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In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system. In most cases, this comes down to its rules having the property of preserving truth; the converse of soundness is known as completeness. A system with syntactic entailment ⊢ and semantic entailment ⊨ is sound if for any sequence A 1, A 2... A n of sentences in its language, if A 1, A 2... A n ⊢ C A 1, A 2... A n ⊨ C. In other words, a system is sound. Soundness is among the most fundamental properties of mathematical logic; the soundness property provides the initial reason for counting a logical system as desirable. The completeness property means. Together they imply that only validities are provable. Most proofs of soundness are trivial. For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity. If the system allows Hilbert-style deduction, it requires only verifying the validity of the axioms and one rule of inference, namely modus ponens.

Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter. Soundness of a deductive system is the property that any sentence, provable in that deductive system is true on all interpretations or structures of the semantic theory for the language upon which that theory is based. In symbols, where S is the deductive system, L the language together with its semantic theory, P a sentence of L: if ⊢S P also ⊨L P. Strong soundness of a deductive system is the property that any sentence P of the language upon which the deductive system is based, derivable from a set Γ of sentences of that language is a logical consequence of that set, in the sense that any model that makes all members of Γ true will make P true. In symbols where Γ is a set of sentences of L: if Γ ⊢S P also Γ ⊨L P. Notice that in the statement of strong soundness, when Γ is empty, we have the statement of weak soundness. If T is a theory whose objects of discourse can be interpreted as natural numbers, we say T is arithmetically sound if all theorems of T are true about the standard mathematical integers.

For further information, see ω-consistent theory. The converse of the soundness property is the semantic completeness property. A deductive system with a semantic theory is complete if every sentence P, a semantic consequence of a set of sentences Γ can be derived in the deduction system from that set. In symbols: whenever Γ ⊨ P also Γ ⊢ P. Completeness of first-order logic was first explicitly established by Gödel, though some of the main results were contained in earlier work of Skolem. Informally, a soundness theorem for a deductive system expresses that all provable sentences are true. Completeness states. Gödel's first incompleteness theorem shows that for languages sufficient for doing a certain amount of arithmetic, there can be no consistent and effective deductive system, complete with respect to the intended interpretation of the symbolism of that language. Thus, not all sound deductive systems are complete in this special sense of completeness, in which the class of models is restricted to the intended one.

The original completeness proof applies to all classical models, not some special proper subclass of intended ones. Validity Completeness Soundness Hinman, P.. Fundamentals of Mathematical Logic. A K Peters. ISBN 1-56881-262-0. Copi, Symbolic Logic, Macmillan Publishing Co. ISBN 0-02-324880-7 Boolos, Jeffrey. Computability and Logic, 4th Ed, Cambridge, 2002. Validity and Soundness in the Internet Encyclopedia of Philosophy

Peter Persidis

Peter Persidis was an international Austrian footballer. His father Kostas Persidis was a footballer in Greece, he played at Proodeftiki F. C. and Aris Piraeous. Persidis started his professional career at First Vienna, than returned to his father's home country in the early 1970s, went on to win three Greek titles with Olympiacos prior to returning to Vienna in 1975 to play for SK Rapid Wien. A sweeper, the club's captain from 1978 to 1980, he won the 1981–82 Austrian title with Rapid under Hickersberger, he coached VSE St. Pölten, he later worked as Josef Hickersberger's assistant at Rapid and was the club's caretaker manager. Persidis took over as Under-19 head coach last summer, having worked as assistant to Hickersberger at UEFA EURO 2008. However, he was forced to step down soon afterwards after being diagnosed with a serious illness. Persidis died in Vienna on 21 January 2009 at the age of 61, with the Austrian Football Association holding a minute's silence in his honour at the national team's friendly against Sweden in Graz on 11 February.

Peter Persidis at Peter Persidis at Profile - Rapidarchiv

Luxair Flight 9642

Luxair Flight 9642 was a scheduled international passenger flight flying from Berlin Tempelhof Airport, Germany, to Luxembourg Findel Airport, Luxembourg. The flight carried 3 crew members; the flight was operated by the flag carrier of Luxembourg. The plane was a Fokker 50 and registered as LX-LGB. Lufthansa had a codeshare on the flight as LH2420. On 6 November 2002, the flight crashed while on final approach to Luxembourg Findel Airport about 2 nautical miles short of the runway while trying to land in fog. 20 out of the 22 passengers and crew perished. The crash is the deadliest aviation disaster; the crews were approaching Findel Airport in foggy conditions. 09:02:57 ATC: « Luxair 9642 good morning, continue approach. The wind is calm RVR beginning 250 meters, mid section 250 meters, stop end 225 meters». 09:03:08 Flight 9642: «That’s copied Luxair 9642… but we need 300 meters for the approach». 09:03:18 ATC: «9642 copied… uh so continue approach and I’ll keep you advised we didn’t have 300 uh… uh during the last time ».

09:03:28 Flight 9642: «Euh Roger 9642, we keep you advised we’re proceeding to ELU now and … uh standing by 9642». The flight crews decided to go-around, but they aborted the go-around and continued their approach. 09:04:46 Flight 9642: «Yes, well we do a go-around, missed approach». 09:04:57 ATC: «Luxair 9642 RVR 300 meters 275 meters stop end 275 meters». 09:05:05 Flight 9642: «9642 Roger so we continue». 09:05:08 ATC: «9642 you are cleared to land, wind 180°….knots». The co-pilot acknowledged this message, it was the last communication with the ATC. As the landing gear retracted, the pitch angle of the two propellers reached a value, lower than the minimum values for flight; this setting caused the aircraft's altitude to decrease rapidly. A few seconds both engines stopped and the flight data recorders ceased functioning; the first impact marks are found on the south edge of the road RN1. They represent the fuselage tail cone; the left wing tip scratched across the road before hitting an embankment at the north side of the road RN1.

Both wheels and blades came off from the aircraft. The aircraft bounced. At this point, the empennage and part of the right wing broke away, the aft portion of the fuselage turned around to the right and the aircraft came to rest 25 meters further away. At 09:05:42, the aircraft disappeared from the radar screen, it was found that the aircraft had crashed in a field 700 meters to the north of runway centreline. The fog was so thick. Most of them claimed not to have seen or heard anything when the crash occurred, only realized that something had happened nearby when ambulances and emergency services arrived at the crash site. Rescue services found; some passengers were still attached to their seat and others were not. The cabin crew member was found in the corridor next to the fuselage front entrance. Due to the cockpit not catching fire the captain survived, he was trapped in the cockpit and rescuers cut a hole to retrieve him. Most of the passengers were business officials from Germany. Seventeen were found dead at the crash site with five survivors.

By nightfall, 18 bodies out of the 20 dead were found. The bodies were thought to be buried under the smoldering fuselage. Rescue workers were using a crane to disentangle the charred remains. Amongst the passengers killed on the flight was artist Michel Majerus; the Captain, was 26-year-old Claude Poeckes, who had a total flying experience of 4,242 flight hours and 2,864 hours on type. The First Officer was an unnamed 32-year-old male with a total flight hours of 1,156 and 443 hours on type; the aircraft was inspected by a maintenance crew on the evening before the flight. While the aircraft passed inspection, it was found out that the aircraft's antiskid system on the right hand landing gear was inoperative; this had been an issue with the system and was detected on 27 September 2002 being replaced after. However, on 24 October 2002, the same antiskid system was inoperative again. Despite changing the outboard wheel speed sensor, the system remained inoperative. On 5 November 2002, one day before the accident, the problem was solved by replacing the inboard wheel speed sensor.

Investigators noted. Nearby residents of Niederanven stated that the fog at the time of the accident was thick, so much that nearby residents couldn't see or hear the moment of impact though Niederanven was in close proximity to the crash site. According to analysis of the Cockpit Voice Recorder, the flight was cleared for the approach as it descended through 6000 ft at a distance of thirteen nautical miles from the airport; the crew expressed some surprise that they were cleared to land ahead of all aircraft in the holding pattern, but began to prepare the aircraft for approach and landing. The preparation process was abbreviated due to the crew being caught off guard by the landing priority given to them. At 09:02:12, the captain told the First Officer: "Tell him … that if we don’t have 300 meters at Echo, we are going to perform a go-around"; this message was never delivered to ATC because the flight was transmitting on the tower frequency at this time. The Captain decided to perform a go-around.

However, the copilot did not react and instead continued with the approach checklist, placing the ground idle stop in the OFF position, this being the last action on the ch

Giulia Steingruber

Giulia Steingruber is a Swiss artistic gymnast. She is the 2016 Olympic bronze medalist on vault and a European champion in all-around and floor. Steingruber competed for Switzerland at the 2012 Summer Olympics, she is the first Swiss female gymnast to win the European all-around title and the first Swiss female gymnast to win an Olympic gymnastics medal of any color. At the 2011 World Artistic Gymnastics Championships, Steingruber finished 16th in the all-around and 5th on vault. Steingruber won the bronze medal on vault in the 2012 European Women's Artistic Gymnastics Championships. Competing at the 2012 Summer Olympics as the only women's gymnast from Switzerland, Steingruber finished 14th in the women's individual all-around with a score of 56.148. She was a reserve for the vault final. In December 2012, she competed at the World Cup event in Stuttgart and won bronze with a total score of 55.565, which included an impressive vault score of 15.400. Steingruber competed at the City of Jesolo Trophy in March and placed 8th in the individual all-around, with a total score of 55.550.

That month, she competed at the La Roche-sur-Yon World Cup event in France and placed first on the vault and uneven bars with scores of 13.433 and 13.600 respectively. She went on to win bronze in the vault final at the Doha World Cup, scoring a 15.225 on her first vault and a 14.100 on her second, for an average of 14.662. At the 2013 European Artistic Gymnastics Championships in Moscow, she qualified first into the vault final and went on to take gold with an average of 14.750. She qualified for the individual all-around and floor finals. In the all-around final, she tied for fourth with Romanian gymnast Diana Bulimar with a score of 57.065, while on floor she finished 6th with a score of 14.100. At the 2013 World Artistic Gymnastics Championships, Steingruber finished seventh in the all-around, fourth on vault, fifth on floor exercise. At the 2014 European Championships, Steingruber won a gold medal on vault with a score of 14.666. At the 2014 World Artistic Gymnastics Championships, Steingruber qualified to the all-around final and placed 15th with a score of 55.132.

She tied for 5th place in the vault final with Great Britain's Claudia Fragapane, with a score of 14.716. At the 2015 European Artistic Gymnastics Championships, Steingruber won the all-around title ahead of Maria Kharenkova of Russia and Ellie Downie of Great Britain, with a score of 57.873, becoming the first Swiss gymnast to win the European All-Around title. However, she failed to defend her vault title, was beaten by the 2012 Olympic vault bronze medalist Maria Paseka, she qualified to the uneven bars final and placed 6th with a score of 13.766. Steingruber qualified first to the floor final and ended up winning the bronze medal with a score of 14.466 behind silver medalist Claudia Fragapane of Great Britain and gold medalist Ksenia Afanasyeva of Russia. Steingruber's three medals made her the most decorated gymnast from these championships. In June she competed at the 2015 European Games held in Baku, along with teammates Jessica Diacci and Caterina Barloggio, she won the silver medal in the all-around, with a score of 56.699.

In addition, she won the gold medal on vault, with a total score of 14.999 and on floor, with a score of 14.266. She was the bronze medalist on the balance beam, with a 13.700. She competed in the 2015 Glasgow World Championships, she qualified to the all around final and vault finals. She withdrew from the floor final. At the 2016 European Championships, Steingruber helped the Swiss team qualify to the team final in third place behind only Great Britain and Russia, she qualified first to the vault final with an average score of 15.433, eighth to the bars final with a score of 14.033, second to the floor final with a score of 14.966. In the team final, she contributed an all-around score of 57.657 to help lead the Swiss team to a fourth place finish. In event finals, Steingruber won her third European vault title with an average score of 14.983, just 0.05 ahead of Ellie Downie, becoming the first gymnast in history to win three European championship titles on vault. She placed sixth in the uneven bars final with a score of 14.166, won the floor final for her first first European title on the event with a massive score of 15.200, finishing 0.634 ahead of Downie, the silver medalist.

At the 2016 Summer Olympics, where she was the sole female gymnast for Switzerland, Steingruber was chosen to be the flag bearer at the opening ceremony, becoming the second gymnast to receive this honor since Daniel Giubellini in 1992, the first female gymnast to do so. She delivered an excellent performance in the qualification round and qualified in 14th place to the all-around final with a score of 56.899. She qualified 3rd to the vault final with an average of 15.266, 4th to the floor final with a score of 14.666. In the individual all-around final, Steingruber finished in a respectable 10th place with a score of 57.565, the highest finish by a Swiss gymnast in a non-boycotted Olympic games. Her scores on both vault and floor were among the top four of all the gymnasts that competed in the all-around. In the vault final, she performed a clean layout Rudi and a double twisting Yurchenko to win the bronze medal with an average of 15.216, 0.037 behind silver medalist Maria Paseka of Russia.

American Simone Biles won the vault title with an average of 15.966. Steingruber's bronze is the first


Estepona is a town and municipality in the comarca of the Costa del Sol, southern Spain. It is located in the province of part of the autonomous community of Andalusia, its district covers an area of 137 square kilometers in a fertile valley crossed by small streams and a mountainous areas dominated by the Sierra Bermeja, which reaches an elevation of 1,449 m at the peak of Los Reales. Estepona is renowned for its beaches, it is a popular holiday destination. Due to its natural environment, surrounded by the sea and the mountains, Estepona has a micro-climate with over 325 days of sunshine per year. Estepona is a popular year-round holiday destination; the white-walled town centre has picturesque squares. In the early 1990s, the Walt Disney Company chose Estepona as the original site for its Eurodisney project, but Paris, France was awarded the installation; the area has been occupied since prehistoric times. Romans occupied the area. Archeologists have unearthed some foundations and ceramics, although the disaster's effects make further finds unlikely.

References to'Salduba' or'Silniana' as an important natural port in old documents may refer to this town, or Marbella's San Pedro Alcantara district. The name'Estepona' comes from the Moorish Astabbuna or Al-extebunna. In 1342, the Battle of Estepona took place in the Bay of Estepona between the fleet of the Kingdom of Aragon and that of the Marinid Dynasty, with the victorious Aragonese fleet subsequently destroyed near Gibraltar, but Christian forces winning the Siege of Algeciras. Aben al Jhatib, writing in the late 14th century, mentioned the town as being in a state of decay, living on its reputation for culinary delicacies, with its monuments deteriorated. Henry IV of Castile captured the town from the Moors in 1457. A church was built over what had been the town mosque, a town grew around it, although it too was subsequently destroyed and all that remains is the old clock tower. San Luis castle was built for coastal defense against Berber pirates. In 1502, the town received its first charter.

However, it was governed as an administrative district of Marbella until 1729. Philip V of Spain granted Estepona its own town charter; as the 20th century began, Estepona had 9000 residents farmers and fisherman. Gibraltar Airport is the nearest international airport serving Estepona, it has direct flights to Manchester, London Gatwick and London Luton. Málaga Airport is the next nearest international airport serving Estepona and is located 80 km away. Estepona is served by the Autovía A-7. There is a toll road, referred to as the Autopista AP-7, which provides faster travel along the route between Málaga and Estepona by-passing many of the urban areas along the route, such as Marbella. There are two toll stations en route and toll charges vary throughout the year. You can travel from Málaga to Estepona for less than 10 euros in toll charges for a normal size car. Estepona Port and Marina is a working fishing port offering bars; the port features daily auctions for a wide variety of seafood. The port is the location of the Estepona street market - a collection of stalls selling numerous textile and leather goods mostly.

The market is in Estepona on Sundays but it travels around the Málaga municipality to areas like Puerto Banús, Casares, Torremolinos and more. Puerto Banús is an upscale community about 30 minutes drive away from Estepona Port with a large number of designer stores. Selwo Safari Park is styled after African safari parks and houses 2000 animals in semi-wild conditions, it is a 20-minute drive from Estepona Port on the public transport route. Palacio de Exposiciones y Congresos de Estepona is the exhibition and congress centre of Estepona, located opposite the supermarket on the eastern edge of Estepona - closest to Marbella; this centre is home to nearly all of Estepona's organised events including product presentations, commercial exhibitions and more. Estepona has over 20 km of coastline, 17 different beaches. Most of these are next to the various hotels and residential complexes outside the town itself; the nearest beaches to the town are the Playa del Cristo, the Playa de la Rada. The Playa del Cristo is five minutes west of Estepona Marina.

It is a small, cove with lifeguards in season and two "chiringuitos" or beach front bar/restaurants, a rough car park, children's play area. As it is both sheltered from the east wind and shallow, it is popular with families with primary-age children. La Rada Beach is more open, it is the town's main beach, is backed by a attractive Paseo Maritimo seafront promenade, has every facility: bars, play areas for children, lavatories, access points for those in wheelchairs, of course lifeguards in season. Parking is in the underground car parks along the seafront. There is a popular naturist/nudist beach of Costa Natura to the west of

Brad Bitler

Brad Lee Bitler is a creative director and former United States Marine. He is both 2003 graduate of Davis Senior High School. While in the service he obtained both the ranks of Corporal and Sergeant meritoriously while stationed at Marine Corps Base Camp Pendleton. "The Orange County Register" and "The Davis Enterprise" interviewed him for stories related to the Iraq war. After transitioning from military service to a career in design, his work has been featured in various video outlets. His creative projects while working with RIAA Certified Gold and Platinum selling recording artists have been featured on over 140 websites with views in over 126 countries. Brad, a graduate of U. C. Berkeley was a brother of the Kappa Alpha Order Alpha Xi Chapter. Official website