In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.
Sahara Net
Sahara Net is an information and communications technology provider (ICT) serving the Saudi market, the company has rapidly grown since 1989 to offer various complementary services such as connectivity, internet, hosting, cloud, optimization, cyber security, and managed services. == History == Sahara Net is a Saudi Joint Stock Company (JSC) and its history goes back to 1989 when Sahara Net established the 1st Saudi Bulletin Board Service (BBS) in the Kingdom. During this period, it operated as a hub for email exchange in the FidoNet network. And in 1994 Sahara Net started offering Internet connectivity and other related services like internet email, web design, web hosting, and Domain name registry services. These services made the first ISP in Saudi Arabia before the official licensing in 1998, when the Saudi Internet market was regulated and Sahara Net received Internet Service Provider (ISP) license and was appointed as the official Local Internet Registry (LIR) in the Kingdom of Saudi Arabia. == Today == The company grew over these years to become one of the main ICTs in the Saudi Arabian market, extending network coverage to all major cities in Saudi Arabia, and offering various connectivity options to business as well as home users. In 2009, the company was partially acquired by Telindus (the ICT investment arm of Belgacom), the famous telecom operator in Belgium and Europe. Then, in 2014, the company was fully acquired by its original founders. Recently, Sahara Net was converted from an LLC to a JSC with over 1200 shareholders by a capital raise (original founders still control 70% of the shares).
LTE (telecommunication)
In telecommunications, Long Term Evolution (LTE) is a standard for wireless broadband communication for cellular mobile devices and data terminals. It is considered to be a "transitional" 4G technology, and is therefore also referred to as 3.95G as a step above 3G. LTE is based on the 2G GSM/EDGE and 3G UMTS/HSPA standards. It improves on those standards' capacity and speed by using a different radio interface and core network improvements. LTE is the upgrade path for carriers with both GSM/UMTS networks and CDMA2000 networks. LTE has been succeeded by LTE Advanced, which is officially defined as a "true" 4G technology and also named "LTE+". == Terminology == The standard is developed by the 3GPP (3rd Generation Partnership Project) and is specified in its Release 8 document series, with minor enhancements described in Release 9. LTE is also called 3.95G and has been marketed as 4G LTE and Advanced 4G; but the original version did not meet the technical criteria of a 4G wireless service, as specified in the 3GPP Release 8 and 9 document series for LTE Advanced. The requirements were set forth by the ITU-R organisation in the IMT Advanced specification; but, because of market pressure and the significant advances that WiMAX, Evolved High Speed Packet Access, and LTE bring to the original 3G technologies, ITU-R later decided that LTE and the aforementioned technologies can be called 4G technologies. The LTE Advanced standard formally satisfies the ITU-R requirements for being considered IMT-Advanced. To differentiate LTE Advanced and WiMAX-Advanced from current 4G technologies, ITU has defined the latter as "True 4G". == Overview == LTE stands for Long Term Evolution and is a registered trademark owned by ETSI (European Telecommunications Standards Institute) for the wireless data communications technology and development of the GSM/UMTS standards. However, other nations and companies do play an active role in the LTE project. The goal of LTE was to increase the capacity and speed of wireless data networks using new DSP (digital signal processing) techniques and modulations that were developed around the turn of the millennium. A further goal was the redesign and simplification of the network architecture to an IP-based system with significantly reduced transfer latency compared with the 3G architecture. The LTE wireless interface is incompatible with 2G and 3G networks, so it must be operated on a separate radio spectrum. The idea of LTE was first proposed in 1998, with the use of the COFDM radio access technique to replace the CDMA and studying its Terrestrial use in the L band at 1428 MHz (TE) In 2004 by Japan's NTT Docomo, with studies on the standard officially commenced in 2005. In May 2007, the LTE/SAE Trial Initiative (LSTI) alliance was founded as a global collaboration between vendors and operators with the goal of verifying and promoting the new standard to ensure the global introduction of the technology as quickly as possible. The LTE standard was finalized in December 2008, and the first publicly available LTE service was launched by TeliaSonera in Oslo and Stockholm on December 14, 2009, as a data connection with a USB modem. The LTE services were launched by major North American carriers as well, with the Samsung SCH-r900 being the world's first LTE Mobile phone starting on September 21, 2010, and Samsung Galaxy Indulge being the world's first LTE smartphone starting on February 10, 2011, both offered by MetroPCS, and the HTC ThunderBolt offered by Verizon starting on March 17 being the second LTE smartphone to be sold commercially. In Canada, Rogers Wireless was the first to launch LTE network on July 7, 2011, offering the Sierra Wireless AirCard 313U USB mobile broadband modem, known as the "LTE Rocket stick" then followed closely by mobile devices from both HTC and Samsung. Initially, CDMA operators planned to upgrade to rival standards called UMB and WiMAX, but major CDMA operators (such as Verizon, Sprint and MetroPCS in the United States, Bell and Telus in Canada, au by KDDI in Japan, SK Telecom in South Korea and China Telecom/China Unicom in China) have announced instead they intend to migrate to LTE. The next version of LTE is LTE Advanced, which was standardized in March 2011. Services commenced in 2013. Additional evolution known as LTE Advanced Pro was approved in 2015. The LTE specification provides downlink peak rates of 300 Mbit/s, uplink peak rates of 75 Mbit/s, and QoS provisions permitting a transfer latency of less than 5 ms in the radio access network. LTE has the ability to manage fast-moving mobiles and supports multicast and broadcast streams. LTE supports scalable carrier bandwidths, from 1.4 MHz to 20 MHz and supports both frequency division duplexing (FDD) and time-division duplexing (TDD). The IP-based network architecture, called the Evolved Packet Core (EPC) designed to replace the GPRS Core Network, supports seamless handovers for both voice and data to cell towers with older network technology such as GSM, UMTS and CDMA2000. The simpler architecture results in lower operating costs (for example, each E-UTRA cell will support up to four times the data and voice capacity supported by HSPA). Because LTE frequencies and bands differ from country to country, only multi-band phones can use LTE in all countries where it is supported. == History == === 3GPP standard development timeline === In 2004, NTT Docomo of Japan proposes LTE as the international standard. In September 2006, Siemens Networks (today Nokia Networks) showed in collaboration with Nomor Research the first live emulation of an LTE network to the media and investors. As live applications, two users streaming an HDTV video in the downlink and playing an interactive game in the uplink have been demonstrated. In February 2007, Ericsson demonstrated for the first time in the world, LTE with bit rates up to 144 Mbit/s In September 2007, NTT Docomo demonstrated LTE data rates of 200 Mbit/s with power level below 100 mW during the test. In November 2007, Infineon presented the world's first RF transceiver named SMARTi LTE, supporting LTE functionality in a single-chip RF silicon processed in CMOS In early 2008, LTE test equipment began shipping from several vendors and at the Mobile World Congress 2008 in Barcelona, Ericsson demonstrated the world's first end-to-end mobile call enabled by LTE on a small handheld device. Motorola demonstrated an LTE RAN (Radio Access Network) standard compliant eNodeB and LTE chipset at the same event. At the February 2008 Mobile World Congress: Motorola demonstrated how LTE can accelerate the delivery of personal media experience with HD video demo streaming, HD video blogging, online gaming, and VoIP over LTE running a RAN standard-compliant LTE network & LTE chipset. Ericsson EMP (later ST-Ericsson) demonstrated the world's first end-to-end LTE call on handheld Ericsson demonstrated LTE FDD and TDD mode on the same base station platform. Freescale Semiconductor demonstrated streaming HD video with peak data rates of 96 Mbit/s downlink and 86 Mbit/s uplink. NXP Semiconductors (later part of ST-Ericsson) demonstrated a multi-mode LTE modem as the basis for a software-defined radio system for use in cellphones. picoChip and Mimoon demonstrated a base station reference design. This runs on a common hardware platform (multi-mode / software-defined radio) with their WiMAX architecture. In April 2008, Motorola demonstrated the first EV-DO to LTE hand-off handling over streaming a video from LTE to a commercial EV-DO network and back to LTE. In April 2008, LG Electronics and Nortel demonstrated LTE data rates of 50 Mbit/s while travelling at 110 km/h (68 mph). In November 2008, Motorola demonstrated industry first over-the-air LTE session in 700 MHz spectrum. Researchers at Nokia Siemens Networks and Heinrich Hertz Institut have demonstrated LTE with 100 Mbit/s Uplink transfer speeds. At the February 2009 Mobile World Congress: Infineon demonstrated a single-chip 65 nm CMOS RF transceiver providing 2G/3G/LTE functionality Launch of ng Connect program, a multi-industry consortium founded by Alcatel-Lucent to identify and develop wireless broadband applications. Motorola provided LTE drive tour on the streets of Barcelona to demonstrate LTE system performance in a real-life metropolitan RF environment In July 2009, Nujira demonstrated efficiencies of more than 60% for an 880 MHz LTE Power Amplifier In August 2009, Nortel and LG Electronics demonstrated the first successful handoff between CDMA and LTE networks in a standards-compliant manner In August 2009, Alcatel-Lucent receives FCC certification for LTE base stations for the 700 MHz spectrum band. In September 2009, Nokia Siemens Networks demonstrated the world's first LTE call on standards-compliant commercial software. In October 2009, Ericsson and Samsung demonstrated interoperability between the first ever commercial LTE device and the live network in
Active networking
Active networking is a communication pattern that allows packets flowing through a telecommunications network to dynamically modify the operation of the network. Active network architecture is composed of execution environments (similar to a unix shell that can execute active packets), a node operating system capable of supporting one or more execution environments. It also consists of active hardware, capable of routing or switching as well as executing code within active packets. This differs from the traditional network architecture which seeks robustness and stability by attempting to remove complexity and the ability to change its fundamental operation from underlying network components. Network processors are one means of implementing active networking concepts. Active networks have also been implemented as overlay networks. == What does it offer? == Active networking allows the possibility of highly tailored and rapid "real-time" changes to the underlying network operation. This enables such ideas as sending code along with packets of information allowing the data to change its form (code) to match the channel characteristics. The smallest program that can generate a sequence of data can be found in the definition of Kolmogorov complexity. The use of real-time genetic algorithms within the network to compose network services is also enabled by active networking. == How it relates to other networking paradigms == Active networking relates to other networking paradigms primarily based upon how computing and communication are partitioned in the architecture. === Active networking and software-defined networking === Active networking is an approach to network architecture with in-network programmability. The name derives from a comparison with network approaches advocating minimization of in-network processing, based on design advice such as the "end-to-end argument". Two major approaches were conceived: programmable network elements ("switches") and capsules, a programmability approach that places computation within packets traveling through the network. Treating packets as programs later became known as "active packets". Software-defined networking decouples the system that makes decisions about where traffic is sent (the control plane) from the underlying systems that forward traffic to the selected destination (the data plane). The concept of a programmable control plane originated at the University of Cambridge in the Systems Research Group, where (using virtual circuit identifiers available in Asynchronous Transfer Mode switches) multiple virtual control planes were made available on a single physical switch. Control Plane Technologies (CPT) was founded to commercialize this concept. == Fundamental challenges == Active network research addresses the nature of how best to incorporate extremely dynamic capability within networks. In order to do this, active network research must address the problem of optimally allocating computation versus communication within communication networks. A similar problem related to the compression of code as a measure of complexity is addressed via algorithmic information theory. One of the challenges of active networking has been the inability of information theory to mathematically model the active network paradigm and enable active network engineering. This is due to the active nature of the network in which communication packets contain code that dynamically change the operation of the network. Fundamental advances in information theory are required in order to understand such networks. == Nanoscale active networks == As the limit in reduction of transistor size is reached with current technology, active networking concepts are being explored as a more efficient means accomplishing computation and communication. More on this can be found in nanoscale networking.
Hardware compatibility list
A hardware compatibility list (HCL) is a list of computer hardware (typically including many types of peripheral devices) that is compatible with a particular operating system or device management software. The list contains both whole computer systems and specific hardware elements including motherboards, sound cards, and video cards. In today's world, there is a vast amount of computer hardware in circulation, and many operating systems too. A hardware compatibility list is a database of hardware models and their compatibility with a certain operating system. HCLs can be centrally controlled (one person or team keeps the list of hardware maintained) or user-driven (users submit reviews on hardware they have used). There are many HCLs. Usually, each operating system will have an official HCL on its website.
Braina
Braina is a virtual assistant and speech-to-text dictation application for Microsoft Windows developed by Brainasoft. Braina uses natural language interface, speech synthesis, and speech recognition technology to interact with its users and allows them to use natural language sentences to perform various tasks on a computer. The name Braina is a short form of "Brain Artificial". Braina is marketed as a Microsoft Copilot alternative. It provides a voice interface for several locally run and cloud large language models, including the latest LLMs from providers such as OpenAI, Anthropic, Google, xAI, Meta, Mistral, etc; while improving data privacy. Braina also allows responses from its in-house large language models like Braina Swift and Braina Pinnacle. It has an "Artificial Brain" feature that provides persistent memory support for supported LLMs. == Features == Braina provides is able to carry out various tasks on a computer, including automation. Braina can take commands inputted through typing or through dictation to store reminders, find information online, perform mathematical operations, open files, generate images from text, transcribe speech, and control open windows or programs. Braina adapts to user behavior over time with a goal of better anticipating needs. === Speech-to-text dictation === Braina Pro can type spoken words into an active window at the location of a user's cursor. Its speech recognition technology supports more than 100 languages and dialects and is able to isolate the recognition of a user's voice from disturbing environmental factors such as background noise, other human voices, or external devices. Braina can also be taught to dictate uncommon legal, medical, and scientific terms. Users can also teach Braina uncommon names and vocabulary. Users can edit or correct dictated text without using a keyboard or mouse by giving built-in voice commands. === Text-to-speech === Braina can read aloud selected texts, such as e-books. === Custom commands and automation === Braina can automate computer tasks. It lets users create custom voice commands to perform tasks such as opening files, programs, websites, or emails, as well as executing keyboard or mouse macros. === Transcription === Braina can transcribe media file formats such as WAV, MP3, and MP4 into text. === Notes and reminders === Braina can store and recall notes and reminders. These can include scheduled or unscheduled commands, checklist items, alarms, chat conversations, memos, website snippets, bookmarks, contacts. === Image and Video generation === Braina can generate AI images and videos from text and image inputs using generative cloud AI models. These include Black Forest Labs' FLUX.2, Google's Veo, Imagen, and Nano Banana Pro, Kuaishou's Kling, Alibaba's Wan, ByteDance's Seedance and Seedream, MiniMax's Hailuo, OpenAI's GPT Image, and Tongyi Lab's Z Image Turbo. == Platforms == In addition to the desktop version for Windows operating systems, Braina is also available for the iOS and Android operating systems. The mobile version of Braina has a feature allowing remote management of a Windows PC connected via Wi-Fi. == Distributions == Braina is distributed in multiple modes. These include Braina Lite, a freeware version with limitations, and premium versions Braina Pro, Pro Plus, and Pro Ultra. Some additional features in the Pro version include dictation, custom vocabulary, video transcription, automation, custom voice commands, and persistent LLM memory. == Reception == TechRadar has consistently listed Braina as one of the best dictation and virtual assistant apps between 2015 and 2024.
Acquisition of DirecTV by AT&T
AT&T Inc. announced an agreement with the DirecTV Group on May 18, 2014, to acquire the company for $48.5 billion in a joint cash-stock transaction and assumed debts of $18.6 billion for a total offer of $67.1 billion. Due to stalling growth in the wireless sector, AT&T began diversifying into mass media to expand its consumer offerings. After regulatory agencies approved the purchase on July 24, 2015, AT&T briefly became the largest Pay-TV provider. DirecTV was brought under AT&T's communication segment and DirecTV Now was launched on November 30, 2016, as an alternative to cord-cutting. In the years following the purchase, DirecTV lost millions of subscribers across its satellite and streaming services and by 2019, calls grew for AT&T to divest itself off the business. Initially, AT&T rejected these calls and defended the acquisition, but by February 2021, it reached a deal with TPG Inc. to transfer ownership of DirecTV. Under the terms of the agreement, AT&T would retain a 70% majority stake in DirecTV but would no longer oversee its daily operations. The deal was finalized by August 2, 2021, with AT&T receiving $7.1 billion. By July 3, 2025, AT&T sold its majority stake to TPG, ending any ties of involvement. == Background and Development == === AT&T's history === The company to bear the name "AT&T" was founded on March 3, 1885, as American Telephone and Telegraph Company (or AT&T Corporation) by Theodore Newton Vail as a long-distance subsidiary of the Bell Telephone Company. By December 1899, the Bell Telephone's assets were transferred to AT&T, with the latter gaining control of the Bell System, a regional network of local telecom companies. Theodore Vail became AT&T's President in 1907 and under his leadership, AT&T gained a monopoly over the telephone sector in the United States. This near century dominance earned AT&T the nickname of "Ma Bell." In 1974, the U.S. Department of Justice sued AT&T on accounts of antitrust violations. AT&T challenged the lawsuit, but in 1982, it reached a settlement with the DOJ to break apart its Bell System monopoly into seven regional companies. On January 1, 1984, the Bell System came to an end and led to a reshaped telecom industry. One of these regional companies, Southwestern Bell, emerged as the smallest, but after the passage of the 1996 Telecom Act, deregulated telecom rules allowed SBC to become a major telecom company. AT&T briefly became the largest cable and broadband company by the end of the 20th Century, but later deconsolidated to exit those industries. In 2005, SBC acquired its former parent, AT&T, and took on its branding as AT&T Inc, while retaining its previous business history. The newly reincorporated AT&T acquired BellSouth in 2006 and reconstituted much of its former Bell System. === DirecTV's history === == Acquisition Timeline == == Managing DirecTV == == Divestment and Spinoff ==