A new edition of the challenging secondary course which prepares students for success in their school-leaving exam. Popular features improved and updated in response to teachers’ feedback.
New Matrix allows students to develop their skills and language for exams and for use in life.
Language presentation and practice explore commonly confused structures and tenses. The contrasting of problem areas allows students to reflect on their understanding of English and to see it fall into place.
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.