A consistent foundation for Isabelle/HOL

The interactive theorem prover Isabelle/HOL is based on well understood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). However, Isabelle/HOL brings its own personal touch to HOL: overloaded constant definitions, used to achieve Haskell-like type classes in the user space. These features are a delight for the users, but unfortunately are not easy to get right as an extension of HOL—they have a history of inconsistent behavior. It has been an open question under which criteria overloaded constant definitions and type definitions can be combined together while still guaranteeing consistency. This paper presents a solution to this problem: non-overlapping definitions and termination of the definition-dependency relation (tracked not only through constants but also through types) ensures relative consistency of Isabelle/HOL

Safety and conservativity of definitions in HOL and Isabelle/HOL

Definitions are traditionally considered to be a safe mechanism for introducing concepts on top of a logic known to be consistent. In contrast to arbitrary axioms, definitions should in principle be treatable as a form of abbreviation, and thus compiled away from the theory without losing provability. In particular, definitions should form a conservative extension of the pure logic. These properties are crucial for modern interactive theorem provers, since they ensure the consistency of the logic, as well as a valid environment for total/certified functional programming. We prove these properties, namely, safety and conservativity, for Higher-Order Logic (HOL), a logic implemented in several mainstream theorem provers and relied upon by thousands of users. Some unique features of HOL, such as the requirement to give non-emptiness proofs when defining new types and the impossibility to unfold type definitions, make the proof of these properties, and also the very formulation of safety, nontrivial. Our study also factors in the essential variation of HOL definitions featured by Isabelle/HOL, a popular member of the HOL-based provers family. The current work improves on recent results which showed a weaker property, consistency of Isabelle/HOL’s definitions

Comprehending Isabelle/HOL's consistency

The proof assistant Isabelle/HOL is based on an extension of Higher-Order Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means—following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs

From types to sets by local type definitions in higher-order logic

Types in Higher-Order Logic (HOL) are naturally interpreted as nonempty sets—this intuition is reflected in the type definition rule for the HOL-based systems (including Isabelle/HOL), where a new type can be defined whenever a nonempty set is exhibited. However, in HOL this definition mechanism cannot be applied inside proof contexts. We propose a more expressive type definition rule that addresses the limitation and we prove its soundness. This higher expressive power opens the opportunity for a HOL tool that relativizes type-based statements to more flexible set-based variants in a principled way. We also address particularities of Isabelle/HOL and show how to perform the relativization in the presence of type classes

Buckled membranes for microstructures

Based on energy variation methods we calculated the deflection of membranes under the combined load of an external pressure and an internal lateral stress. A lateral load gives rise to buckling once a critical load is exceeded. The combination of transversal loads and lateral loads changes the properties of the membrane (and other structures) in the vicinity of the buckling load: The membrane deflects at all lateral loads and the critical load, above which two states are possible shifts. A result important for the design of microsystems, which are based on the buckling phenomenon, is the pressure required to switch the membrane from one state to the other. The theory is tested successfully with micromachined silicon/silicon-dioxide membrane

Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators

The purpose of this paper is to introduce a new class of quasi-contractive operators and to show that the most used fixed point iterative methods, that is, the Picard and Mann iterations, are convergent to the unique fixed point. The comparison of these methods with respect to their convergence rate is obtained

Silicon active microvalves using buckled membranes for actuation

Design considerations and experiments have been made for obtaining a new type of active microvalves using silicon buckled membranes. The properties of the buckled membranes permitting to obtain high deflections and to actuate them more convenient are demonstrated. A thermal actuation using an aluminium ring layer heated with a polysilicon resistor is analysed. The polysilicon and the aluminium ring layers have been deposited in the region of the membrane having the minimum internal stress. The fabrication process consist of photolithography, LPCVD depositions, diffusion, AI sputtering. isotropic, anisotropic etching and anodic bonding. The design and experiments show a convenient low temperature range necessary to actuate the microvalve.\ud \u

Polarization-squeezed light formation in a medium with electronic Kerr nonlinearity

We analyze the formation of polarization-squeezed light in a medium with electronic Kerr nonlinearity. Quantum Stokes parameters are considered and the spectra of their quantum fluctuations are investigated. It is established that the frequency at which the suppression of quantum fluctuations is the greatest can be controlled by adjusting the linear phase difference between pulses. We shown that by varying the intensity or the nonlinear phase shift per photon for one pulse, one can effectively control the suppression of quantum fluctuations of the quantum Stokes parameters.Comment: final version, RevTeX, 10 pages, 5 eps figure

A platform for crowdsourcing corpora for argumentative

One problem that Argument Mining (AM) is facing is the difficultyof obtaining suitable annotated corpora. We propose a web-basedplatform, BookSafari, that allows crowdsourcing of annotated cor-pora forrelation-based AMfrom users providing reviews for booksand exchanging opinions about these reviews to facilitate argumen-tative dialogue. The annotations amount to pairwise argumentativerelations ofattackandsupportbetween opinions and between opin-ions and reviews. As a result of the annotations, reviews and opinionsform structured debates which can be understood as bipolar argu-mentation frameworks. The platform also empowers annotationsof the same pairs by multiple annotators and can support differentmeasures of inter-annotator agreement and corpora selection

Neurobiology of Vascular Dementia

Vascular dementia is, in its current conceptual form, a distinct type of dementia with a spectrum of specific clinical and pathophysiological features. However, in a very large majority of cases, these alterations occur in an already aged brain, characterized by a milieu of cellular and molecular events common for different neurodegenerative diseases. The cell signaling defects and molecular dyshomeostasis might lead to neuronal malfunction prior to the death of neurons and the alteration of neuronal networks. In the present paper, we explore some of the molecular mechanisms underlying brain malfunction triggered by cerebrovascular disease and risk factors. We suggest that, in the age of genetic investigation and molecular diagnosis, the concept of vascular dementia needs a new approach