In the British tradition, which is then continued in Italy in the late 14th century and 15th century (Courtenay 1982), the definition of consequence in terms of necessary truth-preservation (TP) is also unanimously adopted, as for example in Billingham (Billingham/Weber 2003, 80), Strode (cited in (Pozzi 1978, 237)) and Paul of Venice (Logica Parva, p. 167).
He formulates a definition of consequences in terms of 'howsoever the antecedent/consequent signifies things to be' in order to accommodate such counterexamples, but adds that in most cases, the simpler definition is sufficiently accurate.
In consequence, definitions of engines are relatively short, so they can be modified and extended with no particular effort.
Using these ideas, we introduce a new definition of logical consequence in the context of active logic, as well as a new definition of soundness such that, when reasoning with consistent premises, all classically sound rules remain sound in our new sense.
In consequence, the above definition of a "gene" should be put in question.
This is noticeable not only in the definitions of formal (as opposed to material) consequence, but also in the very definitions of consequence which begin to mention mental acts, such as: "a consequence is a derivation (illatio) of the consequent from the antecedent" (Strode, quoted in Normore 1993, 449).
In consequence the preceding definitions of logical truth, logical falsity and logical analyticity are not applicable to purely logical propositions, since they do not contain any extra-logical idea.
Nor does their definition include the Baltic states, which were taken over by the Soviets in consequence of an agreement that Stalin made with Hitler.
(This is Tarski's definition of logical consequence from 1936).
In consequence, there is little point in trying to identify a 'correct' definition which may be contrasted with other 'incorrect' definitions.
Ballets suffer in consequence.
