2023/08/03 by Doratossadat Dastgheib, Dastgheib, Doratossadat, Hadi Farahani +1
Computer Science · Economics, Econometrics and Finance · #Advanced Algebra and Logic #FOS: Mathematics #Game Theory and Voting Systems #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2308.01623
openalex publication_date 2023/08/03 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
In this paper we give a new proof for the completeness of infinite valued propositional Łukasiewicz logic introduced by Łukasiewicz and Tarski in 1930. Our approach employs a Hilbert-style proof that relies on the concept of maximal consistent extensions, and unlike classical logic, in this context, the maximal extensions are not required to include all formulas or their negations. To illustrate this point, we provide examples of such formulas.