Basic primal infon logic

Primal infon logic (PIL) was introduced in 2009 in the framework of policy and trust management. In the meantime, some generalizations appeared, and there have been some changes in the syntax of the basic PIL. This article is on the basic PIL, and one of our purposes is to ‘institutionalize’ the changes. We prove a small-model theorem for the propositional fragment of basic primal infon logic (PPIL), give a simple proof of the PPIL locality theorem and present a linear-time decision algorithm (announced earlier) for PPIL in a form convenient for generalizations. For the sake of completeness, we cover the universal fragment of basic PIL. We wish that this article becomes a standard reference on basic PIL.