6533b7d6fe1ef96bd12665c8
RESEARCH PRODUCT
Probabilistic semantics for categorical syllogisms of Figure II
Giuseppe SanfilippoNiki Pfeifersubject
Transitive relationSequenceSettore MAT/06 - Probabilita' E Statistica MatematicaProbabilistic logicSyllogismConditional probability02 engineering and technologyCoherence (philosophical gambling strategy)Imprecise probabilityCombinatoricscoherence conditional events defaults generalized quantifiers imprecise probability.020204 information systems0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingCategorical variableMathematicsdescription
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 \(\bar{P}|S\) from the premise set \(\{M|P,\bar{M}|S\}\) is not informative, we add \(p(S|(S \vee P))>0\) 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 \((M|P,\bar{M}|S, S|(S \vee P))\) to the conclusion \(\bar{P}|S\). 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-01-01 |