We introduce a multi-sorted stratified syllogistic, called 4LQS(R), admitting variables of four sorts and a restricted form of quantification over variables of the first three sorts, and prove that it has a solvable satisfiability problem by showing that it enjoys a small model property. Then, we consider the fragments (4LQS(R))(h) of 4LQS(R), consisting of 4LQS(R)-formulae whose quantifier prefixes have length bounded by h >= 2 and satisfying certain additional syntactical constraints, and prove that each of them has an NP-complete satisfiability problem. Finally we show that the modal logic K45 can be expressed in (4LQS(R))(3)
On the satisfiability problem for a 4-level quantified syllogistic and some applications to modal logic
CANTONE, Domenico;NICOLOSI ASMUNDO, MARIANNA
2013-01-01
Abstract
We introduce a multi-sorted stratified syllogistic, called 4LQS(R), admitting variables of four sorts and a restricted form of quantification over variables of the first three sorts, and prove that it has a solvable satisfiability problem by showing that it enjoys a small model property. Then, we consider the fragments (4LQS(R))(h) of 4LQS(R), consisting of 4LQS(R)-formulae whose quantifier prefixes have length bounded by h >= 2 and satisfying certain additional syntactical constraints, and prove that each of them has an NP-complete satisfiability problem. Finally we show that the modal logic K45 can be expressed in (4LQS(R))(3)File | Dimensione | Formato | |
---|---|---|---|
FI2013.pdf
solo gestori archivio
Tipologia:
Versione Editoriale (PDF)
Dimensione
171.33 kB
Formato
Adobe PDF
|
171.33 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.