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.
15029835
Quasi-Prime Algebraic Domains
Abstract The purpose of this paper is to introduce a new class of domains called quasi-prime algebraic domains. We show that this class is a good candidate for the purpose of denotational semantics of programming languages. This is achieved by exhibiting many constructions usually needed for denotational semantics on quasi-prime algebraic domains. In the first part we motivate the notion of quasi-primes and quasi-prime algebraic domains by studying the effect of linear functions on domains that are not prime algebraic. In the second part we study categories of quasi-prime algebraic domains by representing them as irreducible information systems. We introduce a symmetric monoidal closed category of quasi-prime algebraic domains with quasi-linear functions. We show further that with the usual Scott continuous functions as morphisms, quasi-prime algebraic domains are cartesian closed. In the third part we show the existence of a saturated quasi-prime algebraic domain, and introduce a framework for solving domain equations in quasi-prime algebraic domains. It is then possible to give, for example, a model for the un-typed lambda calculus with a reflexive quasi-prime algebraic domain.
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.
27034466
Power Defaults
We present a spectrum of default logics, using powerdomains to encode default constraints. The resulting nonmonotonic entailment relations all satisfy the law of reasoning by cases. This result is a consequence of two general theorems valid for any Scott domain: the Dichotomy Theorem and the Extension Splitting Theorem. We briefly indicate that for propositional logic, the complexity of entailment is complete for co-NP(3).
205118584
dI-Domains as Prime Information Systems
Abstract This paper introduces prime information systems. Prime information systems determine dI-domains and stable approximable mappings give stable functions, and vice versa. The notion of rigid embedding is captured by a subsystem relation. Under this relation, prime information systems form a complete partial order (cpo). Constructions like lifting, sum, product, and function space are proposed which induce continuous functions on the cpo. In this way recursive prime information systems can be defined using fixed point theory.
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.
30701744
Single change covering designs
A single-change covering designSC (v, k, b) on av-setV is a sequence ofb k-sets (blocks) onV which together cover every pair of elements ofV at least once, such that two successive blocks havek−1 elements in common. It is desirable to minimizeb. Some constructions and lower bounds forb are given.
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
38503566
Pseudo-one-factorizations of regular graphs of odd order - II. products of graphs
Abstract We study the pseudo-one-factorization of regular graphs of odd order. It is shown that some classes of products (including composition and cartesian product) of graphs are pseudo-one- factorizable. In particular, we prove that a complete regular t -partite graph of odd order has this property.
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.