Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.

In the traditional decision theories the role of forecasts is to a large extent swept under the carpet. I believe that a recognition of the connections between forecasts and decisions will be of benefit both for decision theory and for the art of forecasting.In this paper I have tried to analyse which factors, apart from the utilities of the outcomes of the decision alternatives, determine the value of a decision. I have outlined two answers to the question why a decision (...) which is made on the basis of a forecast is better than a decision which is based on a guess. Neither of these answers is universally valid. An assumption which is necessary for the first answer, i.e. Good's result, is that Bayes' rule is accepted as a correct and generally applicable decision principle. The second answer, which was given with the aid of probability intervals, departed from a more general decision principle, the maximin criterion for expected utilities, which was formulated in order to evade some of the criticism against Bayes' rule. However, the argument leading to the ansser is based on the assumption that the probability intervals associated with the states of nature represent certain knowledge. For this reason this answer is only approximatively valid.As a number of quotations in the section on “the weight of evidence” show, it is not sufficient to describe the knowledge about the states of nature by a single number, representing the (subjective) probability of the state, but something else has to be invoked which measures the amount of information on which a decision is based. Several authors have tried to characterize this mysterious quantity, which here was called the weight of evidence. However, there seems to be little agreement as to how this quantity should be measured. (shrink)

Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.