4-step inference method for natural language propositions involving fuzzy quantifiers and truth-qualifiers

Abstract

In this paper, we propose an 4-step inference method which is necessary to construct natural language communication system. The method is referred to how to estimate Fuzzy Quantifier Q''' when QA is F is γ ⇔ Q'''(m'A) is mF is m''γ is inferred (Q, Q''':Qquantifiers, A: Fuzzy subject, m, m', m'':Modifier, F:Fuzzy predicate, γ:Truth-qualifier). We showed the Q''' is resolved by 4-step procedure for two types of Q. These two types include a nonincreasing type (FEW,...) and a nondecreasingtype (MOST,...). First step we infer QA is F is γ ⇔ Q''(m'A) is F is γ, we transform A → m'A, and get Q'. Second step we infer ''Q'(m'A) is F is γ ⇔ Q''(m'A) is mF is γ, we transform F → mF, and get Q''. Third step we infer Q''(m'A) is mF is γ ⇔ Q(m'A) is mF is TT, we transform Q'' → Q, and get truth-qualifier TT. Forth step we infer Q(m'A) is mF is TT ⇔ Q'''(m'A) is mF is m''γ, we transform truth-qualifier TT → m''γ, and get Q'''. By above 4-step, we get the inference result as a fuzzy quantifier in case of transforming simultaneously a fuzzy subject and a fuzzy predicate and a truth-qualifier.