Artificial Intelligence
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Some first-order probability logics
Theoretical Computer Science
Some Varieties of Qualitative Probability
IPMU'94 Selected papers from the 5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems, Advances in Intelligent Computing
Reasoning about Uncertainty
Strong non-standard completeness for fuzzy logics
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue (pp 315-357) "Ordered structures in many-valued logic"
On triangular norms and uninorms definable in Ł Π12
International Journal of Approximate Reasoning
A logic with approximate conditional probabilities that can model default reasoning
International Journal of Approximate Reasoning
AIMSA '08 Proceedings of the 13th international conference on Artificial Intelligence: Methodology, Systems, and Applications
How to Restore Compactness into Probabilistic Logics?
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
A probabilistic logic with polynomial weight formulas
FoIKS'08 Proceedings of the 5th international conference on Foundations of information and knowledge systems
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
On real-valued evaluation of propositional formulas
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
Jensen and Chebyshev inequalities for pseudo-integrals of set-valued functions
Fuzzy Sets and Systems
Hi-index | 0.20 |
Suppose that e is any [0,1]-valued evaluation of the set of propositional letters. Then, e can be uniquely extended to finitely additive probability product and Godel's measures on the set of classical propositional formulas. Those measures satisfy that the measure of any conjunction of distinct propositional letters is equal to the product of, or to the minimum of the measures of the propositional letters, respectively. Product measures correspond to the one extreme - stochastic or probability independence of elementary events (propositional letters), while Godel's measures correspond to the other extreme - logical dependence of elementary events. Any linear convex combination of a product measure and a Godel's measure is also a finitely additive probability measure. In that way infinitely many intermediate measures that corresponds to various degrees of dependence of propositional letters can be generated. Such measures give certain truth-functional flavor to probability, enabling applications to preferential problems, in particular classifications according to predefined criteria. Some examples are provided to illustrate this possibility. We present the proof-theoretical and the model-theoretical approaches to a probabilistic logic which allows reasoning about the mentioned types of probabilistic functions. The logical language enables formalization of classification problems with the corresponding criteria expressible as propositional formulas. However, more complex criteria, for example involving arithmetical functions, cannot be represented in that framework. We analyze the well-known problem proposed by Grabisch to illustrate interpretation of such classification problems in fuzzy logic.