We provide an extension of universal algebra and its equational logic from first to second order. Conservative extension, soundness, and completeness results are established.

Similarity in contextual behavior between words is considered a source of “lexical cohesion,” which is otherwise hard to measure or quantify. Such contextual similarity is used by an implementation for text segmentation, the VecTile system, which uses precompiled vector representations of words to produce similarity curves over texts. The performance of this system is shown to improve over that...

Second order algorithms belong to the class of repetitive heuristic techniques, where a greedy heuristic is applied to different subsets of the space of feasible solutions of a problem. The algorithm establishes a sequence of self-contained solutions subspaces, defining an iterative process that guides a subordinate greedy heuristic through those subspaces. This steepest descent process establi...

We give explicit solutions to two longstanding problems on coupled second–order recurrences.

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...

The paper presents the eecient training program of multilayer feedforward neu-ral networks. It is based on the best second order optimization algorithms including variable metric and conjugate gradient as well as application of directional minimization in each step. Its eeciency is proved on the standard tests, including parity, dichotomy, logistic and 2-spiral problems. The application of the ...

Second-order patterns, together with second-order matching, enable concise specification of program transformation, and have been implemented in several program transformation systems. However, second-order matching in general is nondeterministic, and the matching algorithm is so expensive that the matching is NP-complete. It is orthodox to impose constraints on the form of higher-order pattern...

Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the vie...

We present a new class of second-order uniication problems, which we have called linear. We deal with completely general second-order typed uniication problems, but we restrict the set of uniiers under consideration: they instantiate free variables by linear terms, i.e. terms where any-abstractions bind one and only one occurrence of a bound variable. Linear second-order uniication properly ext...

This paper discusses how numerically imprecise information can be modelled and how a risk evaluation process can be elaborated by integrating procedures for numerically imprecise probabilities and utilities. More recently, representations and methods for stating and analysing probabilities and values (utilities) with belief distributions over them (second order representations) have been sugges...