This course explores the limitations of classical logic and some of the expansions and modifications of classical semantics that have been introduced to address these shortcomings. On the one hand, discussions about ways the world might have been, what could or could not have been the case, what is contingent, possible, impossible or necessary, have evident philosophical interest in and of themselves, and also play a crucial role in many areas of philosophy. Modal logic is the expansion of classical logic that provides the foundation for a systematic approach to these questions. On the other hand, classical semantics has been challenged on the grounds that it cannot capture notions such as indeterminacy, overdeterminacy, or degrees of truth, all of which play a crucial role in the philosophical analysis of vagueness, semantic paradoxes, and other philosophical problems. This course provides an introduction to modal logic, many-valued logics, and their applications.
Students are expected to have a background equivalent to an introductory course in propositional and quantificational classical logic.
Syllabus:
1.- Introduction: necessity and possibility, possible worlds, extensions vs. alternative logics.
2.- Review of classical propositional logic.
3.- Propositional Modal Logic.
3.1 Syntax.
3.2 Semantics: models and possible worlds.
3.3 A system of derivation: semantic tableaux.
3.4 Normal modal logics.
3.5 Non-normal modal logics.
3.6 Intuitionistic logic
4.- Many-valued propositional logics.
4.1 Expressibility of classical operators.
4.2 Three-valued logics: Kleene, Bochvar, LP, Lukasiewicz.
4.3 Other many-valued logics: Dunn-Belnap, fuzzy logic.
4.4 Substructural many-valued logics: ST, TS.
4.5 Truth and vagueness.