Marta Martins

This paper proposes an approach to information-based logics using many-logic modal structures (). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice, which contains the semantics of each logic as a down-complete sublattice. are suitable for representing connections between information states (i.e., configurations of databases) and the evolution of information states over time. We will illustrate the application of by means of the six-valued logic of evidence and truth $${ LET}_{K}^+$$ LET K +, related to the lattice L6, and some four-, three-, and two-valued logics related to down-complete sublattices of L6. These logics are capable of representing paracomplete, paraconsistent, and classical contexts with six-, four-, three-, and two-valued scenarios.

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper’s main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics