Ebook: Modal logic

For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators. It starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantic and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist can use the book as a source of references. Results and methods of many directions in propositional modal logic, from completeness and duality to algorithmic problems, are collected and systematically presented in one volume.

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Modal logic is a branch of mathematical logic studying mathematical models of correct reasoning which involves various kinds of necessity-like and possibility-like operators. The first modal systems were created in the 1910s and later by Lewis (cf. Lewis and Langford, 1932) who used the operators "it is necessary" and "it is possible" for analyzing other logical connectives, in particular implication. Orlov 1928) and Godel 1933) constructed modal systems with the operator "it is provable" and exploited them to interpret Heyting's intuitionistic logic. More recently numerous modal systems have originated from different sources.