IKT^ω and Łukasiewicz-models

2020/11/13 by Andreas Fjellstad, Fjellstad, Andreas, Jan-Fredrik Olsen +2
Computer Science · Decision Sciences · #03B47 #03C75 #03C90 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2011.06991

openalex publication_date 2020/11/13 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this note, we show that the first-order logic IK^ω is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKT^ω obtained by expanding IK^ω with transparent truth because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKT^ω depends on how vacuous quantification is treated.

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