Modalities and MultimodalitiesIn the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator. |
Contents
| 1 | |
The syntax of normal modal systems | 25 |
The semantics of normal modal systems | 49 |
Completeness and canonicity | 87 |
Incompleteness and finite models | 117 |
Temporal logics | 141 |
knowledge and belief | 183 |
Multimodal logics | 205 |
Towards quantified modal logic 241 | 240 |
Bibliography | 273 |
| 289 | |
| 297 | |
Other editions - View all
Common terms and phrases
accessibility relations affirmative agent algebra already applying arbitrary argument assignment atomic variables axiom axiomatized called canonical model Chapter characterized closed complete with respect completeness condition connectives Consequently consider consistent contains contradiction converse corresponding defined Definition derived diagram different disjunction distinct elements equivalent example Exercise exists expressed extension fact false finite first formula frame given hence holds idea identity iff implies induction instance interesting introduced knowledge language Lemma maximal consistent means method modal logic modal operators modal system multimodal Note notion objects obtained obviously operators philosophical possible preserve problem procedure proof properties Proposition provable prove quantifiers receives reference reflexive relation Remark result rules schema seen semantics sense sound standard steps subformulas Suppose symbols tableau temporal theorem transitive treated true truth universal valid wff