mv logics and gröbner bases
DESCRIPTION
MV logics and Gröbner bases. History of Logic in Serbia , Belgrade , 14-15. 06. 2010. Motivation. ,,History of Logic in Serbia” History of Logic in Serbia Recent interests: Gröbner bases Search: Logic+Gröbner bases→MVL+GB The talk is missing the topic of the conference, - PowerPoint PPT PresentationTRANSCRIPT
MV logics and Gröbner bases
History of Logic in Serbia,
Belgrade, 14-15. 06. 2010.
,,History of Logic in Serbia”
History of Logic in Serbia
Recent interests: Gröbner bases
Search: Logic+Gröbner bases→MVL+GB
The talk • is missing the topic of the conference,• has no original results,• relies on few references, etc.
Motivation
Boolean algebra ↔ Boolean ring
A polynomial model for propositional logic
Ideals
A polynomial model for propositional logic
This model cannot be extended to p-valued modal logics, but something can be done. We map propositional variables to polynomial variables and logic operations (connectives) to polynomial operations using interpolation formula.
Ideals
GB
All ideals are radical ideals, i.e. each is equal to its radical.
In Boolean case, all ideals are principal.
Additional properties
Kleene’s and Łukasiewicz’s three-valued logic
Kleene’s three-valued logic
Łukasiewicz’s three-valued logic
Polynomial translation of the logical connectives
Tautological consequence
Connecting “To be a tautological consequence” with an ideal membership
The main theorem adapted to knowledge extraction in RBES
Backward reasoning in rule based expert systems whose underlying logic is classic Boolean logic
RBES rule based expert systems CAS computer algebra system
Shortcuts and RBES
RBES
RBES
RBES
RBES
Abstarct 2008
2009
Abstarct 2009
Reference