Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level.     

On intermediate inquisitive and dependence logics: An algebraic study

This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete for all intermediate inquisitive and dependence logics. To this end, we define inquisitive and dependence algebras and we investigate their model-theoretic properties. We then focus on finite, core-generated, well-connected inquisitive and dependence algebras: we show they witness the validity of formulas true in inquisitive algebras, and of formulas true in well-connected dependence algebras. Finally, we obtain representation theorems for finite, core-generated, well-connected, inquisitive and dependence algebras and we prove some results connecting team and algebraic semantics.     

Infinite lexicographic products

We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define dense substructures in infinite products and show that any countable product of countable transitive homogeneous structures has a unique countable dense substructure, up to isomorphism. Furthermore, this dense substructure is transitive, homogeneous and elementarily embeds into the product. This result is then utilized to construct a rigid elementarily indivisible structure.     

The fluted fragment with transitive relations

The fluted fragment is a fragment of first-order logic (without equality) in which, roughly speaking, the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that this fragment has the finite model property. We consider extensions of the fluted fragment with various numbers of transitive relations, as well as the equality predicate. In the presence of one transitive relation (together with equality), the finite model property is lost; nevertheless, we show that the satisfiability and finite satisfiability problems for this extension remain decidable. We also show that the corresponding problems in the presence of two transitive relations (with equality) or three transitive relations (without equality) are undecidable, even for the two-variable sub-fragment.     

Unifying hidden-variable problems from quantum mechanics by logics of dependence and independence

We study hidden-variable models from quantum mechanics and their abstractions in purely probabilistic and relational frameworks by means of logics of dependence and independence, which are based on team semantics. We show that common desirable properties of hidden-variable models can be defined in an elegant and concise way in dependence and independence logic. The relationship between different properties and their simultaneous realisability can thus be formulated and proven on a purely logical level, as problems of entailment and satisfiability of logical formulae. Connections between probabilistic and relational entailment in dependence and independence logic allow us to simplify proofs. In many cases, we can establish results on both probabilistic and relational hidden-variable models by a single proof, because one case implies the other, depending on purely syntactic criteria. We also discuss the ‘no-go’ theorems by Bell and Kochen-Specker and provide a purely logical variant of the latter, introducing non-contextual choice as a team-semantical property.     

Measurement error and the Albert-Loewer problem

Modal interpretations of QM have the welcome consequence that unitarily evolved post-measurement states which superpose eigenstates of the anticipated pointer observable can represent devices registering determinate measurement outcomes. Albert and Loewer have claimed that modal interpretations cannot account for the outcomes of error-prone measurements. But Albert, Loewer, and their commentators have not always appreciated the relation of measurement error to the Albert-Loewer problem. I argue that measurement error is neither necessary nor sufficient to generate the Albert-Loewer problem, and use the Araki-Yanase theorem to show that measurements of a large class of observables, if they are error-free, are beset by the Albert-Loewer problem.     

双折射光纤中克尔效应及光纤－光学逻辑门

本文详细地研究了单模双折射光纤中的克尔效应．讨论了其应用于光纤－光学逻辑门的优点,给出了有关的理论分析和计算结果以实验装置,确定了强度型逻辑门的“１／０”状态,测出了输出光脉冲宽度．理论分析和实验结果符合良好．     

Unprovability of a “precognition” effect in quantum mechanics

It is shown that nonlocality gives rise to an undecidable proposition, meaning it cannot be proved true nor proved false from the usual assumptions, but is independent of them. A variation on the usual thought experiment is considered in which the observers are timelike separated, but the nonlocality fails to become a precognition effect because of this independence result.     

Measurement: It ain't over till it's over

Elby (1993) has raised certain problems that appear to be devastating for modal interpretations of quantum mechanics, but do not arise for Bohm's pilot wave theory. Here I show that the features Elby identifies as objectionable in my version of the modal interpretation have their counterpart in Bohm's theory. To the extent that Bohm's theory works as a no collapse solution to the measurement problem - and I think it does - so does my modal interpretation.     

Rumer's transformation,in biology,as the negation,in classical logic

In this article, we make a connection between the Rumer transformation, used in the study of the genetic code‐doublets, and the negation of classic logic. A unified classification is given, relying on two Klein's 4‐groups describing the symmetries of the 16 doublets of nitrogenous bases and those of the 16 binary connectives of classic logic, both groups being subgroups of a larger noncommutative group with eight elements we identify as the dihedral group D₄. Also, some connections with other works are briefly considered. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003