In this paper, it is argued that single function dual process theory is a more credible psychological account of non-monotonicity in human conditional reasoning than recent attempts to apply logic programming (LP) approaches in artificial intelligence to these data. LP is introduced and among other critiques, it is argued that it is psychologically unrealistic in a similar way to hash coding in...

LP is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LP and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LP into progr...

The purpose of this paper is to discuss some categorical properties of probabilistic convergence spaces. Its main theses are: (1) the construct P-PrTop of probabilistic pretopological spaces is the extensional topological hull of the construct FTPcs of FT -diagonal probabilistic convergence spaces for every triangular norm T ; (2) the construct P-PsTop of probabilistic pseudotopological spaces ...

We consider the predictions provided by the inductive theories. For these theories predictions are performed by the Inductive Statistical (I-S) inferences. It was noted by Hempel that the I-S inference is statistically ambiguous. To avoid this ambiguity we need to use the rules that satisfy the Requirement of Maximum Specificity (RMS). The formal definition of the RMS wasn’t given by Hempel. We...

In this paper we define concepts of statistical convergence and statistical Cauchy on probabilistic normed spaces. Then we give a useful characterization for statistically convergent sequences. Furthermore, we display an example such that our method of convergence is stronger than the usual convergence on probabilistic normed spaces. We also introduce statistical limit points, statistical clust...

We calculate partition functions for lens spaces Lp,q up to p = 8 and for genus 1 and 2 handlebodies H1, H2 in the Turaev-Viro framework. These can be interpreted as transition amplitudes in 3D quantum gravity. In the case of lens spaces Lp,q these are vacuum-to-vacuum amplitudes Ø → Ø, whereas for the 1and 2-handlebodies H1, H2 they represent genuinely topological transition amplitudes Ø → T 2...

We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p = 2 or n = 1. The results are app...

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in Lp(R) (1 ≤ p ≤ ∞). Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on Z. Moreover, we show that such a shiftinvariant space provides Lp-appro...

We construct classes of von Neumann algebra modules by considering “column sums” of noncommutative Lp spaces. Our abstract characterization is based on an Lp/2-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L2 case, the concept of Lp bimodule (p 6= 2) turns out to be nearly trivial.

We analyse the well-posedness of the initial value problem for the dissipative quasigeostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. We prove that the only small self-similar solution in the strong Lp space is the null solution while infinitely many self-similar solutions do ...