We provide the foundations of automated deduction in the propositional Gödel logic. The propositional Gödel logic is one of the simplest infinitely valued fuzzy logics, which generalizes classical propositional logic. We propose an extension of the Davis–Putnam–Logemann–Loveland (DPLL) procedure to this logic and prove its refutational soundness and finite completeness. Using the DPLL procedure, we solve the deduction problem ${T\models \phi }$ ($\boldsymbol{T}$ is a finite theory and $\boldsymbol{\phi }$ a formula), which covers the finite SAT problem for a theory and the VAL problem for a formula, obviously. This paper serves, on the one side, as a technical basis for the design of a SAT solver; on the other side, gives some preliminary theoretical results concerning the logical and computational foundations of fuzzy inference, which is our main aim.

中文翻译：

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用于命题 Goedel 逻辑的基于 DPLL 的 SAT 求解器的技术基础

我们提供命题哥德尔逻辑中自动演绎的基础。命题哥德尔逻辑是最简单的无限值模糊逻辑之一，它概括了经典命题逻辑。我们建议扩展 Davis-Putnam-Logemann-Loveland (锁相环) 程序，并证明其反驳的合理性和有限完备性。使用锁相环 程序，我们解决了演绎问题 ${T\models \phi }$ ($\boldsymbol{T}$ 是一个有限理论并且 $\boldsymbol{\phi }$ 一个公式），它涵盖了有限的 SAT考试 一个理论的问题和 价值显然，公式的问题。一方面，本文作为设计一个的技术基础。SAT考试求解器；另一方面，给出了一些关于模糊推理的逻辑和计算基础的初步理论结果，这是我们的主要目标。