Related papers: The Logic of Approximate Dependence
A new reference state for density functional theory, termed the independent atom ansatz, is introduced in this work. This ansatz allows for the exact representation of electron density in terms of non-interacting, atom-localized orbitals.…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements…
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…
We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
Let $U$ be a bounded open subset of the complex plane and let $A_{\alpha}(U)$ denote the set of functions analytic on $U$ that also belong to the little Lipschitz class with Lipschitz exponent $\alpha$. It is shown that if $A_{\alpha}(U)$…
One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
This article makes no claim to originality, other than, perhaps, the simple statement here called the {\it Abstract Maximum Principle}. Actually, the whole contents are strongly based on some H. Sussmann's and coauthors' papers, in which,…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
This paper discusses the time-dependence of the threshold function in the perfect plasticity model. In physical terms, it is natural that the threshold function depends on some unknown variable. Therefore, it is meaningful to discuss the…
The computation of a solution concept of a cooperative game usually depends on values of all coalitions. However, in some applications, values of some of the coalitions might be unknown due to various reasons. We introduce a method to…
We obtain an almost sure limit theorem for the maximum of nonstationary random fields under some dependence conditions.
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
This paper presents a logic of preference and functional dependence (LPFD) and its hybrid extension (HLPFD), both of whose sound and strongly complete axiomatization are provided. The decidability of LPFD is also proved. The application of…
Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…
We start the study of the enumeration complexity of different satisfiability problems in first-order team logics. Since many of our problems go beyond DelP, we use a framework for hard enumeration analogous to the polynomial hierarchy,…