On Many-logic modal structures and information-based logics

TL;DR

This paper introduces many-logic modal structures (MLMS) for representing complex information states across various logical systems, enabling nuanced modeling of evolving database configurations.

Contribution

It develops a novel framework using MLMS to connect different logics via a base lattice, illustrating applications with multi-valued logics including LET+K.

Findings

MLMS can express accessibility relations between worlds with different underlying logics.

MLMS effectively models the evolution of information states over time.

The framework accommodates various logical contexts, including paracomplete, paraconsistent, and classical.

Abstract

This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). 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. MLMS 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 MLMS by means of the six-valued logic of evidence and truth 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.