One sometimes reads in a mathematical proof that a certain assumption can be made ‘without loss of generality’ (WLOG). In other words, it is claimed that considering what first appears only a special case does nevertheless suffice to prove the general result. Typically the intuitive justification for this is that one can exploit symmetry in the problem. We examine how to formalize such ‘WLOG’ a...

The purpose of this note is pedagogi-cal. It discusses how one can reduce the computational cost of applying a set of operators (or predicates) by breaking them up into combinations of commonly occurring, simpler ones. This can be thought of as a process of generalization, in the sense that the common, simple operators are more "general" than the original, more complex ones. We are thus suggest...

Several recent papers Cohen, 1990c; Flann and Dietterich, 1989] have presented learning systems that use, as background knowledge, an initial domain theory that is overgeneral: that is, a theory that deenes a concept that is a superset of the concept to be learned. Learning then becomes a problem of specializing the initial theory. Such an overgeneral theory is, of course, only one of many poss...

This paper presents a first set of test results on the generality and transferability of an evaluation tool which can ensure the habitability and usability of spoken dialogues. Building on the assumption that most, if not all, dialogue design errors can be viewed as problems of non-cooperative system behaviour, the tool has two closely related aspects to its use. Firstly, it may be used for the...

This chapter proposes a conception of lexical meaning as use-potential, in contrast to prevailing atomistic and reificational views. The issues are illustrated on the example of spatial expressions, pre-eminently prepositions. It is argued that the dichotomy between polysemy and semantic generality is a false one, with expressions occupying points on a continuum from full homonymy to full monos...

Figure 1. Samples of some of the datasets that we used in this analysis. From top to bottom: MNIST [1], MNIST-rotated [2], MNIST-random-background [2], MNIST-rotated-background [2], Google street view house numbers [3], Char 74k English [4], Char 74k Kannada [4]. Last two rows, first five from left are CIFAR 10 and the rest are Caltech101 [5, 6]. The bottom row is the colonoscopy dataset. We us...

One hypothesis is more general than another one if it covers all instances that are also covered by the later one. The former hypothesis is called a generalization of the later, and the later a specialization of the former. When using logical formulae as hypotheses, the generality relation coincides with the notion of logical entailment, which implies that the generality relation can be analyze...

2. Generality A patent that is being cited by a broader array of technology classes is viewed as having greater generality. Generality is calculated as the Herfindahl index of citing patents, used to capture the dispersion across technology classes of patents using the patent. To account for cases with a small number of patents within technology classes, I use the bias correction described in J...