Logica modalis classica

Logica modalis classica L in logica modali est ulla logica quae, ut axioma vel theorema, continet dualitatem operatorum modalium

$\Diamond A\equiv \lnot \Box \lnot A$

quod etiam est clausura deductiva sub regula

$A\equiv B\vdash \Box A\equiv \Box B.$

Invicem definitio dualis huius L dari potest per quam L est classicum si, et solum si, continet, ut axioma vel theorema,

$\Box A\equiv \lnot \Diamond \lnot A$

et clauditur sub regula

$A\equiv B\vdash \Diamond A\equiv \Diamond B.$

Tenuissima ratio classica aliquando appellatur E et non normalis est. Semanticae ambae algebraica et vicina notas describunt rationes modales classicas quae tenuiores quam tenuissima logica modalis normalis, K.

Omnis logica modalis regularis est classica, et omnis logica modalis normalis est regularis et ergo classica.

Bibliographia

• Arló-Costa, Horacio, et Eric Pacuit. 2005. First-order classical modal logic: applications in logics of knowledge and probability. TARK '05 Proceedings of the 10th conference on Theoretical aspects of rationality and knowledge. Singapurae: National University of Singapore, 262-278. ISBN 9810534124.
• Chellas, Brian. 1980. Modal Logic: An Introduction. Cantabrigiae: Cambridge University Press.
• Segerberg, Krister. 1971. An Essay in Classical Modal Logic. Dissertatio PhD, Universitas Stanfordiensis.