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Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
In this chapter, the Hilbert space framework in the mathematical theory of composite materials is introduced for studying the properties of effective operators. The goal is to introduce some of the key concepts and fundamental theorems in…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the…
It is argued that the concept of free will, like the concept of truth in formal languages, requires a separation between an object level and a meta-level for being consistently defined. The Jamesian two-stage model, which deconstructs free…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
In [{\it On the free implicative semilattice extension of a Hilbert algebra}. Mathematical Logic Quarterly 58, 3 (2012), 188--207], Celani and Jansana give an explicit description of the free implicative semilattice extension of a Hilbert…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment to contexts involving relations of arity greater than two. Quantifiers in this logic are used in…
Von Neumann use 4 assumptions to derive the Hilbert space (HS) formulation of quantum mechanics (QM). Within this theory dispersion free ensembles do not exist. To accommodate a theory of quantum mechanics that allow dispersion free…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
In this paper we obtain a description of the Hermitian operators acting on the Hilbert space $\C^n$, description which gives a complete solution to the over parameterization problem. More precisely we provide an explicit parameterization of…
A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
In the present paper syntax and semantics will be presented for an expansion of ordinary n-agent QML with constant domain, non-rigid constants, rigid variables and including both functions, relations, and equality. Further, the number of…