Some considerations on the logics PFD A logic combining modality and probability
作者:
Wiebe van der Hoeck,
期刊:
Journal of Applied Non-Classical Logics
(Taylor Available online 1997)
卷期:
Volume 7,
issue 3
页码: 287-307
ISSN:1166-3081
年代: 1997
DOI:10.1080/11663081.1997.10510916
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
We investigate a logic PFD, as introduced in [FA]. In our notation, this logic is enriched with operators P>r(r € [0,1]) where the intended meaning of P>rφ is “the probability of φ (at a given world) is strictly greater than r”. We also adopt the semantics of [FA]: a class of “F-restricted probabilistic kripkean models”. We give a completeness proof that essentially differs from that in [FA]: our “peremptory lemma” (a lemma in PFD rather than about it) facilitates the construction of a canonical model for PFD considerably. We show that this construction can be carried out using only finitary means, and also give a filtration-technique for the intended models. We then define an alternative (in some sense more natural) semantics for the logic, and show some of its properties. Finally, we prove decidability of the logic.
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