6533b7d4fe1ef96bd12634f1

RESEARCH PRODUCT

Generalized probabilistic modus ponens

Niki PfeiferAngelo GilioGiuseppe Sanfilippo

subject

Discrete mathematicsSettore MAT/06 - Probabilita' E Statistica MatematicaProbabilistic logicConjoined conditionalPrevision0102 computer and information sciences02 engineering and technologyCoherence (philosophical gambling strategy)Settore MAT/01 - Logica MatematicaModus ponen01 natural sciencesConditional random quantitieTheoretical Computer ScienceModus ponendo tollens010201 computation theory & mathematicsIterated functionComputer Science0202 electrical engineering electronic engineering information engineeringIterated conditional020201 artificial intelligence & image processingRule of inferenceModus ponensCoherenceEvent (probability theory)Mathematics

description

Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the respective bounds on the conclusion for the (non-nested) probabilistic modus ponens.

yearjournalcountryeditionlanguage
2017-01-01
10.1007/978-3-319-61581-3_43http://hdl.handle.net/10447/306100