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Equisatisfiability is generally used in the context of translating formulae, so that one can define a translation to be correct if the original and resulting formulae are equisatisfiable. Examples of translations that preserve equisatisfiability are Skolemization and some translations into conjunctive normal form such as the Tseytin transformation.
The theory first appeared in an article published by linguist Hans Josef Vermeer in the German Journal Lebende Sprachen, 1978. [2]As a realisation of James Holmes’ map of Translation Studies (1972), [3] [4] skopos theory is the core of the four approaches of German functionalist translation theory [5] that emerged around the late twentieth century.
Formal equivalence is often more goal than reality, if only because one language may contain a word for a concept which has no direct equivalent in another language. In such cases, a more dynamic translation may be used or a neologism may be created in the target language to represent the concept (sometimes by borrowing a word from the source ...
In measure theory, a branch of mathematics, Kakutani's theorem is a fundamental result on the equivalence or mutual singularity of countable product measures.It gives an "if and only if" characterisation of when two such measures are equivalent, and hence it is extremely useful when trying to establish change-of-measure formulae for measures on function spaces.
An example: we are given the conditional fact that if it is a bear, then it can swim. Then, all 4 possibilities in the truth table are compared to that fact. If it is a bear, then it can swim — T; If it is a bear, then it can not swim — F; If it is not a bear, then it can swim — T because it doesn’t contradict our initial fact.
The primary difference between a computer algebra system and a traditional calculator is the ability to deal with equations symbolically rather than numerically. The precise uses and capabilities of these systems differ greatly from one system to another, yet their purpose remains the same: manipulation of symbolic equations .
For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...