Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural two-sorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result

In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL).

This report describes the research results obtained during the EPSRC project GR/J14745, giving firstly a summary of the results, with respect to the objectives given in the Research Grant Report and a brief introduction of the project's research field (in Section 1.2)