Connectionist modal logic: Representing modalities in neural networks

AbstractModal logics are amongst the most successful applied logical systems. Neural networks were proved to be effective learning systems. In this paper, we propose to combine the strengths of modal logics and neural networks by introducing Connectionist Modal Logics (CML). CML belongs to the domain of neural-symbolic integration, which concerns the application of problem-specific symbolic knowledge within the neurocomputing paradigm. In CML, one may represent, reason or learn modal logics using a neural network. This is achieved by a Modalities Algorithm that translates modal logic programs into neural network ensembles. We show that the translation is sound, i.e. the network ensemble computes a fixed-point meaning of the original modal program, acting as a distributed computational model for modal logic. We also show that the fixed-point computation terminates whenever the modal program is well-behaved. Finally, we validate CML as a computational model for integrated knowledge representation and learning by applying it to a well-known testbed for distributed knowledge representation. This paves the way for a range of applications on integrated knowledge representation and learning, from practical reasoning to evolving multi-agent systems

Concept of Inverted Refractive-Index-Contrast Grating Mirror and Exemplary Fabrication by 3D Microprinting

Highly reflective mirrors are indispensable components in a variety of state-of-the-art photonic devices. Typically used, bulky, multi-layered distributed Bragg (DBR) reflectors are limited to lattice-matched semiconductors or nonconductive dielectrics. Here, we introduce an inverted refractive-index-contrast grating (ICG), as compact, single layer alternative to DBR. In the ICG, a subwavelength one-dimensional grating made of a low refractive index material is implemented on a high refractive index cladding. Our numerical simulations show that the ICG provides nearly total optical power reflectance for the light incident from the side of the cladding whenever the refractive index of the grating exceeds 1.75, irrespective of the refractive index of the cladding. Additionally, the ICG enables polarization discrimination and phase tuning of the reflected and transmitted light, the property not achievable with the DBR. We experimentally demonstrate a proof-of-concept ICG fabricated according to the proposed design, using the technique of 3D microprinting in which thin stripes of IP-Dip photoresist are deposited on a Si cladding. This one-step method avoids laborious and often destructive etching-based procedures for grating structuration, making it possible to implement the grating on any arbitrary cladding material

Impact of Stripe Shape on the Reflectivity of Monolithic High Contrast Gratings

Monolithic high contrast gratings (MHCGs) composed of a one-dimensional grating patterned in a monolithic layer provide up to 100% optical power reflectance and can be fabricated in almost any semiconductor and dielectric material used in modern optoelectronics. MHCGs enable monolithic integration, polarization selectivity, and versatile phase tuning. They can be from 10 to 20 times thinner than distributed Bragg reflectors. The subwavelength dimensions of MHCGs significantly reduce the possibility of ensuring the smoothness of the sidewalls of the MHCG stripes and make precise control of the shape of the MHCG stripe cross-section difficult during the etching process. The question is then whether it is more beneficial to improve the etching methods to obtain a perfect cross-section shape, as assumed by the design, or whether it is possible to find geometrical parameters that enable high optical power reflectance using the shape that a given etching method provides. Here, we present a numerical study supported by the experimental characterization of MHCGs fabricated in various materials using a variety of common surface nanometer-scale shaping methods. We demonstrate that MHCG stripes with an arbitrary cross-section shape can provide optical power reflectance of nearly 100%, which greatly relaxes their fabrication requirements. Moreover, we show that optical power reflectance exceeding 99% with a record spectral bandwidth of more than 20% can be achieved for quasi-Trapezoidal cross-sections of MHCGs. We also show that sidewall corrugations of the MHCG stripes have only a slight impact on MHCG optical power reflectance if the amplitude of the corrugation is less than 16% of the MHCG period. This level of stripe fabrication precision can be achieved using the most current surface etching methods. Our results are significant for the design and production of a variety of photonic devices employing MHCGs. The flexibility with regard to cross-section shape facilitates the reliable fabrication of highly reflective subwavelength grating mirrors. This in turn will enable the manufacture of monolithically integrated high-quality-factor optical micro-and nanocavity devices

Neuro-symbolic representation of logic programs defining infinite sets

It has been one of the great challenges of neuro-symbolic integration to represent recursive logic programs using neural networks of finite size. In this paper, we propose to implement neural networks that can process recursive programs viewed as inductive definitions.</p

A New Approach for Sensitive Characterization of Semiconductor Laser Beams Using Metal-Semiconductor Thermocouples

This paper presents the results of beam investigations on semiconductor IR lasers using novel detectors based on thermocouples. The work covers the design, the fabrication of detectors, and the experimental validation of their sensitivity to IR radiation. The principle of operation of the manufactured detectors is based on the Seebeck effect (the temperature difference between hot and cold junctions induced voltage appearance). The devices were composed of several thermocouples arranged in a linear array. The nano- and microscale thermocouples (the hot junctions) were fabricated using a typical Si-compatible MEMS process enhanced with focused ion beam (FIB) milling. The performance of the hot junctions was tested, focusing on their sensitivity to IR radiation covering the near-infrared (NIR) radiation (λ = 976 nm). The output voltage was measured as a function of the detector position in the XY plane. The measurement results allowed for reconstructing the Gaussian-like intensity distribution of the incident light beam