A system of relational syllogistic incorporating full Boolean reasoning
Abstract
We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: Some A are Rrelated to some B; Some A are Rrelated to all B; All A are Rrelated to some B; All A are Rrelated to all B. Such primitives formalize sentences from natural language like `All students read some textbooks'. Here A and B denote arbitrary sets (of objects), and R denotes an arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem.
 Publication:

arXiv eprints
 Pub Date:
 February 2011
 arXiv:
 arXiv:1102.4496
 Bibcode:
 2011arXiv1102.4496I
 Keywords:

 Computer Science  Logic in Computer Science;
 03B65
 EPrint:
 Available at http://link.springer.com/article/10.1007/s1084901291651