Modal Logic - An Introduction to its Syntax and Semantics

In this text, a variety of modal logics at the sentential, first-order, and
second-order levels are developed with clarity, precision and philosophical
insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are
constructed. A matrix, or many-valued semantics, for sentential modal logic is
formalized, and an important result that no finite matrix can characterize any
of the standard modal logics is proven. Exercises, some of which show
independence results, help to develop logical skills.

Table Of Contents

1 Introduction
2 The Syntax of Modal Sentential Calculi
3 Matrix Semantics
4 Semantics for Logical Necessity
5 Semantics for S5
6 Relational World Systems
7 Quantified Modal Logic
8 The Semantics of Quantified Modal Logic
9 Second-Order Modal Logic
10 Semantics of Second-Order Modal Logic
Afterword
Bibliography
Index