We present a formal analysis of symbolic learning that predicts significant differences in symbolic learning depending on the sequencing of semantic features and labels. A computational simulation confirms the FeatureLabel-Ordering (FLO) effect in learning that our analysis predicts. Discrimination learning is facilitated when semantic features predict labels, but not when labels predict semant...

The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on R which are homogeneous of degree zero near infinity. The most complete results require the additional assumption that the restriction of the potential to the circle(s) at infinity be Morse. Generalized eigenfunct...

State space explosion is a fundamental obstacle in formal veri cation of designs and protocols. Several techniques for combating this problem have emerged in the past few years, among which two are signi cant: partialorder reductions and symbolic state space search. In asynchronous systems, interleavings of independent concurrent events are equivalent, and only a representative interleaving nee...

Efficient processing of absolute magnitude and relative order numbers is key for arithmetic development. This longitudinal study tested 1) whether there a developmental shift in the contribution symbolic to between Grades 1 2, 2) development numerical abilities characterized by reciprocal predictive relations. In two independent samples (UK: N = 195, Austria: 161), did not predict early change ...

This paper presents a new neural-symbolic reasoning approach based on a sharing of neural multi-space representation for coded fractions of first-order logic. A multi-space is the union of spaces with different dimensions, each one for a different set of distinct features. In our case, we model the distinct aspects of logical formulae as separated spaces attached with vectors of importance weig...

In automated deduction systems that are intended for human use, the presentation of a proof is no less important than its discovery. For most of today’s automated theorem proving systems, this requires a non-trivial translation procedure to extract human-oriented deductions from machine-oriented proofs. Previously known translation procedures, though complete, tend to produce unintuitive deduct...

We discuss how to perform symbolic execution of large programs in a manner that is both compositional (hence more scalable) and demand-driven. Compositional symbolic execution means finding feasible interprocedural program paths by composing symbolic executions of feasible intraprocedural paths. By demand-driven, we mean that as few intraprocedural paths as possible are symbolically executed in...

We present a verification system for a variant of Hoare-logic that supports proving by forward symbolic execution. In addition, no explicit weakening rules are needed and first-order reasoning is automated. The system is suitable for teaching program verification, because the student can concentrate on reasoning about programs following their natural control flow and proofs are machine-checked.

Computer algebra in scientific computation squarely faces the dilemma of natural mathematical expression versus efficiency. While higher-order programming constructs and parametric polymorphism provide a natural and expressive language for mathematical abstractions, they can come at a considerable cost. We investigate how deeply nested type constructions may be optimized to achieve performance ...

This paper considers the decision problem for the existential fragment of the theory of simplification orderings. A simple, polynomial-time procedure for deciding satisfiability of such constraints is given, and it is also shown that the corresponding problem for the theory of total simplification orderings is NP-complete. This latter result can be interpreted as showing that the problem of dec...