Relevance logic

Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. (It is generally, but not universally, called relevant logic by Australian logicians, and relevance logic by other English-speaking logicians.)

Relevance logic aims to capture aspects of implication that are ignored by the "material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then two and two is four" is true when translated as a material implication, yet it seems intuitively false since a true implication must tie the antecedent and consequent together by some notion of relevance. And whether or not I'm a donkey seems in no way relevant to whether two and two is four.

Crash Course

Crash Course (also known as Driving Academy) is a 1988 made for television teen film directed by Oz Scott.

Plot

Crash Course centers on a group of high schoolers in a driver’s education class; many for the second or third time. The recently divorced teacher, super-passive Larry Pearl, is on thin ice with the football fanatic principal, Principal Paulson, who is being pressured by the district superintendent to raise driver’s education completion rates or lose his coveted football program. With this in mind, Principal Paulson and his assistant, with a secret desire for his job, Abner Frasier, hire an outside driver’s education instructor with a very tough reputation, Edna Savage, aka E.W. Savage, who quickly takes control of the class.

The plot focuses mostly on the students and their interactions with their teachers and each other. In the beginning, Rico is the loner with just a few friends, Chadley is the bookish nerd with few friends who longs to be cool and also longs to be a part of Vanessa’s life who is the young, friendly and attractive girl who had to fake her mother’s signature on her driver’s education permission slip. Kichi is the hip-hop Asian kid who often raps what he has to say and constantly flirts with Maria, the rich foreign girl who thinks that the right-of-way on the roadways always goes to (insert awesomely fake foreign Latino accent) “my father’s limo”. Finally you have stereotypical football meathead J.J., who needs to pass his English exam to keep his eligibility and constantly asks out and gets rejected by Alice, the tomboy whose father owns “Santini & Son” Concrete Company. Alice is portrayed as being the “son” her father wanted.

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.