having briefly been reviewed the historical process of changing the formulae for determining the times of islamic prayers, two newly found formulae and a new rule for establishing the times of prayers would be discussed. these matters have been exploited from four texts, still preserved as manuscript: (1) siyyid ¾?y? al-d?n sh?shtar?’s ¼ad b?b dar macrifa al-a½??rl?b, (2) b?r?n?’s ’ist?c?b f? c...

The paper presents a framework to induction of concept hierarchies based on consistent integration of metric and similarity based approaches The hierarchies used are subsump tion lattices induced by the least general generalization operator lgg commonly used in inductive learning Using some basic results from lattice theory the paper introduces a semantic distance measure between objects in con...

An algorithm is presented which eliminates second–order quantifiers over predicate variables in formulae of type ∃P1, . . . , Pnψ where ψ is an arbitrary formula of first– order predicate logic. The resulting formula is equivalent to the original formula – if the algorithm terminates. The algorithm can for example be applied to do interpolation, to eliminate the second–order quantifiers in circ...