The principle of truth-functionality (or compositionality) is a basic principle in many-valued logic in general, and in classical logic in particular. According to this principle, the truth-value of a complex formula is uniquely determined by the truth-values of its subformulas. However, real-world information is inescapably incomplete, uncertain, vague, imprecise or inconsistent, and these phenomena are in an obvious conflict with the principle of truth-functionality. One possible solution to this problem is to relax this principle by borrowing from automata and computability theory the idea of non-deterministic computations, and apply it in evaluations of truth-values of formulas. This leads to the introduction of non-deterministic matrices (Nmatrices) --- a natural generalization of ordinary multi-valued matrices, in which the truth-value of a complex formula can be chosen nondeterministically out of some non-empty set of options. There are many natural motivations for introducing non-determinism into the truth-tables of logical connectives.
|Title of host publication||Handbook of Philosophical Logic: Volume 16|
|Editors||Dov M. Gabbay, Franz Guenthner|
|Place of Publication||Dordrecht|
|Number of pages||78|
|ISBN (Print)||978-94-007-0478-7, 978-94-007-3460-9|
|State||Published - 2011|
|Name||Handbook of Philosophical Logic|