The (Relevant) Logic of Scientific Discovery

TL;DR

This paper develops a weak relevant logic based on four-valued Dunn-Belnap semantics to model information exchange in scientific laboratories, incorporating probabilistic reasoning to handle imperfect regularities in experimental data.

Contribution

It introduces a novel four-valued, non-classical logical framework for scientific discovery, integrating epistemic accessibility relations and probabilistic updates within a laboratory interpretation.

Findings

The logic models confirmation and refutation as independent processes.

Probabilities satisfy a weaker form of Kolmogorov axioms, accommodating non-classical logic.

The framework supports both relative frequency and subjective probability interpretations.

Abstract

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.