Related papers: Generalizing Fuzzy Logic Probabilistic Inferences
Lifted inference algorithms exploit symmetries in probabilistic models to speed up inference. They show impressive performance when calculating unconditional probabilities in relational models, but often resort to non-lifted inference when…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Within classical propositional logic, assigning probabilities to formulas is shown to be equivalent to assigning probabilities to valuations. A novel notion of probabilistic entailment enjoying desirable properties of logical consequence is…
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of…
In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a three…
We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The…
We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…
Recent work has unveiled a theory for reasoning about the decisions made by binary classifiers: a classifier describes a Boolean function, and the reasons behind an instance being classified as positive are the prime-implicants of the…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…
The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…
A construction of a fuzzy logic controller based on an analogy between fuzzy conditional rule of inference and marginal probability in terms of the conditional probability function has been proposed.
This paper shows that the fuzzy temporal logic can model figures of thought to describe decision-making behaviors. In order to exemplify, some economic behaviors observed experimentally were modeled from problems of choice containing time,…
Curved Boolean Logic (CBL) generalizes propositional logic by allowing local truth assignments that do not extend to a single global valuation, analogous to curvature in geometry. We give equivalent sheaf and exclusivity-graph semantics and…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative…