Autumn

Autumn, interchangeably known as fall in North America, is one of the four temperate seasons. Autumn marks the transition from summer into winter, in September (Northern Hemisphere) or March (Southern Hemisphere), when the arrival of night becomes noticeably earlier and the temperature cools considerably. One of its main features is the shedding of leaves from deciduous trees.

Some cultures regard the autumnal equinox as "mid-autumn", while others with a longer temperature lag treat it as the start of autumn. Meteorologists (and most of the temperate countries in the southern hemisphere) use a definition based on months, with autumn being September, October and November in the northern hemisphere, and March, April and May in the southern hemisphere.

In North America, autumn is usually considered to start with the September equinox and end with the winter solstice (21 or 22 December). Popular culture in North America associates Labor Day, the first Monday in September, as the end of summer and the start of autumn; certain summer traditions, such as wearing white, are discouraged after that date. In North America, the wave of color starts in Canada. It then moves into the United States and across the Great Lakes, and continues down into the mountains of the South. Warm days followed by chilly nights provide the catalyst. In traditional East Asian solar term, autumn starts on or around 8 August and ends on or about 7 November. In Ireland, the autumn months according to the national meteorological service, Met Éireann, are September, October and November. However, according to the Irish Calendar, which is based on ancient Gaelic traditions, autumn lasts throughout the months of August, September and October, or possibly a few days later, depending on tradition. In Australia and New Zealand, autumn officially begins on 1 March and ends on 31 May.

Fall (Once Upon a Time)

"Fall" is the ninth episode of the fourth season of the American fantasy drama series Once Upon a Time, which aired on November 30, 2014.

Plot

Opening Sequence

In the forest, snow falls over Elsa and Anna's parents' ship at the bottom of the sea. Gerda's message to her daughters lies on the ocean floor.

In Arendelle and at sea

Anna (Elizabeth Lail) and Kristoff (Scott Michael Foster) are trying to find Elsa when Hans (Tyler Jacob Moore) and his brothers arrive to imprison them for treason. Anna and Kristoff escape and decide to go to the pirate Blackbeard (Charles Mesure), to look for the wishing star which they can use to free Elsa, who is trapped in a magic urn.

They tell Blackbeard that they will pay for the wishing star with his weight in gold, but Hans and his brothers suddenly appear and tell Anna and Kristoff that this a set-up. Hans then says that Arendelle has been frozen for 30 years, which surprises Anna and Kristoff. As they worry about what may have happened to Elsa and what the Snow Queen has done since then, they are put in a trunk, which is then locked and dumped into the sea by Hans and Blackbeard so Hans and his brothers can take over Arendelle.

Fall (Clay Walker song)

"Fall", written by Clay Mills, Sonny LeMaire, and Shane Minor, is a song which has been recorded by both country music singer Clay Walker and pop music singer Kimberley Locke, both of whom are signed to Curb Records. Both versions were released within weeks of each other in mid-2007; while Walker's version was released to country radio, Locke's was released to the adult contemporary radio format. Walker's reached number 5 on the U.S. country singles charts, and Locke's reached Number One on the U.S. Dance charts. Go West front man Peter Cox has recorded a version of "Fall" on his 2010 CD "The S1 Sessions".

Content

"Fall" is a mid-tempo ballad in which the narrator addresses a lover who has had a bad day. The narrator then offers moral support to the lover: "Fall, go on and lose it all / Every doubt, every fear / Every worry, every tear".

Clay Walker version

Walker's version, the first version of the song to be released, was the second single from his 2007 album, which was also titled Fall. A music video was issued on October 17, 2007.

Logic (disambiguation)

Logic may refer to:

Logic may also refer to:

Entertainment

Science and technology

Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. It bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.

Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see Logic in computer science for those.

Since its inception, mathematical logic has both contributed to, and has been motivated by, the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and analysis. In the early 20th century it was shaped by David Hilbert's program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in proving consistency. Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing which parts of mathematics can be formalized in particular formal systems (as in reverse mathematics) rather than trying to find theories in which all of mathematics can be developed.

Boolean-valued function

A boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true.

In the formal sciences, mathematics, mathematical logic, statistics, and their applied disciplines, a boolean-valued function may also be referred to as a characteristic function, indicator function, predicate, or proposition. In all of these uses it is understood that the various terms refer to a mathematical object and not the corresponding semiotic sign or syntactic expression.

In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for logic, that formalizes the intuitive concept that is normally expressed by saying that a sentence is true. A truth predicate may have additional domains beyond the formal language domain, if that is what is required to determine a final truth value.