A Logic for Aristotle's Modal Syllogistic

We propose a new modal logic endowed with simple deductive system to interpret Aristotle's theory of the syllogism. While being inspired by standard propositional logic, it is also terms that admits (sound) extensional semantics involving possible states-of-affairs in given world. Applied analysis syllogistic as found Prior Analytics A8-22, sheds light on various fine-grained distinctions which when made allow us clarify some ambiguities and obtain completely consistent prove all syllogisms considered valid Aristotle. This allows make connection axioms modern perceive what extent these are implicit reasoning. Further work will involve addressing question completeness this (or variants thereof) together an extension include calculus relations (for instance relational treated Galen's Introduction Logic) Slomkowsky has argued already Topics.