This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of $P|S$ from the premise set ${P|M, S|M}$ is not informative, we add $p(M|(S ee M))>0$ as a probabilistic constraint (i.e., an ``existential import assumption'') to obtain probabilistic informativeness. We show how to propagate the assigned premise probabilities to the conclusion. Thereby, we give a probabilistic meaning to all syllogisms of Figure~III. We discuss applications like generalised quantifiers (like Most $S$ are $P$) and (negated) defaults

Pfeifer, N., Sanfilippo Giuseppe (2019). Probability Propagation in Selected Aristotelian Syllogisms. In G. Kern-Isberner, Z. Ognjanovic (a cura di), Symbolic and Quantitative Approaches to Reasoning with Uncertainty 15th European Conference, ECSQARU 2019 Belgrade, Serbia, September 18–20, 2019 Proceedings (pp. 419-431) [10.1007/978-3-030-29765-7_35].

Probability Propagation in Selected Aristotelian Syllogisms

Sanfilippo, Giuseppe
2019-01-01

Abstract

This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of $P|S$ from the premise set ${P|M, S|M}$ is not informative, we add $p(M|(S ee M))>0$ as a probabilistic constraint (i.e., an ``existential import assumption'') to obtain probabilistic informativeness. We show how to propagate the assigned premise probabilities to the conclusion. Thereby, we give a probabilistic meaning to all syllogisms of Figure~III. We discuss applications like generalised quantifiers (like Most $S$ are $P$) and (negated) defaults
2019
Settore MAT/06 - Probabilita' E Statistica Matematica
Settore MAT/01 - Logica Matematica
978-3-030-29764-0
978-3-030-29765-7
Pfeifer, N., Sanfilippo Giuseppe (2019). Probability Propagation in Selected Aristotelian Syllogisms. In G. Kern-Isberner, Z. Ognjanovic (a cura di), Symbolic and Quantitative Approaches to Reasoning with Uncertainty 15th European Conference, ECSQARU 2019 Belgrade, Serbia, September 18–20, 2019 Proceedings (pp. 419-431) [10.1007/978-3-030-29765-7_35].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/369492
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