An Extension of Gödel Logic for Reasoning under Both Vagueness and Possibilistic Uncertainty

Abstract

Abstract. In this paper we introduce a logic called FNG∼(Q) that combines the well-known Gödel logic with a strong negation, rational truthconstants and Possibilistic logic. In this way, we can formalize reasoning involving both vagueness and (possibilistic) uncertainty. We show that the defined logical system is useful to capture the kind of reasoning at work in the medical diagnosis system CADIAG-2, and we finish by pointing out some of its potential advantages to be developed in future work.

Formal approaches to rule-based systems in medicine: The case of CADIAG-2

“…This is the main point addressed in the present paper. Taking the system CADIAG-2 as a specific example, we discussed three mathematical models recently introduced by the authors in [14,31,36] to interpret the numbers and the inferential mechanism. We compiled the features of the three quite different approaches; we mentioned advantages and disadvantages and we focused on the question in which way numerical values are understood.…”

“…The logic PGL combines RGL ∼ with Possibilistic Logic, see [36] for details. We start with two sets of variables: S and D. The variables σ 1 , .…”

“…The third approach, which we describe below, takes both aspects into account; it is thus the only approach which formalises vagueness and uncertainty in an independent way. The approach is based on a logic recently introduced in [36].…”

“…Indeed the definition of suitable SAT-solvers or theorem provers for PGL seem to be beyond the current state of the art, if possible at all (note here that the only available proof system for PGL in [36] is Hilbert-style, which is not usable for this purpose).…”