We revisit the crucial issue of natural game equivalences, and semantics of game logics based on these. We present reasons for investigating finer concepts of game equivalence than equality of standard powers, though staying short of modal bisimulation. Concretely, we propose a more finegrained notion of equality of ‘basic powers’ which record what players can force plus what they leave to othe...

In 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti’s formulation is extended to construct a model of set theory ...

In the context of Natural Language Processing, annotation is about recovering implicit information that is useful for natural language applications. In this paper we describe a “tense” annotation task for Chinese, a language that does not have grammatical tense, that is designed to infer the temporal location of a situation in relation to the temporal deixis, the moment of speech. If successful...

Let denote a distance-regular graph with diameter D ≥ 3, valency k, and intersection numbers ai , bi , ci . Let X denote the vertex set of and fix x ∈ X . Let denote the vertex-subgraph of induced on the set of vertices in X adjacent x . Observe has k vertices and is regular with valency a1. Let η1 ≥ η2 ≥ · · · ≥ ηk denote the eigenvalues of and observe η1 = a1. Let denote the set of distinct s...

We formalize the notion of vector semi-inner products and introduce a class seminorms which are built from these maps. The classical Pythagorean theorem parallelogram law then generalized to that have geometric mean closed lattice for codomain. In special case this codomain is square root closed, semiprime $f$-algebra, we provide sharpening triangle inequality as well condition equality.

The distribution of eigenvalues and the upper bounds for spread interval matrices are significant in various fields mathematics applied sciences, including linear algebra, numerical analysis, control theory, combinatorial optimization. We present within determine their using Geršgorin’s theorem. Specifically, through an equality variance a discrete random variable, we derive symmetric matrices....

STRUCTURED CONDITIONING OF MATRIX FUNCTIONS∗ PHILIP I. DAVIES† Abstract. The existing theory of conditioning for matrix functions f(X):Cn×n → Cn×n does not cater for structure in the matrix X. An extension of this theory is presented in which when X has structure, all perturbations of X are required to have the same structure. Two classes of structured matrices are considered, those comprising ...

Let M be a compact manifold and D a Dirac type differential operator on M . Let A be a C∗-algebra. Given a bundle W (with connection) of A-modules over M , the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for these indices. Our result does complement the Mishchenko-Fomenko index theor...