Generalized Quantifiers: Logic and Language

The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement

The Square of Opposition with “most” and “many”

Our concern is with constructing a traditional square of opposition into which “most” and “many” are integrated. Our basic position is in favor of traditional formal logic that originated with Aristotle, but the present discussion have taken liberties with recent developments of formal semantics to such an extent that they make contribution to more understanding of what the square of opposition looks like. The concept of directionality of monotonicity and especially our tests contribute to our conclusion. Still our discussion finds crucial insight in Keynes, one of formal logicians of a century ago. We propose as a conclusion a traditional square of opposition in which a near universal and near particular are neatly incorporated into a traditional proto-type square in such a way that they are entirely wrapped up.departmental bulletin pape

Oppositions in a line segment

Traditional oppositions are at least two-dimensional in the sense that they are built based on a famous bidimensional object called square of oppositions and on one of its extensions such as Blanch\'e's hexagon. Instead of two-dimensional objects, this article proposes a construction to deal with oppositions in a one-dimensional line segment.Comment: This is the version accepted for publication (South American Journal of Logic, 2018

Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information Processin