On squares and rhombi: An attainable introduction to modal logic
Keywords:
modal logic, propositional modal logic, Kripke semantics, relational semantics, possible worlds, automated theorem proving, tableaux, natural deduction, non-classical logicsSynopsis
Modal logic is an active field of research that attracts the attention of scholars from quite diverse disciplines such as philosophy, linguistics, mathematics or computer sciences. These pages are intended to be the first open access basic textbook on modal logic written in Spanish. It is characterised by its introductory character, meaning that it has been designed to be comprehensible to any person with a minimal background in logic. Moreover, we have tried our best in making it a didactic writing, by filling some explicative gaps that more advanced books leave intentionally.
The book is divided into a preface, five chapters and an appendix. The preface contains a presentation of the book as well as the needed formal background. In Chapter 1, we introduce the notion of athletic modals (namely, necessity, possibility, impossibility and contingency) and we explain how they can be mutually defined from an intuitive point of view. The language and semantics of propositional modal logic are covered in Chapter 2. Chapter 3, in turn, proposes an axiomatic approach to some of the most well-known normal modal logics. Chapters 4 and 5, which can be read independently from each other, are devoted to two different methods to prove the validity of formal modal arguments. Chapter 4 focuses on modal tableaux, an automated proof method that also solves the satisfiability problem of finite sets of modal formulas. On its side, Chapter 5 introduces Jaskowski/Fitch style natural deduction calculi for the studied modal logics. The appendix contains solutions to all the exercises proposed throughout the book.
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December 4, 2024
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978-84-1335-389-0
