We explore the notions of permission and obligation and their role in knowledge representation, especially as guides to action for planning systems. We first present a simple conditional deontic logic (or more accurately a preference logic) of the type common in the literature and demonstrate its equivalence to a number of modal and conditional systems for default reasoning. We show how the tec...

Several different uncertain inference systems (UISs) have been developed for representing uncertainty in rule-based expert systems. Some of these, such as Mycin's Certainty Factors, Prospector, and Bayes' Networks were designed as approximations to probability, and others, such as Fuzzy Set Theory and DempsterShafer Belief Functions were not. How different are these UISs in practice, and does i...

Maximum Likelihood (ML) estimation is extensively used for estimating emission densities from clumped and incomplete nzeasurement data in Positron Emission Tomography (PEU modality. Reconstruction produced by ML-algorithm has been found noisy because it does not make use of available prior knowledge. Bayesian estimation provides such a platform for the inclusion of prior knowledge in the recons...

The infinite fuzzy logic controller, based on Bayesian learning rules, is used for the simulation of a discrete countable controlled Markov chain , with adaptive techniques .

Classical logic is usually interpreted as the logic of propositions. But from Boole’s original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (non-empty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoreti...

It is now well-established that the so-called focalization property plays a central role in the design of programming languages based on proof search, and more generally in the proof theory of linear logic. We present here a sequent calculus for non-commutative logic (NL) which enjoys the focalization property. In the multiplicative case, we give a focalized sequentialization theorem, and in th...

The handling of uncertain information is of crucial importance for the success of expert systems. This paper gives an overview on logic-based approaches to probabilistic reasoning and goes into more details about recent developments for relational, respectively first-order, probabilistic methods like Markov logic networks, and Bayesian logic programs. In particular, we will feature the maximum ...

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.

the estimate of entropy (sample entropy), has been introduced by vasicek (1976), for the first time. in this paper, we provide an estimate of entropy of order statistics, that is the extention of the entropy estimate. then we present an application of the entropy estimate of order statistics as a test statistic for symmetry of distribution versus skewness. the proposed test has been compared wi...

Yager’s entropy was proposed to compute the information of fuzzy indiscernibility relation. In this paper we present a novel interpretation of Yager’s entropy in discernibility power of a relation point of view. Then some basic definitions in Shannon’s information theory are generalized based on Yager’s entropy. We introduce joint entropy, conditional entropy, mutual information and relative en...