Modal logic originated in philosophy as the logic of necessity and possibility. We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. We wish to extend it to make it a bit more expressive. He wrote the equations (a= ǫ), (b= η) and (c= θ) to express that ais a certainty, bis an impossibility, and cis a variable. Modal Logic We have now seen the propositional calculus. In the Hellenistic period, the logicians Diodorus Cronus, Philo the Dialectician and the Stoic Chrysippuseach developed a modal system that accounted f…

In addition to his non-modal syllogistic, Aristotle also developed a modal syllogistic in Book I of his Prior Analytics (chs 8–22), which Theophrastus attempted to improve.

In this article, however, we will paint on a larger canvas and introduce the reader to what modal logic as a field has become a century hence. Elements of modal logic were in essence already known to Aristotle (4th century B.C.) The Handbook of Mathematical Logic (Barwise 1989) makes a rough division of contemporary mathematical logic into four areas: Still, for a start, it is important to realize that modal notions have a long historical pedigree. A modal is an expression (like necessarily or possibly) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions it is necessary that and it is possible that. These include logics for belief, for tense and other temporal expressions, for the deontic (moral) expressions such as it is … However, the term modal logic may be used more broadly for a family of related systems. There are also passages in Aristotle's work, such as the famous sea-battle argument in De Interpretatione §9, that are now seen as anticipations of the connection of modal logic with potentiality and time. Mathematical Modal Logic: A View of its Evolution 5 was “a variable (neither always true nor always false)”. Modal logic as a subject on its own started in the early twentieth century as the formal study of the philosophical notions of necessity and possibility, and this tradition is still very much alive in philosophy (Williamson 2013). and became part of … In mathematical logic various formal systems of modal logic have been considered, interrelations between these systems have been revealed, and their interpretations have been studied. To do this, we add two unary operators to our alphabet: and, …