Naming worlds in modal and temporal logic

TY - JOUR

T1 - Naming worlds in modal and temporal logic

AU - Gabbay, D M

AU - Malod, G

PY - 2002

Y1 - 2002

N2 - We suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y) which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use a proof technique similar to a Henkin completion mixed with a tableau construction. The main elements of the completeness proofs are given for each case, while purely technical results are grouped in the appendix. (10 References).

AB - We suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y) which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order to use a proof technique similar to a Henkin completion mixed with a tableau construction. The main elements of the completeness proofs are given for each case, while purely technical results are grouped in the appendix. (10 References).

U2 - 10.1023/A:1013063928696

DO - 10.1023/A:1013063928696

M3 - Article

VL - 11

SP - 29

EP - 65

JO - Journal of Logic, Language & Information

JF - Journal of Logic, Language & Information

IS - 1

ER -