MV logics and Gröbner bases History of Logic in Serbia, Belgrade, 14-15. 06. 2010.
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Transcript of MV logics and Gröbner bases History of Logic in Serbia, Belgrade, 14-15. 06. 2010.
![Page 1: MV logics and Gröbner bases History of Logic in Serbia, Belgrade, 14-15. 06. 2010.](https://reader035.fdocuments.us/reader035/viewer/2022070415/5697c0301a28abf838cdaabb/html5/thumbnails/1.jpg)
MV logics and Gröbner bases
History of Logic in Serbia,
Belgrade, 14-15. 06. 2010.
![Page 2: MV logics and Gröbner bases History of Logic in Serbia, Belgrade, 14-15. 06. 2010.](https://reader035.fdocuments.us/reader035/viewer/2022070415/5697c0301a28abf838cdaabb/html5/thumbnails/2.jpg)
,,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
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Boolean algebra ↔ Boolean ring
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A polynomial model for propositional logic
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Ideals
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A polynomial model for propositional logic
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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
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GB
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All ideals are radical ideals, i.e. each is equal to its radical.
In Boolean case, all ideals are principal.
Additional properties
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Kleene’s and Łukasiewicz’s three-valued logic
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Kleene’s three-valued logic
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Łukasiewicz’s three-valued logic
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Polynomial translation of the logical connectives
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Tautological consequence
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Connecting “To be a tautological consequence” with an ideal membership
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The main theorem adapted to knowledge extraction in RBES
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Backward reasoning in rule based expert systems whose underlying logic is classic Boolean logic
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RBES rule based expert systems CAS computer algebra system
Shortcuts and RBES
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RBES
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RBES
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RBES
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RBES
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Abstarct 2008
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2009
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Abstarct 2009
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Reference