TY - GEN
T1 - On modal logics of linear inequalities
AU - Kupke, Clemens
AU - Pattinson, Dirk
PY - 2010
Y1 - 2010
N2 - We consider probabilistic modal logic, graded modal logic and stochastic modal logic, where linear inequalities may be used to express numerical constraints between quantities. For each of the logics, we construct a cut-free sequent calculus and show soundness with respect to a natural class of models. The completeness of the associated sequent calculi is then established with the help of coalgebraic semantics which gives completeness over a (typically much smaller) class of models. With respect to either semantics, it follows that the satisfiability problem of each of these logics is decidable in polynomial space.
AB - We consider probabilistic modal logic, graded modal logic and stochastic modal logic, where linear inequalities may be used to express numerical constraints between quantities. For each of the logics, we construct a cut-free sequent calculus and show soundness with respect to a natural class of models. The completeness of the associated sequent calculi is then established with the help of coalgebraic semantics which gives completeness over a (typically much smaller) class of models. With respect to either semantics, it follows that the satisfiability problem of each of these logics is decidable in polynomial space.
KW - Graded modal logic
KW - Linear inequalities
KW - Probabilistic modal logic
UR - http://www.scopus.com/inward/record.url?scp=84858639245&partnerID=8YFLogxK
M3 - Conference contribution
SN - 1904987206
SN - 9781848900134
T3 - Advances in Modal Logic 2006
SP - 235
EP - 255
BT - Advances in Modal Logic 2010
T2 - 8th International Conference on Advances in Modal Logic, AiML-2010
Y2 - 24 August 2010 through 27 August 2010
ER -