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Modal Logic: An Introduction

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Modal logic is the logic of necessity and possibility. It includes "deontic logic" - the logic of duty (and the logic of the law), plus epistemic logic. Modal logic is a simplified form of the first order predicate logic.

The text explains the various axioms of modal logic -- such as "M, C, K, N, P" Other texts include Sally Popkorn (emphasis on semantics), and Hughes & Cresswell (slighly more advanced).

Some notation and terminology is outdated, but Chellas' "Introduction to Modal Logic" is still the best choice to start learning modal logic.
It covers all remarkable topics in the subject.

There are essentially two symmetrical sections to the book. The first covers Kripke models ('standard models' in the jargon of Chellas), axiomatic normal modal logics, and then filtrations of such models to show these logics have the finite model property and are decidable. To tie up the section there is an application with a chapter on deontic logic. The second section has the same structure with the topics being neighborhood models (called 'minimal models' by Chellas) and classical modal logics (some of which are strictly weaker than the weakest normal modal logic K). Unfortunately the application chapters (deontic logic and conditional logic) are poorly motivated, though one might think the whole point of those chapters is to motivate the inclusion or validation of certain deontic or conditional principles.

There is a lot of good stuff that is relegated to sections on exercises--e.g., p-morphisms, a safe extensions theorem, modal algebras, translations and correspondences between modal formulas and their models and first-order ones and their models (known other places as "correspondence/definability theory").

While there is a good number of exercises, most of them I encountered were quite easy and repetitive. Because of this, I found the text better suited to philosophy undergraduates (or novice graduates) than computer science or mathematics students. But at the same time there is little philosophical digression.

The most redeeming feature of the book, I thought, was the latter section on neighboorhood models and weak modal logics. I was also surprised to find the little "correspondence theory" that there was in the book. However, a better variation of exercises (in terms of both difficulty and method of proof/construction) would be greatly welcome.