Logics for reasoning with non-numeric and comparative distances

Mehmet Giritli

We employ a first-order and a polyadic modal language in order to investigate the computational properties of reasoning with non-numeric and comparative distances where statements of the form `the distance between x and y is greater than the distance between x and z' could be made. We borrow Laguna's ``can-connect'' primitive as the relational framework of our formalisms. It turns out that while the first-order comparative distance logics are finitely axiomatizable, sound, semantically complete and undecidable, modal logics of the same ternary relation equipped with an additional global S5 operator is finitely axiomatizable, sound, semantically complete, has the finite model property and strictly less expressive than its first-order counterpart: Reasoning in modal fragment is decidable and PSPACE-complete.