Preliminary notes on a new modal syllogistic.

A Reconstruction of Aristotle’s Modal Syllogistic

Ever since Łukasiewicz, it has been opinio communis that Aristotle’s modal syllogistic is incomprehensible due to its many faults and inconsistencies, and that there is no hope of finding a single consistent formal model for it. The aim of this paper is to disprove these claims by giving such a model. My main points shall be, first, that Aristotle’s syllogistic is a pure term logic that does no...

Pr ecis of Aristotle’s Modal Syllogistic

Aristotle was the founder of modal logic. In his Prior Analytics, he developed a complex system of modal syllogistic. While influential, this system has been disputed since antiquity and is today widely regarded as incoherent or inconsistent. In view of this, Aristotle’s Modal Syllogistic explores the prospects for understanding the modal syllogistic as a coherent and consistent system of modal...

Notes on Mathematical Modal Logic

These notes were written by Wang Yafeng following a course of three intensive lectures on classical themes in mathematical modal logic given by Johan van Benthem in the Berkeley-Stanford Logic Circle, San Francisco, May 2015. Some of this material was collected in the monograph van Benthem [13], [16], other parts come from later publications. We will provide some references to further relevant ...

Preliminary Notes on Galois Theory

Definition 1.1. Let E be a field. An automorphism of E is a (ring) isomorphism from E to itself. The set of all automorphisms of E forms a group under function composition, which we denote by AutE. Let E be a finite extension of a field F . Define the Galois group Gal(E/F ) to be the subset of AutE consisting of all automorphisms σ : E → E such that σ(a) = a for all a ∈ F . We write this last c...

Preliminary Notes on Interpretability Logic