hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Second-order logic
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.

First-order logic quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, quantifies over relations. For example, the second-order sentence  says that for every formula P, and every individual x, either Px is true or not(Px) is true (this is the law of excluded middle). Second-order logic also includes quantification over sets, functions, and other variables (see section below). Both first-order and second-order logic use the idea of a domain of discourse (often called simply the "domain" or the "universe"). The domain is a set over which individual elements may be quantified.

Finitary relation
In mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n-tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of triples such that when substituted to x, y and z, respectively, make the sentence true.

The non-negative integer n that gives the number of "places" in the relation is called the arity, adicity or degree of the relation. A relation with n "places" is variously called an n-ary relation, an n-adic relation or a relation of degree n. Relations with a finite number of places are called finitary relations (or simply relations if the context is clear). It is also possible to generalize the concept to infinitary relations with infinite sequences.
Oakmere House
Oakmere House is a public house and restaurant in Potters Bar, England, and a grade II listed building with Historic England. The pub is under the management of the Harvester company. The rear of the building faces onto Oakmere Park.
The L31 German Zeppelin fell on an old oak tree in the entrance of Wulstan Park after being shot down by Lieutenant Wulstan Tempest on 1 October 1916. His small plane was slightly damaged on landing back at his base, and he suffered a few injuries. He went next day to Oakmere Park, Potters Bar, see what he had done the night before!
This famous zeppelin was captained by the German hero of the time, Heinrich Mathy. He and his 18-man crew were all killed, and buried in the Potters Bar cemetery until their bodies were transferred to Cannock Chase many years later.
The Potters Bar Museum has a section devoted to this important incident in the aerial battles over England. After the death of Mathy, zeppelin raids decreased.

Potters Bar
Potters Bar is a town in Hertfordshire, England, 13 miles (21 km) north of central London. In 2011, it had a population of 21,882. In the 2021 census, the four wards that make up Potters Bar - Bentley Heath & The Royds, Furzefield, Oakmere and Parkfield - had a combined population of 22,536; this includes several smaller outlying hamlets contained in the Bentley Heath & The Royds ward, such as Bentley Heath and Ganwick Corner. In 2022, the population was around 23,325.

Within the historic county of Middlesex until 1965, the town dates to the early 13th century but remained a small, mainly agricultural, settlement until the arrival of the Great Northern Railway in 1850. It is now part of the London commuter belt.
Rune Dahmke
Rune Dahmke (born 10 April 1993) is a German professional handball player for THW Kiel and the Germany national team.

He was a part of the German team, that won gold medals at the 2016 European Men's Handball Championship. He was also on the German team that won silver medals at the 2024 Olympics.

Germany men's national handball team
The Germany national handball team is the country's national men's handball team and represents Germany in international tournaments in men's handball and is one of the most successful handball teams in the world, having won three World Championships and two European Championship.
Angel's chameleon
The Angel's chameleon (Furcifer angeli), initially described as Chamaeleo angeli, is a species of chameleon, a lizard in the family Chamaeleonidae. The species is endemic to Madagascar, and was originally described by Édouard-Raoul Brygoo and Charles Antoine Domergue in 1968.

Charles Domergue
Charles Antoine Domergue (5 January 1914 – 31 December 2008) was a French naturalist, ornithologist, herpetologist, spelunker and geologist who spent much of his life in Madagascar. He also dealt with the effects of pollution.
History of electrochemistry
Electrochemistry, a branch of chemistry, went through several changes during its evolution from early principles related to magnets in the early 16th and 17th centuries, to complex theories involving conductivity, electric charge and mathematical methods. The term electrochemistry was used to describe electrical phenomena in the late 19th and 20th centuries. In recent decades, electrochemistry has become an area of current research, including research in batteries and fuel cells, preventing corrosion of metals, the use of electrochemical cells to remove refractory organics and similar contaminants in wastewater electrocoagulation and improving techniques in refining chemicals with electrolysis and electrophoresis.

Electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference and identifiable chemical change. These reactions involve electrons moving via an electronically conducting phase (typically an external electric circuit, but not necessarily, as in electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic species in a solution).

When a chemical reaction is driven by an electrical potential difference, as in electrolysis, or if a potential difference results from a chemical reaction as in an electric battery or fuel cell, it is called an electrochemical reaction. In electrochemical reactions, unlike in other chemical reactions,  electrons are not transferred directly between atoms, ions, or molecules, but via the aforementioned electric circuit. This phenomenon is what distinguishes an electrochemical reaction from a conventional chemical reaction.
Nilavu
Nilavu (transl. Moonlight) is a 2010 Malayalam romantic film written and directed by Ajith Nair. Nilavu is the soul touching story of an indefinable relationship between two lonely individuals, who meet by chance. The whole film revolves around the strange bond that develops between them and how their relationship evolves. The film is about the emotional complexities of expatriate life in the Persian Gulf region.

Arab states of the Persian Gulf
The Arab states of the Persian Gulf (Arabic: دول الخليج الفارسي, romanized: duwal al-Khalīj al-ʿfarsi), are a group of Arab states bordering the Persian Gulf, including Bahrain, Kuwait, Iraq, Oman, Qatar, Saudi Arabia, and the United Arab Emirates.

The term has been used in different contexts to refer to a number of Arab states in the Persian Gulf region. The prominent political union of the region is the Gulf Cooperation Council, which includes all Persian Gulf states except Iraq. Most Persian Gulf states are former protectorates of the British Empire.
Frank Schwalba-Hoth
Frank Schwalba-Hoth (born 12 December 1952 in Hamburg, Germany) is a former politician, founding member of the German Greens, and former MEP. After his graduation from high school (Otto-Hahn-Gymnasium in Geesthacht) and his military service, Frank Schwalba-Hoth studied at the University of Marburg from 1974 to 1981. Frank Schwalba-Hoth has one daughter.

Marburg University
Marburg University (German: Philipps-Universität Marburg) is a public research university located in Marburg, Germany. It was founded in 1527 by Philip I, Landgrave of Hesse, which makes it one of Germany's oldest universities and the oldest still operating Protestant university in the world. It is now a public university of the state of Hesse, without religious affiliation.

Marburg University has 21,162 students (2024/25) and is located in Marburg. It offers an International summer university programme and offers student exchanges through the Erasmus programme.
King Baudouin Ice Shelf
The King Baudouin Ice Shelf (also called Roi Baudouin Ice shelf, from French: Plateforme de glace Roi Baudouin) in Dronning Maud Land, East Antarctica, is within the Norwegian part of Antarctica. It is named after King Baudouin of Belgium (1930-1993).

East Antarctica
80°S 80°E﻿ / ﻿80°S 80°E﻿ / -80; 80

East Antarctica, also called Greater Antarctica, constitutes the majority (two-thirds) of the Antarctic continent, lying primarily in the Eastern Hemisphere south of the Indian Ocean, and separated from West Antarctica by the Transantarctic Mountains. It is generally greater in elevation than West Antarctica, and includes the Gamburtsev Mountain Range in the center. The geographic South Pole is located within East Antarctica.

Apart from small areas of the coast, East Antarctica is permanently covered by ice and it has relatively low biodiversity, with only a small number of species of terrestrial plants, animals, algae, and lichens. The coasts are the breeding ground for various seabirds and penguins, and the leopard seal, Weddell seal, elephant seal, crabeater seal and Ross seal breed on the surrounding pack ice in summer.
Global Indian School, Ajman
Global Indian School (formerly Indian School Ajman) is a private Indian K-12 school in Ajman, United Arab Emirates, established in 1988. The school is recognized by the UAE's Ministry of Education and affiliated with the Central Board of Secondary Education in New Delhi, India.

Indian School Ajman was recognized as one of the best schools in the UAE by EW Global School Rankings, 2019.

The Principal, Malathi Das, was awarded the CBSE's Teacher of the Year award in 2002.

Central Board of Secondary Education
The Central Board of Secondary Education (CBSE) is a national-level board of education in India for public and private schools, controlled and managed by the Government of India. Established in 1929 by a government resolution, the Board was an experiment in inter-state integration and cooperation in the sphere of secondary education. There are more than 27,000 schools in India and 240 schools in 28 foreign countries affiliated with the CBSE. All schools affiliated with CBSE follow the NCERT curriculum, especially those in classes 9 to 12. The current Chairperson of CBSE is Rahul Singh, IAS.

The constitution of the Board was amended in 1952 to give its present name, the Central Board of Secondary Education. The Board was reconstituted on 1 July 1962 to make its services available to students and various educational institutions across the country.
Swing equation
A power system consists of a number of synchronous machines operating synchronously under all operating conditions. Under normal operating conditions, the relative position of the rotor axis and the resultant magnetic field axis is fixed. The angle between the two is known as the power angle,  torque angle, or rotor angle. During any disturbance, the rotor decelerates or accelerates with respect to the synchronously rotating air gap magnetomotive force, creating relative motion. The equation describing the relative motion is known as the swing equation, which is a non-linear second order differential equation that describes the swing of the rotor of synchronous machine. The power exchange between the mechanical rotor and the electrical grid due to the rotor swing (acceleration and deceleration) is called Inertial response.

Alternator
An alternator (or synchronous generator) is an electrical generator that converts mechanical energy to electrical energy in the form of alternating current. For reasons of cost and simplicity, most alternators use a rotating magnetic field with a stationary armature. Occasionally, a linear alternator or a rotating armature with a stationary magnetic field is used. In principle, any AC electrical generator can be called an alternator, but usually, the term refers to small rotating machines driven by automotive and other internal combustion engines.

An alternator that uses a permanent magnet for its magnetic field is called a magneto. Alternators in power stations driven by steam turbines are called turbo-alternators.  Large 50 or 60 Hz three-phase alternators in power plants generate most of the world's electric power, which is distributed by electric power grids.
Timeline of the Syrian civil war (May–August 2012)
The following is a timeline of the Syrian Civil War from May to August 2012. The majority of death tolls reported for each day comes from the Local Coordination Committees, an opposition activist group based in Syria, and the Syrian Observatory for Human Rights, another opposition group based in London.

Local Coordination Committees of Syria
The Local Coordination Committees of Syria (Arabic: لجان التنسيق المحلية في سوريا, romanized: Lijān al-Tansīq al-Maḥallīyah fī Sūriyā; LCCSyria or LCCs) were a network of local groups that organise and report on protests as part of the Syrian uprising. In June 2011, the network was described by The New York Times as beginning to "emerge as a pivotal force" in Syria. As of August 2011, the network supported civil disobedience and opposed local armed resistance and international military intervention as methods of opposing the Syrian government.
Tuscalee
Tuscalee (foaled 1960) was an American Thoroughbred racehorse that competed in both flat racing and steeplechase events from 1962 through 1972 for owner and breeder Alfred H. Smith Sr. The gelded son of Tuscany began his career racing on the flat with only modest success but as a steeplechase competitor became a National Champion in 1966 and finish his career having won more American steeplechase races than any horse in history. Tuscalee would be inducted into the U. S. Racing Hall of Fame and the Maryland Thoroughbred Hall of Fame. As at 2018, Tuscalee's American record of 37 Steeplechase wins still stands.

Gelding
A gelding (/ˈɡɛldɪŋ/) is a castrated male horse or other equine, such as a pony, donkey or a mule. The term is also used with certain other animals and livestock, such as domesticated camels. The equivalent terms for castrated male cattle are steer or bullock, and wether for sheep and goats.

Castration renders the male animal calmer, better-behaved, less sexually aggressive, and more responsive to training efforts. This makes the animal generally more suitable as an everyday working animal, or as a pet in the case of companion animals. The gerund and participle "gelding" and the infinitive "to geld" refer to the castration procedure itself.
Alexandre Saint-Yves d'Alveydre
Joseph Alexandre Saint-Yves, Marquis d’Alveydre (French: [sɛ̃tiv]; 26 March 1842 – 5 February 1909) was a French occultist who adapted the works of Fabre d'Olivet (1767–1825) and, in turn, had his ideas adapted by Gérard Encausse alias Papus. His work on L'Archéomètre deeply influenced the young René Guénon.

He developed the term "synarchy"—the association of everyone with everyone else—into a political philosophy, and his ideas about this type of government proved influential in politics and the occult.

René Guénon
René Jean-Marie-Joseph Guénon (15 November 1886 – 7 January 1951), also known as Abdalwahid Yahia (Arabic: عبد الـواحد يحيی; ʿAbd al-Wāḥid Yaḥiā), was a French-Egyptian intellectual who wrote on topics ranging from esotericism, "sacred science" and "traditional studies" to symbolism and initiation.

In his writings, Guénon proposes to hand down eastern metaphysics and traditions, these doctrines being defined by him as of "universal character", and adapt them to western readers "while keeping strictly faithful to their spirit".

Initiated into Islamic esotericism from as early as 1910 when he was 24, Guénon mainly wrote and published in French, and his works have been translated into more than twenty languages; he also wrote in Arabic an article for the journal Al Marifah.
Samuel S. Brannan
Samuel Stephen Brannan (February 5, 1835 – April 5, 1880) was an American newspaper editor, Republican politician, and Wisconsin pioneer.  He was the 13th mayor of Portage, Wisconsin, and represented northern Columbia County in the Wisconsin State Assembly during the 1873 session.

Columbia County, Wisconsin
Columbia County is a county located in the U.S. state of Wisconsin. As of the 2020 census, the population was 58,490. Its county seat and largest city is Portage. The county was created in 1846 as part of Wisconsin Territory. Columbia County is part of the Madison, WI Metropolitan Statistical Area as well as the Madison-Janesville-Beloit, WI Combined Statistical Area.
Rubroshorea inaequilateralis
Rubroshorea inaequilateralis (called, along with some other species in the genus Rubroshorea, red balau) is a species of tree in the family Dipterocarpaceae. It is endemic to Brunei and Sarawak on the island of Borneo. It grows in peat swamp forest, where it can reach 45 metres tall. It is threatened by habitat loss.

The species was first described as Shorea inaequilateralis by Colin Fraser Symington in 1935. In 2022 Peter Shaw Ashton and Jacqueline Heckenhauer placed the species in genus Rubroshorea as R. inaequilateralis.

Rubroshorea
Rubroshorea is a genus of flowering plants in the family Dipterocarpaceae. It includes 71 species of trees native to Borneo, Caroline Islands, Java, Malaya, Maluku, the Philippines, Sumatra and Thailand.

The genus corresponds to the Red meranti group in the Dipterocarp timber classification system.
Taxation in ancient Rome
In ancient Rome, there were four primary kinds of taxation: a cattle tax, a land tax, customs, and a tax on the profits of any profession. These taxes were typically collected by local aristocrats. The Roman state would set a fixed amount of money each region needed to provide in taxes, and the local officials would decide who paid the taxes and how much they paid. Once collected the taxes would be used to fund the military, create public works, establish trade networks, stimulate the economy, and to fund the cursus publicum.

Tributum
In Ancient Rome, Tributum was a tax imposed on the citizenry to fund the costs of war. The Tributum was one of the central reasons for the conducting of the census on assets, as it rose with wealth. It included cash assets, land, property and moveable goods (i.e. slaves). Several types of tributum have been attested to, including tributum in capita, tributum temerarium (emergency levy), and tributum ex censu (amount proportional to citizen's census financial rating).
Buffy the Vampire Slayer season 5
The fifth season of the television series Buffy the Vampire Slayer premiered on September 26, 2000, on The WB and concluded its 22-episode season on May 22, 2001. It maintained its previous timeslot, airing Tuesdays at 8:00 pm ET. This was the final season to air on The WB before it moved to UPN; The WB billed the season five finale as "The WB series finale".

Angel season 2
The second season of the television series Angel, the spin-off of Buffy the Vampire Slayer, premiered on September 26, 2000, on The WB and concluded its 22-episode season on May 22, 2001. It maintained its previous timeslot, airing Tuesdays at 9:00 pm ET, following Buffy.
Solo Darling
Christina Solomita (born February 19, 1987), better known by her ring name Solo Darling, is an American retired professional wrestler best known for her time with various promotions such as Game Changer Wrestling and Shimmer Women Athletes.

Shimmer Women Athletes
Shimmer Women Athletes (often referred to and stylized as SHIMMER) was an American, Chicago-based independent women's professional wrestling promotion which held its first event on November 6, 2005. Established by Dave Prazak and run by both him and Allison Danger, the promotion was created to give female wrestling talent from North America and beyond a serious, non-objectifying platform on which to display their skills. On November 1, 2021, the promotion was shut down.
Australia's Got Talent season 7
Australia's Got Talent is an Australian reality television show, based on the original UK series, to find new talent. The seventh season aired on the Nine Network from 11 August 2013 until 10 November 2013. Kyle Sandilands returned as a judge for his fourth season, and was joined by Dawn French, Timomatic and Geri Halliwell, as well as Julia Morris as the new host. Halliwell, French and Timomatic who is the additional fourth judge replaced original judge Dannii Minogue and Brian McFadden, while Morris replaced Grant Denyer. It was the first time that the show aired on another network, following its axing from the Seven Network in October 2012. The auditions took place from March–April 2013.

Grant Denyer
Grant Craig Denyer (born 12 September 1977) is an Australian television and radio presenter and motor racing driver, who has worked for several television networks, including Seven Network and Network 10, mostly serving as a presenter. He previously hosted 
Family Feud and Australia's Got Talent. Currently, he hosts channel 10's main game show Deal or No Deal.

In 2018, he won a Gold Logie Award for Most Popular Personality on Australian Television.
Alum Creek State Park
Alum Creek State Park is a 4,630-acre (1,870 ha) Ohio state park in Delaware County, Ohio, in the United States. Alum Creek Lake was constructed from 1970 to 1974 as part of the Flood Control Act of 1962. Alum Creek Dam was constructed on Alum Creek, a tributary of Big Walnut Creek, which drains into the Scioto River. Alum Creek Reservoir holds 3,387 acres (1,371 ha) of water and is open to fishing, boating, ice fishing, ice boating, and swimming. The park is just north of the state capital of Columbus and contains the remnants of a settlement by freed slaves that arrived in Ohio from North Carolina.

Alum Creek (Ohio)
Alum Creek is a 58-mile (93 km) long creek that runs north to south in central Ohio. The creek originates in Morrow County and then flows through Delaware County and finally into Franklin County, where it ends at Big Walnut Creek, which drains into the Scioto River. Alum Creek is a source of drinking water for the city of Westerville, Ohio. It has also been known as Allum Creek, Elk Creek, Seckle Creek, Sepung Creek, and Salt Creek.
Ryuta Homma
Ryuta Homma (本間 隆太, Homma Ryūta, born 17 October 1991) is a Japanese male Volleyball player. On club level, he captained JTEKT Stings team, in V.League Division 1, since 2019–20 season. He is a former member of the Japan men's national volleyball team.

V.League (Japan)
The V.League (Japanese: Vリーグ) is the second-level professional volleyball league for both men and women in Japan. The league started in 1994.

The competitions are organized by the Japan Volleyball League Organization. The league was called V.Premier League before the reform took place in 2018. The SV.League succeeded the V.League as the premier volleyball tournament in Japan in 2024.
Jeff Brand
Jeff Brand is an American politician who served in the Minnesota House of Representatives from 2023 to 2025 and from 2019 to 2021. A member of the Minnesota Democratic–Farmer–Labor Party (DFL), Brand represented District 18A in south-central Minnesota, which includes the cities of St. Peter and North Mankato, Nicollet County, and parts of Blue Earth and Le Sueur Counties.

St. Peter, Minnesota
St. Peter is a city and the county seat of Nicollet County, Minnesota, United States. It is 10 miles north of the Mankato–North Mankato metropolitan area. The population was 12,066 at the 2020 census. It is home to Gustavus Adolphus College.

U.S. Highway 169 and Minnesota State Highways 22 and 99 are three of the city's main routes. St. Peter is known for being located on the scenic Minnesota River valley, being home to the St. Peter State Hospital Museum, the Traverse Des Sioux historic site and the St. Peter Armory. Also, St. Peter's sister city is Petatlán, Guerrero, Mexico.