TY - GEN

T1 - Probabilistic Semantics for Categorical Syllogisms of Figure II

AU - Sanfilippo, Giuseppe

AU - Pfeifer, Niki

PY - 2018

Y1 - 2018

N2 - 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

AB - 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

UR - http://hdl.handle.net/10447/302429

UR - https://link.springer.com/chapter/10.1007/978-3-030-00461-3_14

M3 - Conference contribution

SN - 978-3-030-00460-6; 978-3-030-00461-3

T3 - LECTURE NOTES IN COMPUTER SCIENCE

SP - 196

EP - 211

BT - Scalable Uncertainty Management. SUM 2018

ER -