Abstract

A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is not informative, we add ????(????|(????∨????))>0 as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events (????|????,~????|????,????|(????∨????)) to the conclusion ~????|???? . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults.