We present new sound and complete axiomatizations of type equality and subtype inequality for a first-order type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle), which has the f...

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying many AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at leas...

A mutation whose fixation is independent of natural selection is termed a neutral mutation. Therefore selective neutrality of a mutation can be defined by independence of its fixation from natural selection. By the population genetic approach, Kimura [Kimura, M. (1962) Genetics 47, 713-719] predicted that the probability of fixation of a neutral mutation (u) is equal to the frequency of the new...

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...

Background: Gender equality is recognized as an important political, social, and economic goal in many countries around the world. At a country level, there evidence that gender may have influence on health. Historically has mainly been measured to allow for between-country, rather than within-country comparisons; association between health outcomes within under-researched. This article thus ai...

The purpose of this paper is to survey our recent research in computability and definability over continuous data types such as the real numbers, real-valued functions and functionals. We investigate the expressive power and algorithmic properties of the language of Σ-formulas intended to represent computability over the real numbers. In order to adequately represent computability we extend the...

In this series of lectures the basic ideas of the 1/mQ expansion in QCD (mQ is the mass of a heavy quark) are outlined. Applications to exclusive and inclusive decays are given.