First-order logicFirst-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable.
Types of volcanic eruptionsSeveral types of volcanic eruptions—during which lava, tephra (ash, lapilli, volcanic bombs, and volcanic blocks), and assorted gases are expelled from a volcanic vent or fissure—have been distinguished by volcanologists. These are often named after famous volcanoes where that type of behavior has been observed. Some volcanoes may exhibit only one characteristic type of eruption during a period of activity, while others may display an entire sequence of types all in one eruptive series.
Theory (mathematical logic)In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem.
Pyroclastic flowA pyroclastic flow (also known as a pyroclastic density current or a pyroclastic cloud) is a fast-moving current of hot gas and volcanic matter (collectively known as tephra) that flows along the ground away from a volcano at average speeds of (~62 mph) but is capable of reaching speeds up to (~435 mph). The gases and tephra can reach temperatures of about . Pyroclastic flows are the most deadly of all volcanic hazards and are produced as a result of certain explosive eruptions; they normally touch the ground and hurtle downhill, or spread laterally under gravity.
Peano axiomsIn mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.
Explosive eruptionIn volcanology, an explosive eruption is a volcanic eruption of the most violent type. A notable example is the 1980 eruption of Mount St. Helens. Such eruptions result when sufficient gas has dissolved under pressure within a viscous magma such that expelled lava violently froths into volcanic ash when pressure is suddenly lowered at the vent. Sometimes a lava plug will block the conduit to the summit, and when this occurs, eruptions are more violent.
