Function definitions in term rewriting and applicative programming

The frameworks of unconditional and conditional Term Rewriting and Applicative systems are explored with the objective of using them for defining functions. In particular, a new operational semantics, Tue-Reduction, is elaborated for conditional term rewriting systems. For each framework, the concept of evaluation of terms invoking defined functions is formalized. We then discuss how it may be ensured that a function definition in each of these frameworks is meaningful, by defining restrictions that may be imposed to guarantee termination, unambiguity, and completeness of definition. The three frameworks are then compared, studying when a definition may be translated from one formalism to another

Term Rewriting with Conditionals and Priority Orderings

Conditional rewriting and priority rewriting are two recent generalizations of term rewriting systems. In the former, each rewrite rule is accompanied by an antecedent which must be shown to hold before rewriting can occur. In the latter, rewrite rules can be used only in a particular order. We compare these formalisms: neither formalism encompasses the other in a practical sense, but we give restrictions under which priority and conditional rewriting can be equivalent. We combine the two operational mechanisms, obtaining a natural and expressive formalism called Priority Conditional Rewriting Systems (PCRS). PCRS can be used to “fully-define” data type specifications and function specifications. Towards this goal, restrictions are given that encourage modularity of specifications and ensure properties of termination, confluence, and total reducibility of ground terms. A logical semantics for priority conditional rewriting is described, using equational formulas ε(R) obtained from the rules in the PCRS R; we give conditions under which rewriting with PCRS is sound and complete

Fitting Semantics for Conditional Term Rewriting

This paper investigates the semantics of conditional term rewriting systems with negation which do not satisfy useful properties like termination. It is shown that the approach used by Fitting [5] for Prolog-style logic programs is applicable in this context. A monotone operator is developed, whose fixpoints describe the semantics of conditional rewriting. Several examples illustrate this semantics for non-terminating rewrite systems which could not be easily handled by previous approaches

A Clustering based Discretization for Supervised Learning

We address the problem of discretization of continuous variables for machine learning classification algorithms. Existing procedures do not use interdependence between the variables towards this goal. Our proposed method uses clustering to exploit such interdependence. Numerical results show that this improves the classification performance in almost all cases. Even if an existing algorithm can successfully operate with continuous variables, better performance is obtained if variables are first discretized. An additional advantage of discretization is that it reduces the overall time-complexity

Forecasting the Behavior of Multivariate Time Series using Neural Networks

This paper presents a neural network approach to multivariate time-series analysis. Real world observations of flour prices in three cities have been used as a benchmark in our experiments. Feedforward connectionist networks have been designed to model flour prices over the period from August 1972 to November 1980 for the cities of Buffalo, Minneapolis, and Kansas City. Remarkable success has been achieved in training the networks to learn the price curve for each of these cities, and thereby to make accurate price predictions. Our results show that the neural network approach leads to better predictions than the autoregressive moving average(ARMA) model of Tiao and Tsay [TiTs 89]. Our method is not problem-specific, and can be applied to other problems in the fields of dynamical system modeling, recognition, prediction and control

Partial Shape Matching Using Genetic Algorithms

Shape recognition is a challenging task when images contain overlapping, noisy, occluded, partial shapes. This paper addresses the task of matching input shapes with model shapes described in terms of features such as line segments and angles. The quality of matching is gauged using a measure derived from attributed shape grammars. We apply genetic algorithms to the partial shape-matching task. Preliminary results, using model shapes with 6 to 70 features each, are extremely encouraging

Reference Set Metrics for Multi-objective Algorithms

Several metrics and indicators have been suggested in the past to evaluate multi-objective evolutionary and non-evolutionary algo- rithms. However, these metrics are known to have many problems that make their application sometimes unsound, and sometimes infeasible. This paper proposes a new approach, in which metrics are parameter- ized with respect to a reference set, on which depend the properties of any metric

An Improved Algorithm for Neural Network Classification of Imbalanced Training Sets

In this paper, we analyze the reason for the slow rate of convergence of net output error when using the backpropagation algorithm to train neural networks for a two-class problems in which the numbers of exemplars for the two classes differ greatly. This occurs because the negative gradient vector computed by backpropagation for an imbalanced training set does not point initially in a downhill direction for the class with the smaller number of exemplars. Consequently, in the initial iteration, the net error for the exemplars in this class increases significantly. The subsequent rate of convergence of the net error is very low. We suggest a modified technique for calculating a direction in weight-space which is downhill for both classes. Using this algorithm, we have been able to accelerate the rate of learning for two-class classification problems by an order of magnitude

Unification in Modal Theorem Proving

Modal formulas can be proved by translating them into a three-typed logic and then using unification and resolution, with axioms describing properties of the reachability relation among possible worlds. In this paper, we improve on the algorithms in [1], showing that strong skolemisation and occurrence checks are not needed for proving theorems of Q, T, Q4, and S4. We also extend the \u27path logic\u27 approach to S5, give the appropriate unification algorithm, and prove its correctness

An Evolutionary Multi-Objective Crowding Algorithm (EMOCA): Benchmark Test Function Results

A new evolutionary multi-objective crowding algorithm (EMOCA) is evaluated using nine benchmark multiobjective optimization problems, and shown to produce non-dominated solutions with significant diversity, outperforming state-of-the-art multi-objective evolutionary algorithms viz., Non-dominated Sorting Genetic Algorithm – II (NSGA-II), Strength Pareto Evolutionary algorithm II (SPEA-II) and Pareto Archived Evolution Strategy (PAES) on most of the test problems. The key new approach in EMOCA is to use a diversity-emphasizing probabilistic approach in determining whether an offspring individual is considered in the replacement selection phase, along with the use of a non-domination ranking scheme. This approach appears to provide a useful compromise between the two concerns of dominance and diversity in the evolving population