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 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...

Adaptive learning technology solutions often use a learner model to trace and make pedagogical decisions. The present research introduces formalized methodology for specifying models, logistic knowledge tracing (LKT), that consolidates many extant modeling methods. strength of LKT is the specification symbolic notation system alternative regression models powerful enough specify in literature n...

The General Problem Solver (GPS) is a computer program which has been used for explorations into both general mechanisms involved in problem solving and the way that humans solve problems. The program has existed in several versions since its conception in 1957. This report describes attempts to generalize one version, GPS-2-5; i.e., to have it solve many different kinds of problems. GPS's perf...