zbMATH — the first resource for mathematics

Proof systems for probabilistic uncertain reasoning. (English) Zbl 0918.03015
In the paper several deductive systems for reasoning about uncertain knowledge are proposed. Belief is identified with subjective probability, while knowledge consists of consistent finite sets of linear constraints on a belief function. The deductive systems correspond to classes of inference processes satisfying certain conditions like equivalence, renaming, obstinacy, or minimum information principle. An inference process is a function \(N\) on a knowledge \(CL\) such that for every set \(K\in CL\), \(N(K)\) is a probability function satisfying \(K\). The main results of the paper are the completeness theorems for the considered deductive systems.

03B48 Probability and inductive logic
68T30 Knowledge representation
03B60 Other nonclassical logic
68T27 Logic in artificial intelligence
PDF BibTeX Cite
Full Text: DOI
[1] A mathematical theory of evidence (1976) · Zbl 0359.62002
[2] Statistical reasoning with imprecise probabilities (1991) · Zbl 0732.62004
[3] DOI: 10.1016/0888-613X(91)90005-7 · Zbl 0723.03015
[4] Proceedings of the first international conference on principles of knowledge representation and reasoning (1989)
[5] Journal of the Royal Statistical Society 50 pp 157– (1988)
[6] DOI: 10.1016/0004-3702(90)90101-5 · Zbl 0782.03012
[7] Finite Markov chains (1959)
[8] Proceedings of the NATO advanced study institute on logic and concurrent systems pp 439– (1985)
[9] Proceedings of the 3rd IEEE symposium on logic in computer science pp 277– (1988)
[10] Probabilistic reasoning in intelligent systems (1988)
[11] Philosophy and cognitive science pp 221– (1996)
[12] DOI: 10.1016/0888-613X(92)90022-R · Zbl 0779.68086
[13] DOI: 10.1016/0888-613X(90)90020-3 · Zbl 0697.68089
[14] Handbook of learning and cognitive processes (1978)
[15] DOI: 10.1007/978-94-015-7860-8_41
[16] Logic, methodology and philosophy of science VIII pp 111– (1988)
[17] The uncertain reasoner’s companion (1994) · Zbl 0838.68104
[18] DOI: 10.1016/0004-3702(86)90031-7 · Zbl 0589.03007
[19] Introduction to graph theory (1972)
[20] Proceedings of the second international workshop on non-monotonic reasoning pp 1– (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.