Abstract
This paper brings a solution to the open problem of recursive enumerability of unsatisfiable formulae in the first-order Gödel logic. The answer is affirmative even for a useful expansion by intermediate truth constants and the equality, 
, strict order, \(\prec \), projection \(\Delta \) operators. The affirmative result for unsatisfiable prenex formulae of \(G_\infty ^\Delta \) has been stated in [1]. In [7], we have generalised the well-known hyperresolution principle to the first-order Gödel logic for the general case. We now propose a modification of the hyperresolution calculus suitable for automated deduction with explicit partial truth.
D. Guller—This work is partially supported by VEGA Grant 1/0592/14.
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Guller, D. (2015). Unsatisfiable Formulae of Gödel Logic with Truth Constants and 
, \(\prec \), \(\Delta \) Are Recursively Enumerable.
In: Tan, Y., Shi, Y., Buarque, F., Gelbukh, A., Das, S., Engelbrecht, A. (eds) Advances in Swarm and Computational Intelligence. ICSI 2015. Lecture Notes in Computer Science(), vol 9142. Springer, Cham. https://doi.org/10.1007/978-3-319-20469-7_27
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DOI: https://doi.org/10.1007/978-3-319-20469-7_27
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