Defeasible inheritance with doubt index and its axiomatic characterization

This article introduces and uses a representation of defeasible inheritance networks where links in the network are viewed as propositions, and where defeasible links are tagged with a quantitative indication of the proportion of exceptions, called the doubt index. This doubt index is used for restricting the length of the chains of inference.The representation also introduces the use of defeater literals that disable the chaining of subsumption links. The use of defeater literals replaces the use of negative defeasible inheritance links, expressing “most A are not B”. The new representation improves the expressivity significantly.Inference in inheritance networks is defined by a combination of axioms that constrain the contents of network extensions, a heuristic restriction that also has that effect, and a nonmonotonic operation of minimizing the set of defeater literals while retaining consistency.We introduce an underlying semantics that defines the meaning of literals in a network, and prove that the axioms are sound with respect to this semantics. We also discuss the conditions for obtaining completeness.Traditional concepts, assumptions and issues in research on nonmonotonic or defeasible inheritance are reviewed in the perspective of this approach.     

Physics inspired algorithms for (co)homology computations of three-dimensional combinatorial manifolds with boundary

The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue may be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a physics inspired algorithm for first cohomology group computations on three-dimensional complexes. The algorithm is general and exhibits orders of magnitude speed up with respect to competing ones, allowing to handle problems not addressable before. In particular, when generators are employed in the physical modeling of magneto-quasistatic problems, this algorithm solves one of the most long-lasting problems in low-frequency computational electromagnetics. In this case, the effectiveness of the algorithm and its ease of implementation may be even improved by introducing the novel concept of lazy cohomology generators.     

Isolated nonnegative solutions of infinite-dimensional algebraic Riccati equations

For an infinite-dimensional continuous (or discrete)-time linear system, based on the study of the representation of nonnegative solutions of the algebraic Riccati equation (ARE), we get some sufficient and necessary conditions for a nonnegative solution of (ARE) to be isolated in the set of all nonnegative solution of (ARE) with respect to the norm topology, the strong operator topology and weak operator topology, respectively.     

Are word representations abstract or instance-based? Effects of spelling inconsistency in orthographic learning.

In Experiment 1, 62 10-year-old children studied printed pseudowords with semantic information. The items were later represented in a different format for reading, with half of the items spelled in the same way as before and half displayed in a new phonologically equivalent spelling. In a dictation test, the exposure to an alternative spelling substantially increased the number of errors that matched the alternative spelling, especially in good spellers. Orthographic learning predicted word identification when accuracy on orthographic choice for words was controlled. In Experiment 2, the effects on dictation responses of exposure to a misspelling versus the correct spelling, and the interactive effect of spelling ability, were confirmed relative to a no-exposure control in adults. The results support a single-lexicon view of reading and spelling and have implications for abstractionist and instance-based theories of orthographic representations. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

The dynamic behavior of a droplet on a solid surface is simulated by the lattice Boltzmann method (LBM) for two-phase fluids with large density differences; the wetting boundary condition on solid walls is incorporated in this simulation. By using the method, the dynamic behavior of a droplet impinging on a horizontal wall is investigated in terms of various Weber numbers. The dynamic contact angle, the contact line velocity, and the wet length are calculated, and found to be in good agreement with available experimental data. In addition, the method is applied to simulations of the collision of a falling droplet with a stationary droplet on a solid surface. The behavior of the droplets and the mixing process during their collision are simulated in terms of various impact velocities and several static contact angles on the solid surface. It is seen that mixing occurs around the rim of the coalescent droplet due to the circular flows. Also, the relationship between the mixing rate of the primary coalescent droplet and Weber number is investigated.     

Strong equivalence of logic programs under the infinite-valued semantics

We consider the notion of strong equivalence [V. Lifschitz, D. Pearce, A. Valverde, Strongly equivalent logic programs, ACM Transactions on Computational Logic 2 (4) (2001) 526-541] of normal propositional logic programs under the infinite-valued semantics [P. Rondogiannis, W.W. Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6 (2) (2005) 441-467] (which is a purely model-theoretic semantics that is compatible with the well-founded one). We demonstrate that two such programs are strongly equivalent under the infinite-valued semantics if and only if they are logically equivalent in the corresponding infinite-valued logic. In particular, we show that strong equivalence of normal propositional logic programs is decidable, and more specifically coNP-complete. Our results have a direct implication for the well-founded semantics since, as we demonstrate, if two programs are strongly equivalent under the infinite-valued semantics, then they are also strongly equivalent under the well-founded semantics.     

Thirty years of Polynomial System Solving,and now?

In this introductory paper to the special issue, I describe first my personal view of the history of Polynomial System Solving during my career. Then I describe the main challenges which are now opened by the availability of efficient zero-dimensional solvers.