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- Quantifier Elimination in Quantified Propositional Lukasiewicz Logic
Quantifier Elimination in Quantified Propositional Lukasiewicz Logic
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In this Book we have determined the minimal extension of quantified propositional Lukasiewicz logic which admits quantifier elimination. To obtained this result we solved following problems: we have extended Lukasiewicz logic by all division operators and have proven the completeness of the extended logic. Afterwards we used McNaughton theorem to determine so called minimax points of Lukasiewicz logic truth functions. We expressed this points in the language of Lukasiewicz logic extended by all division operators, then by combining the above mentioned results we have obtained the desired admissibility of quantifier elimination. As a corollary we obtained that quantified propositional Lukasiewicz logic extended by all division operators is semantically complete, decidable and hence recursively enumerable.
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