cautious monotony and default structures with unique extensions. Our results give a theoretical justification for a set of basic rules governing the update of nonmonotonic knowledge bases, demonstrating the derivation of them from the more concrete and primitive construction of extensions. It is also striking to note that proofs of the representation theorems show that only shallow extensions are necessary, in the sense that the number of iterations needed to achieve an extension is at most three. All of these developments are made possible by taking a more liberal view of consistency: consistency is a user defined predicate, satisfying some basic properties.
10438151
Complexity of power default reasoning
This paper derives a new and surprisingly low complexity result for inference in a new form of Reiter's propositional default logic (1980). The problem studied here is the default inference problem whose fundamental importance was pointed out by Kraus, Lehmann, and Magidor (1980). We prove that "normal" default inference, in propositional logic, is a problem complete for co-NP(3), the third level of the Boolean hierarchy. Our result (by changing the underlying semantics) contrasts favorably with a similar result of Gottlob (1992), who proves that standard default inference is II/sub 2//sup P/-complete. Our inference relation also obeys all of the laws for preferential consequence relations set forth by Kraus, Lehmann, and Magidor (1990). In particular we get the property of being able to reason by cases and the law of cautious monotony. Both of these laws fail for standard propositional default logic. The key technique for our results is the use of Scott's domain theory to integrate defaults into partial model theory of the logic, instead of keeping defaults as quasiproof rules in the syntax. In particular, reasoning disjunctively entails using the Smyth powerdomain.
12232435
Rational Transformations of Formal Power Series
Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve rationality, generalizing the recent results of Zhang [15] to the formal power series setting. We show, for example, that the "square-root" operation, while preserving regularity for formal languages, preserves rationality for formal power series when the underlying semiring is commutative or locally finite, but not in general.
1726106
Defaults in Domain Theory
Abstract This paper uses ideas from artificial intelligence to show how default notions can be defined over Scott domains. We combine these ideas with ideas arising in domain theory to shed some light on the properties of nonmonotonicity in a general model-theoretic setting. We consider in particular a notion of default nonmonotonic entailment between prime open sets in the Scott topology of a domain. We investigate in what ways this notion obeys the so-called laws of cautious monotony and cautious cut , proposed by Gabbay, Kraus, Lehmann, and Magidor. Our notion of nonmonotonic entailment does not necessarily satisfy cautious monotony, but does satisfy cautious cut. In fact, we show that any reasonable notion of nonmonotonic entailment on prime opens over a Scott domain, satisfying in particular the law of cautious cut, can be concretely represented using our notion of default entailment. We also give a variety of sufficient conditions for defaults to induce cumulative entailments, those satisfying cautious monotony. In particular, we show that defaults with unique extensions are a representation of cumulative nonmonotonic entailment. Furthermore, a simple characterization is given for those default sets which determine unique extensions in coherent domains. Finally, a characterization is given for Scott domains in which default entailment must be cumulative. This is the class of daisy domains ; it is shown to be cartesian closed, a purely domain-theoretic result.
717123
Experimenting with Power Default Reasoning
In this paper we explore the computational aspects of Propositional Power Default Reasoning (PDR), a form of non-monotonic reasoning in which the underlying logic is Kleene's 3-valued propositional logic. PDR leads to a concise meaning of the problem of skeptical entailment which has better complexity characteristics than the usual formalisms (co-NP(3)-Complete instead of ?2P-Complete). We take advantage of this in an implementation called powdef to encode and solve hard graph problems and explore randomly generated instances of skeptical entailment.
14595938
Clausal Logic and Logic Programming in Algebraic Domains
We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo. 2001 Elsevier Science
8455393
Moment-Entropy Inequalities for a Random Vector
The pth moment matrix is defined for a real random vector, generalizing the classical covariance matrix. Sharp inequalities relating the pth moment and Renyi entropy are established, generalizing the classical inequality relating the second moment and the Shannon entropy. The extremal distributions for these inequalities are completely characterized
2928763
GeoGrid: A Scalable Location Service Network
This paper presents GeoGrid, a geographical location service overlay network system, for providing scalable location-based services to a large and growing number of mobile users. GeoGrid is designed as a decentralized and geographical location aware overlay network and provides system-level facilities and optimizations for balancing load in the presence of node heterogeneity, dynamically moving hot-spots (location queries), and unpredictable rate of node join, departure and failure. GeoGrid uses geographical mapping of nodes to regions and geographical proximity based routing to take advantage of the similarity between physical and network proximity. Furthermore, GeoGrid exploits multiple opportunities for dynamic workload adaptation in the presence of static hotspot queries and moving hotspot queries. Its dynamic load balancing algorithms can efficiently utilize the heterogeneous capacities of end systems and balance both the location query workload and the routing workload. Our initial prototype development and experimental study demonstrate that GeoGrid can effectively reduce the workload imbalance by an order of magnitude.
42909091
Combining path relinking and genetic algorithms for the multiple-level warehouse layout problem
Path relinking is a method to generate new solution by exploring trajectories that connect high quality solutions. In this paper, a class of new hybrid heuristics are proposed by combining a genetic algorithm and path relinking and applying these to a multiple-level warehouse layout problem. Parallel and series combinations to integrate crossover and mutation operations of a genetic algorithm with path relinking are investigated. We proposed position and sequence based path relinking methods to connect two solutions, which are either elites or ones selected randomly. Extensive experiments are carried out to compare the performance of the new heuristics.
41994930
On the partition and coloring of a graph by cliques
Abstract We first introduce the concept of the k -chromatic index of a graph, and then discuss some of its properties. A characterization of the clique partition number of the graph G ⋁ K c m for any simple graph G is given, together with some of its applications. Graphs with maximum valency 3 are also considered.
7172030
Information-theoretic inequalities for contoured probability distributions
We show that for a special class of probability distributions that we call contoured distributions, information-theoretic invariants and inequalities are equivalent to geometric invariants and inequalities of bodies in Euclidean space associated with the distributions. Using this, we obtain characterizations of contoured distributions with extremal Shannon and Renyi entropy. We also obtain a new reverse information-theoretic inequality for contoured distributions.