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Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member, append, . . . ) and how inductive definitions are expressed in mathematical text, is not coincidental but essential. We argue here that this provides a natural solution to the main lingering semantic questions of Logic Programming and its extensions.

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An approach to quantisation in terms of a transitive group of symplectic transformations of the classical phase space is discussed. This is applied to general relativity where the phase space is nonlinear and it is shown that the appropriate canonical algebra (i.e. the analogue of the canonical commutation relations for the case of a linear phase space) is that of the affine commutation relations.

In this paper we use a logic-based representation and a combination of Abduction and Induction to model inhibition in metabolic networks. In general, the integration of abduction and induction is required when the following two conditions hold. Firstly, the given background knowledge is incomplete. Secondly, the problem must require the learning of general rules in the circumstance in which the hypothesis language is disjoint from the observation language. Both these conditions hold in the application considered in this paper. Inhibition is very important from the therapeutic point of view since many substances designed to be used as drugs can have an inhibitory effect on other enzymes. Any system able to predict the inhibitory effect of substances on the metabolic network would therefore be very useful in assessing the potential harmful side-effects of drugs. In modelling the phenomenon of inhibition in metabolic networks, background knowledge is used which describes the network topology and functional classes of inhibitors and enzymes. This background knowledge, which represents the present state of understanding, is incomplete. In order to overcome this incompleteness hypotheses are considered which consist of a mixture of specific inhibitions of enzymes (ground facts) together with general (non-ground) rules which predict classes of enzymes likely to be inhibited by the toxin. The foreground examples are derived from in vivo experiments involving NMR analysis of time-varying metabolite concentrations in Mach Learn (2006) 64:209-230 rat urine following injections of toxins. The model's performance is evaluated on training and test sets randomly generated from a real metabolic network. It is shown that even in the case where the hypotheses are restricted to be ground, the predictive accuracy increases with the number of training examples and in all cases exceeds the default (majority class). Experimental results also suggest that when sufficient training data is provided, non-ground hypotheses show a better predictive accuracy than ground hypotheses. The model is also evaluated in terms of the biological insight that it provides.

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