logischen

Logischen is an inflected form of the German adjective logisch, which means logical or relating to logic. In German, adjectives change their endings depending on gender, number, and case, and logischen appears in several common contexts, for example after definite articles in masculine singular accusative (den logischen Schluss) and in plural forms (die logischen Schlüsse, den logischen Schlüssen). The base form logisch corresponds to the English word “logical.”

In usage, logisch is standard in philosophy, logic, mathematics, and computer science to describe arguments, theories, proofs, or systems that follow the principles of logical reasoning. Typical phrases include logische Schlüsse (logical conclusions), logische Beweise (logical proofs), logische Verknüpfungen (logical connectives), and logische Folgerungen (logical inferences). The form logischen frequently appears in technical terms and academic prose when the associated noun requires a plural or a particular case.

Etymologically, logisch derives from the Greek logos, via Latin logica, and entered German with the broader development of the concept of logic. In modern German, logische and its inflected forms are common beyond strict formal logic, extending to descriptions of coherent reasoning in everyday language as well as to formal disciplines.

Overall, logischen functions as a grammatical form tied to the adjective logisch, signaling that the noun it modifies is evaluated according to the rules and standards of logic or rational argument.