We solve the minimization problem for finitely axiomatizable theories in Gödel infinite-valued propositional logic. That is, we obtain an algorithm that when input a formula α(X1,..,Xn) outputs a formula β(X1,..,Xm) such that (i) the theories singly axiomatized by α and β have isomorphic algebraic semantics, and (ii) if β'(X1,..,Xm') is any formula satisfying (i), then m'≥m.
Computing minimal axiomatisations in Gödel propositional logic / S. Aguzzoli, O. D'Antona, V. Marra. - In: JOURNAL OF LOGIC AND COMPUTATION. - ISSN 0955-792X. - 21:5(2011), pp. 791-812.
Computing minimal axiomatisations in Gödel propositional logic
S. AguzzoliPrimo
;O. D'AntonaSecondo
;V. MarraUltimo
2011
Abstract
We solve the minimization problem for finitely axiomatizable theories in Gödel infinite-valued propositional logic. That is, we obtain an algorithm that when input a formula α(X1,..,Xn) outputs a formula β(X1,..,Xm) such that (i) the theories singly axiomatized by α and β have isomorphic algebraic semantics, and (ii) if β'(X1,..,Xm') is any formula satisfying (i), then m'≥m.
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