  This paper presents a thoroughgoing interpretation of a weak relevant logic
built over the Dunn-Belnap four-valued semantics in terms of the communication
of information in a network of sites of knowledge production (laboratories).
The knowledge communicated concerns experimental data and the regularities
tested using it. There have been many nods to interpretations similar to ours -
for example, in Dunn (1976), Belnap (1977). The laboratory interpretation was
outlined in Bilkova et al. (2010).
  Our system is built on the Routley--Meyer semantics for relevant logic
equipped with a four-valued valuation of formulas, where labs stand in for
situations, and the four values reflect the complexity of assessing results of
experiments. This semantics avoids using the Routley star, on the cost of
introducing a further relation, required in evaluating falsity assignments of
implication. We can however provide a natural interpretation of two
accessibility relations - confirmation and refutation of hypotheses are two
independent processes in our laboratory setup. This setup motivates various
basic properties of the accessibility relations, as well as a number of other
possible restrictions. This gives us a flexible modular system which can be
adjusted to specific epistemic contexts.
  As perfect regularities are rarely, or perhaps never, actually observed, we
add probabilities to the logical framework. As our logical framework is
non-classical, the probability is non-classical as well, satisfying a weaker
version of Kolmogorov axioms (cf. Priest 2006). We show that these
probabilities allow for a relative frequency as well as for a subjective
interpretation (we provide a Dutch book argument). We further show how to
update the probabilities and to distinguish conditional probabilities from the
probability of conditionals.
