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An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if ..., then ...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily...
Let us consider the following situation: An oracle provides us with a finite set of examples considered as words belonging to a regular language. This oracle is not available again. In this paper we study a new and general inference algorithm of fuzzy regular grammars based on this set of words. This algorithm is created by adapting a process discovery method. The main issues in the adaptation are the development of a fuzzy version, the assignation of membership degrees to each production in the...
We consider endomorphisms of a monoid defined by a special confluent rewriting system that admit a continuous extension to the completion given by reduced infinite words, and study from a dynamical viewpoint the nature of their infinite periodic points. For prefix-convergent endomorphisms and expanding endomorphisms, we determine the structure of the set of all infinite periodic points in terms of adherence values, bound the periods and show that all regular periodic points are attractors.
Richomme asked the following question:
what is the infimum of the real numbers α > 2 such that
there exists an infinite word that avoids α-powers but
contains arbitrarily large squares beginning at every position?
We resolve this question in the case of a binary alphabet by showing
that the answer is α = 7/3.
Markov Decision Processes (MDPs) are a classical framework for
stochastic sequential decision problems, based on an enumerated state
space representation. More compact and structured representations have
been proposed: factorization techniques use state variables
representations, while decomposition techniques are based on a
partition of the state space into sub-regions and take advantage of
the resulting structure of the state transition graph. We use a family
of probabilistic exploration-like...
The information boundedness principle requires that the knowledge obtained as a result of an inference process should not have more information than that contained in the consequent of the rule. From this point of view relevancy transformation operators as a generalization of implications are investigated.
The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.
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