The definition of identity in terms of other logical symbols is a recurrent issue in logic. In particular, in First-Order Logic (FOL) there is no way of defining the global relation of identity, while in standard Second-Order Logic (SOL) this definition is not only possible, but widely used. In this paper, the reverse question is posed and affirmatively answered: Can we define with only equalit...

An algorithm is given for computing the Hausdorff dimension of the set(s) Λ = Λ(β,D) of real numbers with representations x = ∑∞ n=1 dnβ −n, where each dn ∈ D, a finite set of “digits”, and β > 0 is a Pisot number. The Hausdorff dimension is shown to be log λ/ log β, where λ is the top eigenvalue of a finite 0-1 matrix A, and a simple algorithm for generating A from the data β,D is given.

The minimal relevant logic B+, seen as a type discipline, includes an extension of Curry types known as the intersection type discipline. We will show that the full logic B+ gives a type assignment system which produces a model of Plotkin’s call-by-value λ-calculus.

We present the Curry–Howard correspondence for constructive logic via natural deduction, typed λ-calculus and cartesian closed categories. We then examine how the correspondence may be extended to classical logic and non-constructive proofs, and discuss some of the problems and questions that then arise.

We consider policy evaluation algorithms within the context of infinite-horizon dynamic programming problems with discounted cost. We focus on discrete-time dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradient-like algorithm involving least-squares subprob...

one of the main concerns of the mining industry is to determine ultimate pit limits. final pit is a collection of blocks, which can be removed with maximum profit while following restrictions on the slope of the mine’s walls. the size, location and final shape of an open-pit are very important in designing the location of waste dumps, stockpiles, processing plants, access roads and other surfac...

We present a new algorithm for computing all Schur functions sλ(x1, x2, . . . , xn) for all partitions λ of integers not exceedingN in timeO(nKN ), whereKN ≡ #{λ| |λ| ≤ N} is the number of those partitions. In particular, this algorithm has optimal complexity for evaluating truncated series of Schur functions such as the hypergeometric function of a matrix argument.