Program Verification of Numerical Computation

These notes outline a formal method for program verification of numerical computation. It forms the basis of the software package VPC in its initial phase of development. Much of the style of presentation is in the form of notes that outline the definitions and rules upon which VPC is based. The initial motivation of this project was to address some practical issues of computation, especially of numerically intensive programs that are commonplace in computer models. The project evolved into a wider area for program construction as proofs leading to a model of inference in a more general sense. Some basic results of machine arithmetic are derived as a demonstration of VPC

Combining decision procedures for the reals

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which "local" decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let Tadd[Q] be the first-order theory of the real numbers in the language of ordered groups, with negation, a constant 1, and function symbols for multiplication by rational constants. Let Tmult[Q] be the analogous theory for the multiplicative structure, and let T[Q] be the union of the two. We show that although T[Q] is undecidable, the universal fragment of T[Q] is decidable. We also show that terms of T[Q]can fruitfully be put in a normal form. We prove analogous results for theories in which Q is replaced, more generally, by suitable subfields F of the reals. Finally, we consider practical methods of establishing quantifier-free validities that approximate our (impractical) decidability results.Comment: Will appear in Logical Methods in Computer Scienc

An observation on Carnapʼs Continuum and stochastic independencies

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate

Core Finding for Relational Structures

The computation of cores of relational structures has a variety of applications. In this project, we revise a core computation algorithm by Pichler and Savenkov, designed for the data exchange context, to work in a more general setting. Contributions to research from this project include the observation that the previous algorithm by Pichler and Savenkov may not work when disjunctions are present in theories, a revised algorithm for the new setting, and an implementation of the algorithm in Haskell. We use signature testing as a heuristic to improve the running time of the algorithm

The Ideal Candidate. Analysis of Professional Competences through Text Mining of Job Offers

The aim of this paper is to propose analytical tools for identifying peculiar aspects of job market for graduates. We propose a strategy for dealing with daa tat have different source and nature