An Etymological Dictionary of Astronomy and Astrophysics
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Of, relating to, or based on analogy; expressing or implying analogy.

→ analogy + -i + → -al.

A solution to Einstein's theory of → general relativity that is spatially homogeneous but allows for rotation and/or shear. See also → Bianchi cosmological model.

→ anisotropic; → homogeneous; → cosmological; → model.

Of or relating to → asteroseismology.

→ spectropolarimetry; → -ic.

A cosmological model based on the theory of → general relativity, which is homogeneous but → anisotropic. There are actually ten dinstinct Bianchi types, classified according to the particular kinds of symmetry they posses.

Luigi Bianchi (1856-1928), Italian mathematician; → cosmological; → model.

A logical system, such as → classical logic, in which every declarative sentence expressing a → proposition has exactly one → truth value, either → true or → false. Bivalent logic is just a sub-set of a more powerful type of logic known as → fuzzy logic. See also → polyvalent logic.

→ bivalent; → logic.

The traditional logic in which → sets are sharply defined (→ crisp set) for example, the number of students registered for a course, or the names beginning with P in a given telephone directory. Classical logic also defines relations between sets of → propositions. Consider for example two sets: elephants and mammals, a simple proposition would be the assertion that all elephants are mammals, that is E ⊂ M, where E is the elephant set and M is the mammal set. The classical logic proposition is either true or false. Compare with → fuzzy logic.

→ classical; → logic.

Pertaining or relating to → cosmology.

→ cosmology; → -al.

A term introduced by Einstein into his gravitational → field equations in order to allow a solution corresponding to a → static Universe. The cosmological constant is physically interpreted as due to the → vacuum energy of quantized fields. See also → dark energy.

→ cosmological; → constant.

The impressive discrepancy of about 120 orders of magnitude between the theoretical value of the → cosmological constant and its observed value. → Quantum field theory interprets the cosmological constant as the density of the → vacuum energy. This density can be derived from the maximum energy at which the theory is valid, i.e. the → Planck energy scale (10¹⁸ GeV). The theoretical vacuum → energy density is (10¹⁸ GeV)⁴ = (10²⁷ eV)⁴ = 10¹¹² erg cm^-3. On the other hand, the observed vacuum energy density is estimated to be about (10^-3 eV)⁴ = 10^-8 erg cm^-3. There is, therefore, a discrepancy of about 120 orders of magnitude.

→ cosmological; → constant; → problem.

The distance to a remote galaxy based on its redshift assuming that the redshift is caused by the → Doppler effect and reflects the general expansion of the Universe.

→ cosmological; → distance .

→ cosmological; → epoch.

A mathematical description of the Universe, based on observation, which tries to explain its current aspect, and to describe its evolution during time.

→ cosmological; → model.

The → hypothesis that on → large scales the → Universe is → isotropic and → homogeneous, that is, it appears the same at all places and, from any one place, looks the same in all directions. See also → perfect cosmological principle.

Introduced by E.A. Milne in 1933; → cosmological; → principle.

The → redshift of a remote object (galaxy, quasar, supenova) due to the expansion of the Universe.

→ cosmological; → redshift.

The → Universe at the → redshift z = 0.

→ current; → cosmological; → epoch.

A system of → formal logic that is an extension of → propositional logic. It is also known as → first-order predicate calculus and → predicate logic. FOL eliminates deficiencies of propositional logic by: representing → objects (their properties, relations and statements about them), introducing → variables, and introducing → quantifiers.

→ first; → order; → predicate; → logic.

The traditional or → classical logic in which the → validity or → invalidity of a conclusion is deduced from two or more statements (→ premises). Based on Aristotle's (384-322 BC) theory of → syllogism, systematized in his book "Organon," its focus is not on what is stated (the content) but on the structure (form) of the → argument and the validity of the inference drawn from the premises of the argument; if the premises are true then the logical consequence must also be true. Formal logic is → bivalent, that is it recognizes only two → truth values: → true and → false. The basic principles of formal logic are: 1) → principle of identity, 2) → principle of excluded middle, and 3) → principle of non-contradiction. See also → symbolic logic, → fuzzy logic.

→ formal; → logic.

A mathematical logic that recognizes more than simple → true and → false → propositions. With fuzzy logic, propositions can be represented with degrees of truthfulness and falsehood. In this system, → truth values are → fuzzy sets without sharp boundaries (→ crisp set) in contrast with → classical logic. Fuzzy logic is applied to a wide range of problems including: industrial control, domestic goods, decision making, robotics, intelligent machines, and image processing in medicine.

→ fuzzy; → logic.

An engineering system which uses → fuzzy logic. It generally consists of four main components: → fuzzification interface (fuzzifier), → fuzzy rule base, → fuzzy inferencing unit, and → defuzzification interface (difuzzifier). Also called → fuzzy inference system.

→ fuzzy; → logic; → system.

Of, pertaining to, or based on → geology. Also geological.

From geolog(y), → geology, + → -ic.