In [1] Bueno-Soler et al introduce the propositional logic LETF by extending First-Degree Entailment (F DE) with two consistency operators, ○ and ●. LETF , which is a Logic of Formal Inconsistency and Undeterminedness, is provided in [1] with a valuation semantics and a corresponding natural deduction calculus that includes specific rules for both ○ and ● (in addition to those of F DE). In this talk I shall describe how that system can be extended in order to deliver a first-order version of LETF , QLETF , and indicate the strategy used for proving its completeness. As we shall see, although the general structure of the proof is somewhat similar to the proof of the completeness of QmbC to be found in [2], some of the crucial definitions were specifically designed in order to simplify several of the steps involved in the proof.
References
[1] Bueno-Soler, J., Carnielli, W., and Rodrigues, A. Measuring Evidence: A Probabilistic
Approach to an Extension of Benalp-Dunn Logic. Forthcoming (2019).
[2] Carnielli, W. A., and Coniglio, M. E. Paraconsistent Logic: Consistency, Contradiction
and Negation. Springer, 2016.