Indefinite probabilities are a novel technique for quantifying uncertainty, which were created as part of the PLN (Probabilistic Logic Networks) logical inference engine, which is a key component of the Novamente Cognition Engine (NCE), an integrative AGI system. Previous papers have discussed the use of indefinite probabilities in the context of a variety of logical inference rules, but have o...

in this paper, after reviewing the classification of quantifiers, we aim toanswer the question of whether the merge position of quantifiers kheili and ba’zi is in the dp. contra moazzami (2006) and samiian (1983), we show that these quantifiers do not originate  in the dp. by appealing to the preference of merge over move and in the light of giusti (1991), we propose that these elements merge a...

Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type ⟨1, 1⟩ fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this contribution, we would like to present some results on strong and pointwise convergence of the...

Ever since the first hybrid fuzzy rough set model was proposed in the early 1990’s, many researchers have focused on the definition of the lower and upper approximation of a fuzzy set by means of a fuzzy relation. In this paper, we review those proposals which generalize the logical connectives and quantifiers present in the rough set approximations by means of corresponding fuzzy logic operati...

This paper first presents a simple explanation for the min/max bounds which are used in interval probability theory ( I n ) [l], possibility theory [2], fuzzy rough sets [4], and vague logic [ 5 ] . Based on this definition, a computable version of first-order fuzzy logic is defined, where all of the upper bounds for instances of a theorem and its negation are guaranteed to eventually be listed...

Linguistic quantifiers are quantifiers defined by linguistic expressions like “around 5” or “most of,” and many types of linguistic quantifiers can be found in the literature (Diaz-Hermida, Bugarin, & Barro, 2003; Glockner, 1997, 2004a, 2004b; Losada, Díaz-Hermida, & Bugarín, 2006) (as semifuzzy quantifiers which allow modeling expressions like “there are twice as many men as women”). We limit ...

The goal of this paper is twofold: first, we give overview of the results of one part of the Fuzzy Natural Logic — the formal theory of intermediate quantifiers and syllogisms based on them. We present 105 valid basic syllogisms and show that for the proof of validity of all of them, we need to prove validity of only few of them so that validity of the other ones immediately follows. In the sec...

Peterson’s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers ‘Many’, ‘Most’ and ‘Almost all’, are studied. It is demonstrated that, by associating certain values V, W and U on standard Lukasiewicz MV–algebra with the first and second premise and the conclusion, respectively, the validity of a corresponding intermediate syllogism is determined by a simple ...