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 P¯|S from the premise set {M|P,M¯|S} is not informative, we add p(S|(S∨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,M¯|S,S|(S∨P)) to the conclusion 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

Niki Pfeifer, Giuseppe Sanfilippo (2018). Probabilistic Semantics for Categorical Syllogisms of Figure II. In D. Ciucci, G. Pasi, B. Vantaggi (a cura di), Scalable Uncertainty Management. SUM 2018 (pp. 196-211) [10.1007/978-3-030-00461-3_14].

Probabilistic Semantics for Categorical Syllogisms of Figure II

Giuseppe Sanfilippo
2018-01-01

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 P¯|S from the premise set {M|P,M¯|S} is not informative, we add p(S|(S∨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,M¯|S,S|(S∨P)) to the conclusion 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
2018
Settore MAT/06 - Probabilita' E Statistica Matematica
978-3-030-00460-6
978-3-030-00461-3
https://link.springer.com/chapter/10.1007/978-3-030-00461-3_14
Niki Pfeifer, Giuseppe Sanfilippo (2018). Probabilistic Semantics for Categorical Syllogisms of Figure II. In D. Ciucci, G. Pasi, B. Vantaggi (a cura di), Scalable Uncertainty Management. SUM 2018 (pp. 196-211) [10.1007/978-3-030-00461-3_14].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/302429
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