Complex valued probability logics | Zendy

Angelina Ilić Stepić | Zendy; Zoran Ognjanović | Zendy

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Complex valued probability logics

Author(s) -

Angelina Ilić Stepić,

Zoran Ognjanović

Publication year - 2014

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1409073i

Subject(s) - mathematics , decidability , axiom , satisfiability , propositional calculus , probabilistic logic , discrete mathematics , propositional variable , calculus (dental) , computer science , intermediate logic , theoretical computer science , description logic , medicine , statistics , geometry , dentistry

We present two complex valued probabilistic logics, LCOMPB and LCOMPS, which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,ρα meaning that the probability of α is in the complex ball with the center z and the radius ρ, while in LCOMPS one can make statements of the form Sz,ρα with the intended meaning - the probability of propositional formula α is in the complex square with the center z and the side 2ρ. The corresponding strongly complete axiom systems are provided. Decidability of the logics are proved by reducing the satisfiability problem for LCOMPB (LCOMPS) to the problem of solving systems of quadratic (linear) inequalities.

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