Aristotle outside Boethius: an epagogic reconstruction of the syllogistic

This text proposes an innovative reconstruction of Aristotle's logical system within the reinterpretative line of Smiley and Corcoran based on algebraic logics, escaping, however, Boethiu's canon by integrating other conceptual tools from the sources, in particular, the use of << negative >> terms (here infinite) is proposed together with the concept of <<epsilon Pi alpha gamma Omicron gamma eta >> presented in the Posterior Analytics as a heuristical context for the system exposed in the Prior Analytics, in which explicit relationships between two universes of terms representing the intensional and extensional realms are established, generating a framework where the ecthetic proof method can be organically incorporated, resulting from its formalization and computable structuralization a more fitter non-classical logical language for syllogistic inference.